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.

Nonlinear Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Everhart, Joel L.; Badavi, Forooz F.

1989-01-01

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

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

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Economic policy optimization based on both one stochastic model and the parametric control theory

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)

Cross scale interactions, nonlinearities, and forecasting catastrophic events

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, Roger A.; Bestelmeyer, Brandon T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, Kris M.

2004-01-01

Catastrophic events share characteristic nonlinear behaviors that are often generated by cross-scale interactions and feedbacks among system elements. These events result in surprises that cannot easily be predicted based on information obtained at a single scale. Progress on catastrophic events has focused on one of the following two areas: nonlinear dynamics through time without an explicit consideration of spatial connectivity [Holling, C. S. (1992) Ecol. Monogr. 62, 447–502] or spatial connectivity and the spread of contagious processes without a consideration of cross-scale interactions and feedbacks [Zeng, N., Neeling, J. D., Lau, L. M. & Tucker, C. J. (1999) Science 286, 1537–1540]. These approaches rarely have ventured beyond traditional disciplinary boundaries. We provide an interdisciplinary, conceptual, and general mathematical framework for understanding and forecasting nonlinear dynamics through time and across space. We illustrate the generality and usefulness of our approach by using new data and recasting published data from ecology (wildfires and desertification), epidemiology (infectious diseases), and engineering (structural failures). We show that decisions that minimize the likelihood of catastrophic events must be based on cross-scale interactions, and such decisions will often be counterintuitive. Given the continuing challenges associated with global change, approaches that cross disciplinary boundaries to include interactions and feedbacks at multiple scales are needed to increase our ability to predict catastrophic events and develop strategies for minimizing their occurrence and impacts. Our framework is an important step in developing predictive tools and designing experiments to examine cross-scale interactions.

A Nonlinear Interactions Approximation Model for Large-Eddy Simulation

NASA Astrophysics Data System (ADS)

Haliloglu, Mehmet U.; Akhavan, Rayhaneh

2003-11-01

A new approach to LES modelling is proposed based on direct approximation of the nonlinear terms \\overlineu_iuj in the filtered Navier-Stokes equations, instead of the subgrid-scale stress, τ_ij. The proposed model, which we call the Nonlinear Interactions Approximation (NIA) model, uses graded filters and deconvolution to parameterize the local interactions across the LES cutoff, and a Smagorinsky eddy viscosity term to parameterize the distant interactions. A dynamic procedure is used to determine the unknown eddy viscosity coefficient, rendering the model free of adjustable parameters. The proposed NIA model has been applied to LES of turbulent channel flows at Re_τ ≈ 210 and Re_τ ≈ 570. The results show good agreement with DNS not only for the mean and resolved second-order turbulence statistics but also for the full (resolved plus subgrid) Reynolds stress and turbulence intensities.

Non-linear blend coding in the moth antennal lobe emerges from random glomerular networks

PubMed Central

Capurro, Alberto; Baroni, Fabiano; Olsson, Shannon B.; Kuebler, Linda S.; Karout, Salah; Hansson, Bill S.; Pearce, Timothy C.

2012-01-01

Neural responses to odor blends often exhibit non-linear interactions to blend components. The first olfactory processing center in insects, the antennal lobe (AL), exhibits a complex network connectivity. We attempt to determine if non-linear blend interactions can arise purely as a function of the AL network connectivity itself, without necessitating additional factors such as competitive ligand binding at the periphery or intrinsic cellular properties. To assess this, we compared blend interactions among responses from single neurons recorded intracellularly in the AL of the moth Manduca sexta with those generated using a population-based computational model constructed from the morphologically based connectivity pattern of projection neurons (PNs) and local interneurons (LNs) with randomized connection probabilities from which we excluded detailed intrinsic neuronal properties. The model accurately predicted most of the proportions of blend interaction types observed in the physiological data. Our simulations also indicate that input from LNs is important in establishing both the type of blend interaction and the nature of the neuronal response (excitation or inhibition) exhibited by AL neurons. For LNs, the only input that significantly impacted the blend interaction type was received from other LNs, while for PNs the input from olfactory sensory neurons and other PNs contributed agonistically with the LN input to shape the AL output. Our results demonstrate that non-linear blend interactions can be a natural consequence of AL connectivity, and highlight the importance of lateral inhibition as a key feature of blend coding to be addressed in future experimental and computational studies. PMID:22529799

The mechanism by which nonlinearity sustains turbulence in plane Couette flow

NASA Astrophysics Data System (ADS)

Nikolaidis, M.-A.; Farrell, B. F.; Ioannou, P. J.

2018-04-01

Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.

Variational analysis of SPM- and IPM-based interactions in cubic non-local nonlinear media

NASA Astrophysics Data System (ADS)

Maleshkov, G.; Bezuhanov, Kalojan; Dreischuh, Aleksander A.

2005-04-01

We analytically show the non-locality of cubic nonlinear media causes an increase of the critical power for self- and induced focusing and influences the condition for signal beam attraction/repulsion in an off-axis geometry.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

An Integrated Crustal Dynamics Simulator

NASA Astrophysics Data System (ADS)

Xing, H. L.; Mora, P.

2007-12-01

Numerical modelling offers an outstanding opportunity to gain an understanding of the crustal dynamics and complex crustal system behaviour. This presentation provides our long-term and ongoing effort on finite element based computational model and software development to simulate the interacting fault system for earthquake forecasting. A R-minimum strategy based finite-element computational model and software tool, PANDAS, for modelling 3-dimensional nonlinear frictional contact behaviour between multiple deformable bodies with the arbitrarily-shaped contact element strategy has been developed by the authors, which builds up a virtual laboratory to simulate interacting fault systems including crustal boundary conditions and various nonlinearities (e.g. from frictional contact, materials, geometry and thermal coupling). It has been successfully applied to large scale computing of the complex nonlinear phenomena in the non-continuum media involving the nonlinear frictional instability, multiple material properties and complex geometries on supercomputers, such as the South Australia (SA) interacting fault system, South California fault model and Sumatra subduction model. It has been also extended and to simulate the hot fractured rock (HFR) geothermal reservoir system in collaboration of Geodynamics Ltd which is constructing the first geothermal reservoir system in Australia and to model the tsunami generation induced by earthquakes. Both are supported by Australian Research Council.

Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

NASA Astrophysics Data System (ADS)

Tobita, Miwa; Omura, Yoshiharu

2018-03-01

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.

Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

NASA Astrophysics Data System (ADS)

Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan

2016-02-01

We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

Numerical investigation of nonlinear fluid-structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

NASA Astrophysics Data System (ADS)

Gong, Chun-Lin; Fang, Zhe; Chen, Gang

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid-structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

A Physics-driven Neural Networks-based Simulation System (PhyNNeSS) for multimodal interactive virtual environments involving nonlinear deformable objects

PubMed Central

De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S.

2012-01-01

Background While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. Methods In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. Results We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. Conclusions A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal Interactive Simulation) for general use. PMID:22629108

Polariton biexciton transitions in a ZnSe-based microcavity

NASA Astrophysics Data System (ADS)

Neukirch, U.; Bolton, S. R.; Fromer, N. A.; Sham, L. J.; Chemla, D. S.

2000-06-01

The optical third-order nonlinearity of a ZnSe-based microcavity is investigated by the pump-and-probe method. In the specially designed non-monolithic sample the biexciton binding energy exceeds all damping constants and the normal-mode splitting between exciton and cavity photon. For counter-circular polarized beams the nonlinear response exhibits strong oscillatory structures in the spectral vicinity of the polariton-biexciton transition. Comparison to model calculations shows that in this case the coherent nonlinearity is completely dominated by biexciton-exciton interactions beyond the Hartree-Fock approximation.

Galerkin finite element scheme for magnetostrictive structures and composites

NASA Astrophysics Data System (ADS)

Kannan, Kidambi Srinivasan

The ever increasing-role of magnetostrictives in actuation and sensing applications is an indication of their importance in the emerging field of smart structures technology. As newer, and more complex, applications are developed, there is a growing need for a reliable computational tool that can effectively address the magneto-mechanical interactions and other nonlinearities in these materials and in structures incorporating them. This thesis presents a continuum level quasi-static, three-dimensional finite element computational scheme for modeling the nonlinear behavior of bulk magnetostrictive materials and particulate magnetostrictive composites. Models for magnetostriction must deal with two sources of nonlinearities-nonlinear body forces/moments in equilibrium equations governing magneto-mechanical interactions in deformable and magnetized bodies; and nonlinear coupled magneto-mechanical constitutive models for the material of interest. In the present work, classical differential formulations for nonlinear magneto-mechanical interactions are recast in integral form using the weighted-residual method. A discretized finite element form is obtained by applying the Galerkin technique. The finite element formulation is based upon three dimensional eight-noded (isoparametric) brick element interpolation functions and magnetostatic infinite elements at the boundary. Two alternative possibilities are explored for establishing the nonlinear incremental constitutive model-characterization in terms of magnetic field or in terms of magnetization. The former methodology is the one most commonly used in the literature. In this work, a detailed comparative study of both methodologies is carried out. The computational scheme is validated, qualitatively and quantitatively, against experimental measurements published in the literature on structures incorporating the magnetostrictive material Terfenol-D. The influence of nonlinear body forces and body moments of magnetic origin, on the response of magnetostrictive structures to complex mechanical and magnetic loading conditions, is carefully examined. While monolithic magnetostrictive materials have been commercially-available since the late eighties, attention in the smart structures research community has recently focussed upon building and using magnetostrictive particulate composite structures for conventional actuation applications and novel sensing methodologies in structural health monitoring. A particulate magnetostrictive composite element has been developed in the present work to model such structures. This composite element incorporates interactions between magnetostrictive particles by combining a numerical micromechanical analysis based on magneto-mechanical Green's functions, with a homogenization scheme based upon the Mori-Tanaka approach. This element has been applied to the simulation of particulate actuators and sensors reported in the literature. Simulation results are compared to experimental data for validation purposes. The computational schemes developed, for bulk materials and for composites, are expected to be of great value to researchers and designers of novel applications based on magnetostrictives.

Many-body effects in nonlinear optical responses of 2D layered semiconductors

DOE PAGES

Aivazian, Grant; Yu, Hongyi; Wu, Sanfeng; ...

2017-01-05

We performed ultrafast degenerate pump-probe spectroscopy on monolayer WSe2 near its exciton resonance. The observed differential reflectance signals exhibit signatures of strong many-body interactions including the exciton-exciton interaction and free carrier induced band gap renormalization. The exciton-exciton interaction results in a resonance blue shift which lasts for the exciton lifetime (several ps), while the band gap renormalization manifests as a resonance red shift with several tens ps lifetime. Our model based on the many-body interactions for the nonlinear optical susceptibility ts well the experimental observations. The power dependence of the spectra shows that with the increase of pump power, themore » exciton population increases linearly and then saturates, while the free carrier density increases superlinearly, implying that exciton Auger recombination could be the origin of these free carriers. Our model demonstrates a simple but efficient method for quantitatively analyzing the spectra, and indicates the important role of Coulomb interactions in nonlinear optical responses of such 2D materials.« less

Many-body effects in nonlinear optical responses of 2D layered semiconductors

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

Aivazian, Grant; Yu, Hongyi; Wu, Sanfeng

We performed ultrafast degenerate pump-probe spectroscopy on monolayer WSe2 near its exciton resonance. The observed differential reflectance signals exhibit signatures of strong many-body interactions including the exciton-exciton interaction and free carrier induced band gap renormalization. The exciton-exciton interaction results in a resonance blue shift which lasts for the exciton lifetime (several ps), while the band gap renormalization manifests as a resonance red shift with several tens ps lifetime. Our model based on the many-body interactions for the nonlinear optical susceptibility ts well the experimental observations. The power dependence of the spectra shows that with the increase of pump power, themore » exciton population increases linearly and then saturates, while the free carrier density increases superlinearly, implying that exciton Auger recombination could be the origin of these free carriers. Our model demonstrates a simple but efficient method for quantitatively analyzing the spectra, and indicates the important role of Coulomb interactions in nonlinear optical responses of such 2D materials.« less

Distributed Coordinated Control of Large-Scale Nonlinear Networks

DOE PAGES

Kundu, Soumya; Anghel, Marian

2015-11-08

We provide a distributed coordinated approach to the stability analysis and control design of largescale nonlinear dynamical systems by using a vector Lyapunov functions approach. In this formulation the large-scale system is decomposed into a network of interacting subsystems and the stability of the system is analyzed through a comparison system. However finding such comparison system is not trivial. In this work, we propose a sum-of-squares based completely decentralized approach for computing the comparison systems for networks of nonlinear systems. Moreover, based on the comparison systems, we introduce a distributed optimal control strategy in which the individual subsystems (agents) coordinatemore » with their immediate neighbors to design local control policies that can exponentially stabilize the full system under initial disturbances.We illustrate the control algorithm on a network of interacting Van der Pol systems.« less

Nonlinear shallow ocean-wave soliton interactions on flat beaches.

PubMed

Ablowitz, Mark J; Baldwin, Douglas E

2012-09-01

Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.

Nonlinear plasmonic imaging techniques and their biological applications

NASA Astrophysics Data System (ADS)

Deka, Gitanjal; Sun, Chi-Kuang; Fujita, Katsumasa; Chu, Shi-Wei

2017-01-01

Nonlinear optics, when combined with microscopy, is known to provide advantages including novel contrast, deep tissue observation, and minimal invasiveness. In addition, special nonlinearities, such as switch on/off and saturation, can enhance the spatial resolution below the diffraction limit, revolutionizing the field of optical microscopy. These nonlinear imaging techniques are extremely useful for biological studies on various scales from molecules to cells to tissues. Nevertheless, in most cases, nonlinear optical interaction requires strong illumination, typically at least gigawatts per square centimeter intensity. Such strong illumination can cause significant phototoxicity or even photodamage to fragile biological samples. Therefore, it is highly desirable to find mechanisms that allow the reduction of illumination intensity. Surface plasmon, which is the collective oscillation of electrons in metal under light excitation, is capable of significantly enhancing the local field around the metal nanostructures and thus boosting up the efficiency of nonlinear optical interactions of the surrounding materials or of the metal itself. In this mini-review, we discuss the recent progress of plasmonics in nonlinear optical microscopy with a special focus on biological applications. The advancement of nonlinear imaging modalities (including incoherent/coherent Raman scattering, two/three-photon luminescence, and second/third harmonic generations that have been amalgamated with plasmonics), as well as the novel subdiffraction limit imaging techniques based on nonlinear behaviors of plasmonic scattering, is addressed.

Modeling of Nonlinear Optical Response in Gaseous Media and Its Comparison with Experiment

NASA Astrophysics Data System (ADS)

Xia, Yi

This thesis demonstrates the model and application of nonlinear optical response with Metastable Electronic State Approach (MESA) in ultrashort laser propagation and verifies accuracy of MESA through extensive comparison with experimental data. The MESA is developed from quantum mechanics to describe the nonlinear off-resonant optical response together with strong-field ionization in gaseous medium. The conventional light-matter interaction models are based on a piece-wise approach where Kerr effect and multi-photon ionization are treated as independent nonlinear responses. In contrast, MESA is self-consistent as the response from freed electrons and bound electrons are microscopically linked. It also can be easily coupled to the Unidirectional Pulse Propagation Equations (UPPE) for large scale simulation of experiments. This work tests the implementation of MESA model in simulation of nonlinear phase transients of ultrashort pulse propagation in a gaseous medium. The phase transient has been measured through Single-Shot Supercontinuum Spectral Interferometry. This technique can achieve high temporal resolution (10 fs) and spatial resolution (5 mum). Our comparison between simulation and experiment gives a quantitive test of MESA model including post-adiabatic corrections. This is the first time such a comparison was achieved for a theory suitable for large scale numerical simulation of modern nonlinear-optics experiments. In more than one respect, ours is a first-of-a-kind achievement. In particular, • Large amount of data are compared. We compare the data of nonlinear response induced by different pump intensity in Ar and Nitrogen. The data sets are three dimensions including two transverse spacial dimensions and one axial temporal dimension which reflect the whole structure of nonlinear response including the interplay between Kerr and plasma-induced effects. The resolutions of spatial and temporal dimension are about a few micrometer and several femtosecond. • The regime of light-matter interaction investigated here is between the strong and perturbative, where the pulse intensity can induce nonlinear refractive index change and partial ionization of dielectric medium. Obviously, such regimes are difficult to study both experimentally and theoretically. • MESA is a quantum based model, but it retains the same computation complexity as conventional light-matter interaction model. MESA contains the response from both bound and continuum states in a single self-consistent "Package". So, it is fair to say that this experiment-theory comparison sets a new standard for nonlinear light-matter interaction models and their verification in the area of extreme nonlinear optics.

Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding

PubMed Central

Tajima, Satohiro; Yanagawa, Toru; Fujii, Naotaka; Toyoizumi, Taro

2015-01-01

Brain-wide interactions generating complex neural dynamics are considered crucial for emergent cognitive functions. However, the irreducible nature of nonlinear and high-dimensional dynamical interactions challenges conventional reductionist approaches. We introduce a model-free method, based on embedding theorems in nonlinear state-space reconstruction, that permits a simultaneous characterization of complexity in local dynamics, directed interactions between brain areas, and how the complexity is produced by the interactions. We demonstrate this method in large-scale electrophysiological recordings from awake and anesthetized monkeys. The cross-embedding method captures structured interaction underlying cortex-wide dynamics that may be missed by conventional correlation-based analysis, demonstrating a critical role of time-series analysis in characterizing brain state. The method reveals a consciousness-related hierarchy of cortical areas, where dynamical complexity increases along with cross-area information flow. These findings demonstrate the advantages of the cross-embedding method in deciphering large-scale and heterogeneous neuronal systems, suggesting a crucial contribution by sensory-frontoparietal interactions to the emergence of complex brain dynamics during consciousness. PMID:26584045

Effect of bottom slope on the nonlinear triad interactions in shallow water

NASA Astrophysics Data System (ADS)

Chen, Hongzhou; Tang, Xiaocheng; Zhang, Ri; Gao, Junliang

2018-05-01

This paper aims at investigating the effect of bottom slope to the nonlinear triad interactions for irregular waves propagating in shallow water. The physical experiments are conducted in a wave flume with respect to the transformation of waves propagating on three bottom slopes ( β = 1/15, 1/30, and 1/45). Irregular waves with different type of breaking that are mechanically generated based on JONSWAP spectra are used for the test. The obviously different variations of spectra measured on each bottom reveal a crucial role of slope effect in the energy transfer between harmonics. The wavelet-based bispectrum were used to examine the bottom slope effect on the nonlinear triad interactions. Results show that the different bottom slopes which waves are propagated on will cause a significant discrepancy of triad interactions. Then, the discussions on the summed bicoherence which denote the distribution of phase coupling on each frequency further clarify the effect of bottom slope. Furthermore, the summed of the real and imaginary parts of bispectrum which could reflect the intensity of frequency components participating in the wave skewness and asymmetry were also investigated. Results indicate that the value of these parameters will increase as the bottom slope gets steeper.

Vector rectangular-shape laser based on reduced graphene oxide interacting with a long fiber taper.

PubMed

Gao, Lei; Zhu, Tao; Huang, Wei; Zeng, Jing

2014-10-01

A vector dual-wavelength rectangular-shape laser (RSL) based on a long fiber taper deposited with reduced graphene oxide is proposed, where nonlinearity is enhanced due to a large evanescent-field-interacting length and strong field confinement of an 8 mm fiber taper with a waist diameter of 4 μm. Graphene flakes are deposited uniformly on the taper waist with light pressure effect, so this structure guarantees both excellent saturable absorption and high nonlinearity. The RSL with a repetition rate of 7.9 MHz shows fast polarization switching in two orthogonal polarization directions, and temporal and spectral characteristics are investigated.

On the real-time estimation of the wheel-rail contact force by means of a new nonlinear estimator design model

NASA Astrophysics Data System (ADS)

Strano, Salvatore; Terzo, Mario

2018-05-01

The dynamics of the railway vehicles is strongly influenced by the interaction between the wheel and the rail. This kind of contact is affected by several conditioning factors such as vehicle speed, wear, adhesion level and, moreover, it is nonlinear. As a consequence, the modelling and the observation of this kind of phenomenon are complex tasks but, at the same time, they constitute a fundamental step for the estimation of the adhesion level or for the vehicle condition monitoring. This paper presents a novel technique for the real time estimation of the wheel-rail contact forces based on an estimator design model that takes into account the nonlinearities of the interaction by means of a fitting model functional to reproduce the contact mechanics in a wide range of slip and to be easily integrated in a complete model based estimator for railway vehicle.

Overview of computational control research at UT Austin

NASA Technical Reports Server (NTRS)

Bong, Wie

1989-01-01

An overview of current research activities at UT Austin is presented to discuss certain technical issues in the following areas: (1) Computer-Aided Nonlinear Control Design: In this project, the describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. INCA program has been enhanced to allow the numerical calculation of describing functions as well as the nonlinear limit cycle analysis capability in the frequency domain; (2) Robust Linear Quadratic Gaussian (LQG) Compensator Synthesis: Robust control design techniques and software tools are developed for flexible space structures with parameter uncertainty. In particular, an interactive, robust multivariable control design capability is being developed for INCA program; and (3) LQR-Based Autonomous Control System for the Space Station: In this project, real time implementation of LQR-based autonomous control system is investigated for the space station with time-varying inertias and with significant multibody dynamic interactions.

Characterisation and calculation of nonlinear vibrations in gas foil bearing systems-An experimental and numerical investigation

NASA Astrophysics Data System (ADS)

Hoffmann, Robert; Liebich, Robert

2018-01-01

This paper states a unique classification to understand the source of the subharmonic vibrations of gas foil bearing (GFB) systems, which will experimentally and numerically tested. The classification is based on two cases, where an isolated system is assumed: Case 1 considers a poorly balance rotor, which results in increased displacement during operation and interacts with the nonlinear progressive structure. It is comparable to a Duffing-Oscillator. In contrast, for case 2 a well/perfectly balanced rotor is assumed. Hence, the only source of nonlinear subharmonic whirling results from the fluid film self-excitation. Experimental tests with different unbalance levels and GFB modifications confirm these assumptions. Furthermore, simulations are able to predict the self-excitations and synchronous and subharmonic resonances of the experimental test. The numerical model is based on a linearised eigenvalue problem. The GFB system uses linearised stiffness and damping parameters by applying a perturbation method on the Reynolds Equation. The nonlinear bump structure is simplified by a link-spring model. It includes Coulomb friction effects inside the elastic corrugated structure and captures the interaction between single bumps.

Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

PubMed

Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

2016-11-14

In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

Nonlinear ring resonator: spatial pattern generation

NASA Astrophysics Data System (ADS)

Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.

2000-03-01

We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.

Revisiting tests for neglected nonlinearity using artificial neural networks.

PubMed

Cho, Jin Seo; Ishida, Isao; White, Halbert

2011-05-01

Tests for regression neglected nonlinearity based on artificial neural networks (ANNs) have so far been studied by separately analyzing the two ways in which the null of regression linearity can hold. This implies that the asymptotic behavior of general ANN-based tests for neglected nonlinearity is still an open question. Here we analyze a convenient ANN-based quasi-likelihood ratio statistic for testing neglected nonlinearity, paying careful attention to both components of the null. We derive the asymptotic null distribution under each component separately and analyze their interaction. Somewhat remarkably, it turns out that the previously known asymptotic null distribution for the type 1 case still applies, but under somewhat stronger conditions than previously recognized. We present Monte Carlo experiments corroborating our theoretical results and showing that standard methods can yield misleading inference when our new, stronger regularity conditions are violated.

Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

Chen, Wei; Shen, Ming; Kong, Qian; Shi, Jielong; Wang, Qi; Krolikowski, Wieslaw

2014-04-01

We investigate analytically and numerically the interactions of dark solitons under competing nonlocal cubic and local quintic nonlinearities. It is shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons, whereas the self-focusing quintic nonlinearity will enhance the repulsive interaction and increase soliton separation. We demonstrate these results by approximate variational approach and direct numerical simulation.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.

Nonlinear flutter analysis of composite panels

NASA Astrophysics Data System (ADS)

An, Xiaomin; Wang, Yan

2018-05-01

Nonlinear panel flutter is an interesting subject of fluid-structure interaction. In this paper, nonlinear flutter characteristics of curved composite panels are studied in very low supersonic flow. The composite panel with geometric nonlinearity is modeled by a nonlinear finite element method; and the responses are computed by the nonlinear Newmark algorithm. An unsteady aerodynamic solver, which contains a flux splitting scheme and dual time marching technology, is employed in calculating the unsteady pressure of the motion of the panel. Based on a half-step staggered coupled solution, the aeroelastic responses of two composite panels with different radius of R = 5 and R = 2.5 are computed and compared with each other at different dynamic pressure for Ma = 1.05. The nonlinear flutter characteristics comprising limited cycle oscillations and chaos are analyzed and discussed.

Non-linear coherent mode interactions and the control of shear layers

NASA Technical Reports Server (NTRS)

Nikitopoulos, D. E.; Liu, J. T. C.

1990-01-01

A nonlinear integral formulation, based on local linear stability considerations, is used to study the collective interactions between discrete wave-modes associated with large-scale structures and the mean flow in a developing shear layer. Aspects of shear layer control are examined in light of the sensitivity of these interactions to the initial frequency parameter, modal energy contents and modal phases. Manipulation of the large-scale structure is argued to be an effective means of controlling the flow, including the small-scale turbulence dominated region far downstream. Cases of fundamental, 1st and 2nd subharmonic forcing are discussed in conjunction with relevant experiments.

Optical bullets and "rockets" in nonlinear dissipative systems and their transformations and interactions.

PubMed

Soto-Crespo, J M; Grelu, Philippe; Akhmediev, Nail

2006-05-01

We demonstrate the existence of stable optical light bullets in nonlinear dissipative media for both cases of normal and anomalous chromatic dispersion. The prediction is based on direct numerical simulations of the (3+1)-dimensional complex cubic-quintic Ginzburg-Landau equation. We do not impose conditions of spherical or cylindrical symmetry. Regions of existence of stable bullets are determined in the parameter space. Beyond the domain of parameters where stable bullets are found, unstable bullets can be transformed into "rockets" i.e. bullets elongated in the temporal domain. A few examples of the interaction between two optical bullets are considered using spatial and temporal interaction planes.

Solute-solvent interactions in chloroform solutions of halogenated symmetric double Schiff bases of 1,1'-bis(4-aminophenyl)cyclohexane at 308.15 K according to ultrasonic and viscosity data

NASA Astrophysics Data System (ADS)

Gangani, B. J.; Patel, J. P.; Parsania, P. H.

2015-12-01

The density, viscosity and ultrasonic speed (2 MHz) of chloroform solutions of halogenated symmetric double Schiff bases of 1,1'-bis(4-aminophenyl)cyclohexane were investigated at 308.15 K. Various acoustical parameters such as specific acoustical impedance ( Z), adiabatic compressibility ( Ka), Rao's molar sound function ( R m), van der Waals constant ( b), internal pressure (π), free volume ( V f), intermolecular free path length ( L f), classical absorption coefficient (α/ f 2)Cl) and viscous relaxation time (τ) were determine using ultrasonic speed ( U), viscosity (η) and density (ρ) data of Schiff bases solutions and correlated with concentration. Linear increase of Z, b, R, τ, and (α/ f 2)Cl except π (nonlinear) and linear decrease of Ka and L f except V f (nonlinear) with increasing concentration of Schiff bases suggested presence of strong molecular interactions in the solutions. The positive values of solvation number further supported strong molecular interactions in the solutions. The nature and position of halogen substituent also affected the strength of molecular interactions.

Counter-propagating wave interaction for contrast-enhanced ultrasound imaging

NASA Astrophysics Data System (ADS)

Renaud, G.; Bosch, J. G.; ten Kate, G. L.; Shamdasani, V.; Entrekin, R.; de Jong, N.; van der Steen, A. F. W.

2012-11-01

Most techniques for contrast-enhanced ultrasound imaging require linear propagation to detect nonlinear scattering of contrast agent microbubbles. Waveform distortion due to nonlinear propagation impairs their ability to distinguish microbubbles from tissue. As a result, tissue can be misclassified as microbubbles, and contrast agent concentration can be overestimated; therefore, these artifacts can significantly impair the quality of medical diagnoses. Contrary to biological tissue, lipid-coated gas microbubbles used as a contrast agent allow the interaction of two acoustic waves propagating in opposite directions (counter-propagation). Based on that principle, we describe a strategy to detect microbubbles that is free from nonlinear propagation artifacts. In vitro images were acquired with an ultrasound scanner in a phantom of tissue-mimicking material with a cavity containing a contrast agent. Unlike the default mode of the scanner using amplitude modulation to detect microbubbles, the pulse sequence exploiting counter-propagating wave interaction creates no pseudoenhancement behind the cavity in the contrast image.

Test particle simulation study of whistler wave packets observed near Comet Giacobini-Zinner

NASA Astrophysics Data System (ADS)

Kaya, N.; Matsumoto, H.; Tsurutani, B. T.

1989-01-01

Nonlinear interactions of water group ions with large-amplitude whistler wave packets detected at the leading edge of steepened magnetosonic waves observed near Comet Giacobini-Zinner (GZ) are studied using test particle simulations of water-ion interactions with a model wave based on GZ data. Some of the water ions are found to be decelerated in the steepened portion of the magnetosonic wave to the resonance velocity with the whistler wave packets. Through resonance and related nonlinear interaction with the large-amplitude whistler waves, the water ions become trapped by the packet. An energy balance calculation demonstrates that the trapped ions lose their kinetic energy during the trapped motion in the packet. Thus, the nonlinear trapping motion in the wave structure leads to effective energy transfer from the water group ions to the whistler wave packets in the leading edge of the steepened MHD waves.

An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

PubMed

Neilson, Peter D; Neilson, Megan D

2005-09-01

Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear interaction and focusing

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1989-01-01

The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.

Hollow Gaussian beam generation through nonlinear interaction of photons with orbital angular momentum

PubMed Central

Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.

2016-01-01

Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs. PMID:27581625

Modulated microwave microscopy and probes used therewith

DOEpatents

Lai, Keji; Kelly, Michael; Shen, Zhi-Xun

2012-09-11

A microwave microscope including a probe tip electrode vertically positionable over a sample and projecting downwardly from the end of a cantilever. A transmission line connecting the tip electrode to the electronic control system extends along the cantilever and is separated from a ground plane at the bottom of the cantilever by a dielectric layer. The probe tip may be vertically tapped near or at the sample surface at a low frequency and the microwave signal reflected from the tip/sample interaction is demodulated at the low frequency. Alternatively, a low-frequency electrical signal is also a non-linear electrical element associated with the probe tip to non-linearly interact with the applied microwave signal and the reflected non-linear microwave signal is detected at the low frequency. The non-linear element may be semiconductor junction formed near the apex of the probe tip or be an FET formed at the base of a semiconducting tip.

All-Optical Control of Linear and Nonlinear Energy Transfer via the Zeno Effect

NASA Astrophysics Data System (ADS)

Guo, Xiang; Zou, Chang-Ling; Jiang, Liang; Tang, Hong X.

2018-05-01

Microresonator-based nonlinear processes are fundamental to applications including microcomb generation, parametric frequency conversion, and harmonics generation. While nonlinear processes involving either second- (χ(2 )) or third- (χ(3 )) order nonlinearity have been extensively studied, the interaction between these two basic nonlinear processes has seldom been reported. In this paper we demonstrate a coherent interplay between second- and third- order nonlinear processes. The parametric (χ(2 ) ) coupling to a lossy ancillary mode shortens the lifetime of the target photonic mode and suppresses its density of states, preventing the photon emissions into the target photonic mode via the Zeno effect. Such an effect is then used to control the stimulated four-wave mixing process and realize a suppression ratio of 34.5.

Nonlinear dispersion effects in elastic plates: numerical modelling and validation

NASA Astrophysics Data System (ADS)

Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.

Exploring the nonlinear regime of light-matter interaction using electronic spins in diamond

NASA Astrophysics Data System (ADS)

Alfasi, Nir; Masis, Sergei; Winik, Roni; Farfurnik, Demitry; Shtempluck, Oleg; Bar-Gill, Nir; Buks, Eyal

2018-06-01

The coupling between defects in diamond and a superconducting microwave resonator is studied in the nonlinear regime. Both negatively charged nitrogen-vacancy and P1 defects are explored. The measured cavity mode response exhibits strong nonlinearity near a spin resonance. Data is compared with theoretical predictions and a good agreement is obtained in a wide range of externally controlled parameters. The nonlinear effect under study in the current paper is expected to play a role in any cavity-based magnetic resonance imaging technique and to impose a fundamental limit upon its sensitivity.

Theory of Interactions of Intense Light with Nonlinear, Inhomogeneous, and Periodic Structures and Its Applications to Optical Bistability, Optic Gyroscopes, Nonlinear Spectroscopy, Radiation Protection, X-Ray Emission, and Related Fields.

DTIC Science & Technology

1987-10-01

bistable interaction of an electromagnetic wave with the simplest microscopic physical object. Most recently, consistent with this prediction , the hysteresis...1985, p. 17) credited both the experimental observation and the theoretical prediction as very important discoveries. London-based journal "Nature...order processes of this kind was also predicted , which was described as higher-order cyclo- -6- Raman effect whereby w, - W2 = nfl, where n is an

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

NASA Astrophysics Data System (ADS)

Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

2018-04-01

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

Enhancement of linear/nonlinear optical responses of molecular vibrations using metal nanoantennas

NASA Astrophysics Data System (ADS)

Morichika, Ikki; Kusa, Fumiya; Takegami, Akinobu; Ashihara, Satoshi

2017-04-01

Plasmonic enhancements of optical near-fields with metal nanostructures offer extensive potential for amplifying lightmatter interactions. We analytically formulate the enhancement of linear and nonlinear optical responses of molecular vibrations through resonant nanoantennas, based on a coupled-dipole model. We apply the formulae to evaluation of signal enhancement factors in the antenna-enhanced vibrational spectroscopy.

The influence of and the identification of nonlinearity in flexible structures

NASA Technical Reports Server (NTRS)

Zavodney, Lawrence D.

1988-01-01

Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

Planning for coordinated space and ground-based ionospheric modification experiments

NASA Technical Reports Server (NTRS)

Lee, M. C.; Burke, William J.; Carlson, Herbert C.; Heckscher, John L.; Kossey, Paul A.; Weber, E. J.; Kuo, S. P.

1990-01-01

The planning and conduction of coordinated space and ground-based ionospheric modification experiments are discussed. The purpose of these experiments is to discuss: (1) the nonlinear VLF wave interaction with the ionospheric plasmas; and (2) the nonlinear propagation of VLF waves in the HF-modified ionosphere. It is expected that the HF-induced ionospheric density striations can render the nonlinear mode conversion of VLF waved into lower hybrid waves. Lower hybrid waves can also be excited parametrically by the VLF waves in the absence of the density striations if the VLF waves are intense enough. Laboratory experiments are planned for crosschecking the results obtained from the field experiments.

Study of nonlinear interaction between bunched beam and intermediate cavities in a relativistic klystron amplifier

NASA Astrophysics Data System (ADS)

Wu, Y.; Xu, Z.; Li, Z. H.; Tang, C. X.

2012-07-01

In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.

Pitch glide effect induced by a nonlinear string-barrier interaction

NASA Astrophysics Data System (ADS)

Kartofelev, Dmitri; Stulov, Anatoli; Välimäki, Vesa

2015-10-01

Interactions of a vibrating string with its supports and other spatially distributed barriers play a significant role in the physics of many stringed musical instruments. It is well known that the tone of the string vibrations is determined by the string supports, and that the boundary conditions of the string termination may cause a short-lasting initial fundamental frequency shifting. Generally, this phenomenon is associated with the nonlinear modulation of the stiff string tension. The aim of this paper is to study the initial frequency glide phenomenon that is induced only by the string-barrier interaction, apart from other possible physical causes, and without the interfering effects of dissipation and dispersion. From a numerical simulation perspective, this highly nonlinear problem may present various difficulties, not the least of which is the risk of numerical instability. We propose a numerically stable and a purely kinematic model of the string-barrier interaction, which is based on the travelling wave solution of the ideal string vibration. The model is capable of reproducing the motion of the vibrating string exhibiting the initial fundamental frequency glide, which is caused solely by the complex nonlinear interaction of the string with its termination. The results presented in this paper can expand our knowledge and understanding of the timbre evolution and the physical principles of sound generation of numerous stringed instruments, such as lutes called the tambura, sitar and biwa.

Concerted Mitigation of O···H and C(π)···H Interactions Prospects Sixfold Gain in Optical Nonlinearity of Ionic Stilbazolium Derivatives

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

Cole, Jacqueline M.; Lin, Tze-Chia; Edwards, Alison J.

2015-03-04

DAST (4-dimethylamino-N-methyl-4-stilbazolium tosylate) is the most commercially successful organic nonlinear optical (NLO) material for frequency-doubling, integrated optics, and THz wave applications. Its success is predicated on its high optical nonlinearity with concurrent sufficient thermal stability. Many chemical derivatives of DAST have therefore been developed to optimize their properties; yet, to date, none have surpassed the overall superiority of DAST for NLO photonic applications. This is perhaps because DAST is an ionic salt wherein its NLO-active cation is influenced by multiple types of subtle intermolecular forces that are hard to quantify, thus, making difficult the molecular engineering of better functioning DASTmore » derivatives. Here, we establish a model parameter, ηinter, that isolates the influence of intermolecular interactions on second-order optical nonlinearity in DAST and its derivatives, using second-harmonic generation (SHG) as a qualifier; by systematically mapping intercorrelations of all possible pairs of intermolecular interactions to ηinter, we uncover a relationship between concerted intermolecular interactions and SHG output. This correlation reveals that a sixfold gain in the intrinsic second-order NLO performance of DAST is possible, by eliminating the identified interactions. This prediction offers the first opportunity to systematically design next-generation DAST-based photonic device nanotechnology to realize such a prospect.« less

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Agent-based modeling of endotoxin-induced acute inflammatory response in human blood leukocytes.

PubMed

Dong, Xu; Foteinou, Panagiota T; Calvano, Steven E; Lowry, Stephen F; Androulakis, Ioannis P

2010-02-18

Inflammation is a highly complex biological response evoked by many stimuli. A persistent challenge in modeling this dynamic process has been the (nonlinear) nature of the response that precludes the single-variable assumption. Systems-based approaches offer a promising possibility for understanding inflammation in its homeostatic context. In order to study the underlying complexity of the acute inflammatory response, an agent-based framework is developed that models the emerging host response as the outcome of orchestrated interactions associated with intricate signaling cascades and intercellular immune system interactions. An agent-based modeling (ABM) framework is proposed to study the nonlinear dynamics of acute human inflammation. The model is implemented using NetLogo software. Interacting agents involve either inflammation-specific molecules or cells essential for the propagation of the inflammatory reaction across the system. Spatial orientation of molecule interactions involved in signaling cascades coupled with the cellular heterogeneity are further taken into account. The proposed in silico model is evaluated through its ability to successfully reproduce a self-limited inflammatory response as well as a series of scenarios indicative of the nonlinear dynamics of the response. Such scenarios involve either a persistent (non)infectious response or innate immune tolerance and potentiation effects followed by perturbations in intracellular signaling molecules and cascades. The ABM framework developed in this study provides insight on the stochastic interactions of the mediators involved in the propagation of endotoxin signaling at the cellular response level. The simulation results are in accordance with our prior research effort associated with the development of deterministic human inflammation models that include transcriptional dynamics, signaling, and physiological components. The hypothetical scenarios explored in this study would potentially improve our understanding of how manipulating the behavior of the molecular species could manifest into emergent behavior of the overall system.

Convergent Cross Mapping: Basic concept, influence of estimation parameters and practical application.

PubMed

Schiecke, Karin; Pester, Britta; Feucht, Martha; Leistritz, Lutz; Witte, Herbert

2015-01-01

In neuroscience, data are typically generated from neural network activity. Complex interactions between measured time series are involved, and nothing or only little is known about the underlying dynamic system. Convergent Cross Mapping (CCM) provides the possibility to investigate nonlinear causal interactions between time series by using nonlinear state space reconstruction. Aim of this study is to investigate the general applicability, and to show potentials and limitation of CCM. Influence of estimation parameters could be demonstrated by means of simulated data, whereas interval-based application of CCM on real data could be adapted for the investigation of interactions between heart rate and specific EEG components of children with temporal lobe epilepsy.

Nonlinear Dynamics and Heterogeneous Interacting Agents

NASA Astrophysics Data System (ADS)

Lux, Thomas; Reitz, Stefan; Samanidou, Eleni

Economic application of nonlinear dynamics, microscopic agent-based modelling, and the use of artificial intelligence techniques as learning devices of boundedly rational actors are among the most exciting interdisciplinary ventures of economic theory over the past decade. This volume provides us with a most fascinating series of examples on "complexity in action" exemplifying the scope and explanatory power of these innovative approaches.

Analysis of complex neural circuits with nonlinear multidimensional hidden state models

PubMed Central

Friedman, Alexander; Slocum, Joshua F.; Tyulmankov, Danil; Gibb, Leif G.; Altshuler, Alex; Ruangwises, Suthee; Shi, Qinru; Toro Arana, Sebastian E.; Beck, Dirk W.; Sholes, Jacquelyn E. C.; Graybiel, Ann M.

2016-01-01

A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear interactions remains an unmet challenge. We present a nonlinear multidimensional hidden state (NMHS) approach that achieves interaction strength analysis and decoding of networks with nonlinear interactions by including latent state variables for each node in the network. We compare NMHS to Granger causality in analyzing neural circuit recordings and simulations, improvised music, and sociodemographic data. We conclude that NMHS significantly extends the scope of analyses of multidimensional, nonlinear networks, notably in coping with the complexity of the brain. PMID:27222584

Head-on collision of the second mode internal solitary waves

NASA Astrophysics Data System (ADS)

Terletska, Kateryna; Maderich, Vladimir; Jung, Kyung Tae

2017-04-01

Second mode internal waves are widespread in offshore areas, and they frequently follow the first mode internal waves on the oceanic shelf. Large amplitude internal solitary waves (ISW) of second mode containing trapped cores associated with closed streamlines can also transport plankton and nutrients. An interaction of ISWs with trapped cores takes place in a specific manner. It motivated us to carry out a computational study of head-on collision of ISWs of second mode propagating in a laboratory-scale numerical tank using the nonhydrostatic 3D numerical model based on the Navier-Stokes equations for a continuously stratified fluid. Three main classes of ISW of second mode propagating in the pycnocline layer of thickness h between homogeneous deep layers can be identified: (i) the weakly nonlinear waves; (ii) the stable strongly nonlinear waves with trapped cores; and (iii) the shear unstable strongly nonlinear waves (Maderich et al., 2015). Four interaction regimes for symmetric collision were separated from simulation results using this classification: (A) an almost elastic interaction of the weakly nonlinear waves; (B) a non-elastic interaction of waves with trapped cores when ISW amplitudes were close to critical non-dimensional amplitude a/h; (C) an almost elastic interaction of stable strongly nonlinear waves with trapped cores; (D) non-elastic interaction of the unstable strongly nonlinear waves. The unexpected result of simulation was that relative loss of energy due to the collision was maximal for regime B. New regime appeared when ISW of different amplitudes belonged to class (ii) collide. In result of interaction the exchange of mass between ISW occurred: the trapped core of smaller wave was entrained by core of larger ISW without mixing forming a new ISW of larger amplitude whereas in smaller ISW core of smaller wave totally substituted by fluid from larger wave. Overall, the wave characteristics induced by head-on collision agree well with the results of several available laboratory experiments. References [1] V. Maderich, K. T. Jung, K. Terletska, I. Brovchenko, T. Talipova, "Incomplete similarity of internal solitary waves with trapped core," Fluid Dynamics Research 47, 035511 (2015).

Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

NASA Technical Reports Server (NTRS)

Balsa, Thomas F.; Gartside, James

1995-01-01

The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

Spatial and temporal ultrafast imaging and control of terahertz wavepackets

NASA Astrophysics Data System (ADS)

Koehl, Richard Michael

Some polar optical phonons couple strongly to far- infrared electromagnetic radiation and move at light-like speeds through dielectric media. These phonon-polaritons retain both ionic and electromagnetic character. One of the fruitful implications of this mixing is that vibrational and electronic nonlinearities in ferroelectric and other highly anharmonic media interact with traveling electromagnetic waves spanning several frequency regimes, permitting nonlinear wave mixing at infrared and optical frequencies. Nonlinear optical mixing techniques are well-developed because optical light is easy to produce, but the lack of similar far- infrared sources has stymied similar efforts at terahertz frequencies. Nonlinear interactions in this frequency regime provide information about vibrational potential energy surfaces and are very strong when the lattice vibration is associated with a phase transition. In this thesis, I review methods based on a well known nonlinear optical technique, impulsive stimulated Raman scattering (ISRS), to monitor the progress of coherent phonon polaritons in a highly nonlinear ferroelectric, lithium tantalate. I also advance multiple-pulse ISRS optical techniques to attempt to elucidate information about the ferroelectric's vibrational potential energy surface, and I discuss significant recent progress that has been made in the development of ultrafast optical tools to generate far-infrared radiation through ISRS at specified times and spatial locations and control the interactions of coherent phonon-polariton wavepackets. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Interaction model between capsule robot and intestine based on nonlinear viscoelasticity.

PubMed

Zhang, Cheng; Liu, Hao; Tan, Renjia; Li, Hongyi

2014-03-01

Active capsule endoscope could also be called capsule robot, has been developed from laboratory research to clinical application. However, the system still has defects, such as poor controllability and failing to realize automatic checks. The imperfection of the interaction model between capsule robot and intestine is one of the dominating reasons causing the above problems. A model is hoped to be established for the control method of the capsule robot in this article. It is established based on nonlinear viscoelasticity. The interaction force of the model consists of environmental resistance, viscous resistance and Coulomb friction. The parameters of the model are identified by experimental investigation. Different methods are used in the experiment to obtain different values of the same parameter at different velocities. The model is proved to be valid by experimental verification. The achievement in this article is the attempted perfection of an interaction model. It is hoped that the model can optimize the control method of the capsule robot in the future.

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

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

NASA Technical Reports Server (NTRS)

Badavi, F. F.; Everhart, Joel L.

1987-01-01

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

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.

Non-linear glasses and metaglasses for photonics, a review: Part II. Kerr nonlinearity and metaglasses of positive and negative refraction

NASA Astrophysics Data System (ADS)

Romaniuk, Ryszard S.

2008-01-01

This is the second part of a paper on nonlinear properties of optical glasses and metaglasses. A subject of the paper is a review of the basic properties of several families of high optical quality glasses for photonics. The emphasis is put on nonlinear properties of these glasses, including nonlinearities of higher order. Nonlinear effects were debated and systematized. Interactions between optical wave of high power density with glass were described. All parameters of the glass increasing the optical nonlinearities were categorized. Optical nonlinearities in glasses were grouped into the following categories: time and frequency domain, amplitude and phase, resonant and non-resonant, elastic and inelastic, lossy and lossless, reversible and irreversible, instant and slow, adiabatic and non-adiabatic, with virtual versus real excitation of glass, destroying and non-destroying, etc. Nonlinear effects in glasses are based on the following effects: optical, thermal, mechanical and/or acoustic, electrical, magnetic, density and refraction modulation, chemical, etc.

Time domain contact model for tyre/road interaction including nonlinear contact stiffness due to small-scale roughness

NASA Astrophysics Data System (ADS)

Andersson, P. B. U.; Kropp, W.

2008-11-01

Rolling resistance, traction, wear, excitation of vibrations, and noise generation are all attributes to consider in optimisation of the interaction between automotive tyres and wearing courses of roads. The key to understand and describe the interaction is to include a wide range of length scales in the description of the contact geometry. This means including scales on the order of micrometres that have been neglected in previous tyre/road interaction models. A time domain contact model for the tyre/road interaction that includes interfacial details is presented. The contact geometry is discretised into multiple elements forming pairs of matching points. The dynamic response of the tyre is calculated by convolving the contact forces with pre-calculated Green's functions. The smaller-length scales are included by using constitutive interfacial relations, i.e. by using nonlinear contact springs, for each pair of contact elements. The method is presented for normal (out-of-plane) contact and a method for assessing the stiffness of the nonlinear springs based on detailed geometry and elastic data of the tread is suggested. The governing equations of the nonlinear contact problem are solved with the Newton-Raphson iterative scheme. Relations between force, indentation, and contact stiffness are calculated for a single tread block in contact with a road surface. The calculated results have the same character as results from measurements found in literature. Comparison to traditional contact formulations shows that the effect of the small-scale roughness is large; the contact stiffness is only up to half of the stiffness that would result if contact is made over the whole element directly to the bulk of the tread. It is concluded that the suggested contact formulation is a suitable model to include more details of the contact interface. Further, the presented result for the tread block in contact with the road is a suitable input for a global tyre/road interaction model that is also based on the presented contact formulation.

Planning for coordinated space and ground-based ionospheric modification experiments

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

Lee, M.C.

1990-10-01

The planning and conducting of coordinated space and ground-based ionospheric modification experiments are discussed. The purpose of these experiments is to investigate (1) the nonlinear VLF wave interaction with the ionospheric plasmas, and (2) the nonlinear propagation of VLF waves in the HF-modified ionosphere. It is expected that the HY-induced ionospheric density striations can render the nonlinear mode conversion of VLF waves into lower hybrid waves. Lower hybrid waves can also be excited parametrically by the VLF waves in the absence of the density striations if the VLF waves are intense enough. Laboratory experiments are planned for crosschecking the resultsmore » obtained from the field experiments.« less

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.

Ultra-low-power hybrid light–matter solitons

PubMed Central

Walker, P. M.; Tinkler, L.; Skryabin, D. V.; Yulin, A.; Royall, B.; Farrer, I.; Ritchie, D. A.; Skolnick, M. S.; Krizhanovskii, D. N.

2015-01-01

New functionalities in nonlinear optics will require systems with giant optical nonlinearity as well as compatibility with photonic circuit fabrication techniques. Here we introduce a platform based on strong light–matter coupling between waveguide photons and quantum-well excitons. On a sub-millimetre length scale we generate picosecond bright temporal solitons at a pulse energy of only 0.5 pJ. From this we deduce a nonlinear refractive index three orders of magnitude larger than in any other ultrafast system. We study both temporal and spatio-temporal nonlinear effects and observe dark–bright spatio-temporal polariton solitons. Theoretical modelling of soliton formation in the strongly coupled system confirms the experimental observations. These results show the promise of our system as a high speed, low power, integrated platform for physics and devices based on strong interactions between photons. PMID:26400748

Ultra-low-power hybrid light-matter solitons.

PubMed

Walker, P M; Tinkler, L; Skryabin, D V; Yulin, A; Royall, B; Farrer, I; Ritchie, D A; Skolnick, M S; Krizhanovskii, D N

2015-09-24

New functionalities in nonlinear optics will require systems with giant optical nonlinearity as well as compatibility with photonic circuit fabrication techniques. Here we introduce a platform based on strong light-matter coupling between waveguide photons and quantum-well excitons. On a sub-millimetre length scale we generate picosecond bright temporal solitons at a pulse energy of only 0.5 pJ. From this we deduce a nonlinear refractive index three orders of magnitude larger than in any other ultrafast system. We study both temporal and spatio-temporal nonlinear effects and observe dark-bright spatio-temporal polariton solitons. Theoretical modelling of soliton formation in the strongly coupled system confirms the experimental observations. These results show the promise of our system as a high speed, low power, integrated platform for physics and devices based on strong interactions between photons.

Model-free inference of direct network interactions from nonlinear collective dynamics.

PubMed

Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

2017-12-19

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

Modulational instability, beak-shaped rogue waves, multi-dark-dark solitons and dynamics in pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2017-07-01

The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.

The generation of a zonal-wind oscillation by nonlinear interactions of internal gravity waves

NASA Astrophysics Data System (ADS)

Campbell, Lucy

2003-11-01

Nonlinear interactions of internal gravity waves give rise to numerous large-scale phenomena that are observed in the atmosphere, for example the quasi-biennial oscillation (QBO). This is an oscillation in zonal wind direction which is observed in the equatorial stratosphere; it is characterized by alternating regimes of easterly and westerly shear that descend with time. In the past few decades, a number of theories have been developed to explain the mechanism by which the QBO is generated. These theories are all based on ``quasi-linear'' representations of wave-mean-flow interactions. In this presentation, a fully nonlinear numerical simulation of the QBO is described. A spectrum of gravity waves over a range of phase speeds is forced at the lower boundary of the computational domain and propagates upwards in a density-stratified shear flow. As a result of the absorption and reflection of the waves at their critical levels, regions of large shear develop in the background flow and propagate downwards with time.

Energy exchange and transition to localization in the asymmetric Fermi-Pasta-Ulam oscillatory chain

NASA Astrophysics Data System (ADS)

Smirnov, Valeri V.; Shepelev, Denis S.; Manevitch, Leonid I.

2013-01-01

A finite (periodic) FPU chain is chosen as a convenient model for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant interaction between high-frequency nonlinear normal modes. This interaction determines both the complete energy exchange between different parts of the chain and the transition to energy localization in an excited group of particles. In the paper, we demonstrate that this mechanism can exist in realistic (asymmetric) models of atomic or molecular oscillatory chains. Also, we study the resonant interaction of conjugated nonlinear normal modes and prove a possibility of linearization of the equations of motion. The theoretical constructions developed in this paper are based on the concepts of "effective particles" and Limiting Phase Trajectories. In particular, an analytical description of energy exchange between the "effective particles" in the terms of non-smooth functions is presented. The analytical results are confirmed with numerical simulations.

Non-Linear Acoustic Concealed Weapons Detector

DTIC Science & Technology

2006-05-01

signature analysis 8 the interactions of the beams with concealed objects. The Khokhlov- Zabolotskaya-Kuznetsov ( KZK ) equation is the most widely used...Hamilton developed a finite difference method based on the KZK equation to model pulsed acoustic emissions from axial symmetric sources. Using a...College of William & Mary, we have developed a simulation code using the KZK equation to model non-linear acoustic beams and visualize beam patterns

Time-gated imaging using nonlinear optical techniques applications to turbid materials

NASA Astrophysics Data System (ADS)

Reintjes, John F.; Duncan, Michael D.; Mahon, Rita; Tankersley, Lawrence L.; Bashkansky, Mark; Prewitt, Judith M. S.

1993-09-01

We describe the use of various nonlinear interactions based on stimulated Raman scattering for time gated imaging and their application to imaging through turbid media. Results are presented showing images obtained through solutions of non dairy creamer with attenuation of e-33 and 100 micrometers resolution, and through 6 mm of raw chicken meat, and 12 mm of human abdominal fat.

Modeling dynamic interactions and coherence between marine zooplankton and fishes linked to environmental variability

NASA Astrophysics Data System (ADS)

Liu, Hui; Fogarty, Michael J.; Hare, Jonathan A.; Hsieh, Chih-hao; Glaser, Sarah M.; Ye, Hao; Deyle, Ethan; Sugihara, George

2014-03-01

The dynamics of marine fishes are closely related to lower trophic levels and the environment. Quantitatively understanding ecosystem dynamics linking environmental variability and prey resources to exploited fishes is crucial for ecosystem-based management of marine living resources. However, standard statistical models typically grounded in the concept of linear system may fail to capture the complexity of ecological processes. We have attempted to model ecosystem dynamics using a flexible, nonparametric class of nonlinear forecasting models. We analyzed annual time series of four environmental indices, 22 marine copepod taxa, and four ecologically and commercially important fish species during 1977 to 2009 on Georges Bank, a highly productive and intensively studied area of the northeast U.S. continental shelf ecosystem. We examined the underlying dynamic features of environmental indices and copepods, quantified the dynamic interactions and coherence with fishes, and explored the potential control mechanisms of ecosystem dynamics from a nonlinear perspective. We found: (1) the dynamics of marine copepods and environmental indices exhibiting clear nonlinearity; (2) little evidence of complex dynamics across taxonomic levels of copepods; (3) strong dynamic interactions and coherence between copepods and fishes; and (4) the bottom-up forcing of fishes and top-down control of copepods coexisting as target trophic levels vary. These findings highlight the nonlinear interactions among ecosystem components and the importance of marine zooplankton to fish populations which point to two forcing mechanisms likely interactively regulating the ecosystem dynamics on Georges Bank under a changing environment.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

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

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong

2018-03-01

We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).

Acoustic Parametric Array for Identifying Standoff Targets

NASA Astrophysics Data System (ADS)

Hinders, M. K.; Rudd, K. E.

2010-02-01

An integrated simulation method for investigating nonlinear sound beams and 3D acoustic scattering from any combination of complicated objects is presented. A standard finite-difference simulation method is used to model pulsed nonlinear sound propagation from a source to a scattering target via the KZK equation. Then, a parallel 3D acoustic simulation method based on the finite integration technique is used to model the acoustic wave interaction with the target. Any combination of objects and material layers can be placed into the 3D simulation space to study the resulting interaction. Several example simulations are presented to demonstrate the simulation method and 3D visualization techniques. The combined simulation method is validated by comparing experimental and simulation data and a demonstration of how this combined simulation method assisted in the development of a nonlinear acoustic concealed weapons detector is also presented.

Multilevel adaptive control of nonlinear interconnected systems.

PubMed

Motallebzadeh, Farzaneh; Ozgoli, Sadjaad; Momeni, Hamid Reza

2015-01-01

This paper presents an adaptive backstepping-based multilevel approach for the first time to control nonlinear interconnected systems with unknown parameters. The system consists of a nonlinear controller at the first level to neutralize the interaction terms, and some adaptive controllers at the second level, in which the gains are optimally tuned using genetic algorithm. The presented scheme can be used in systems with strong couplings where completely ignoring the interactions leads to problems in performance or stability. In order to test the suitability of the method, two case studies are provided: the uncertain double and triple coupled inverted pendulums connected by springs with unknown parameters. The simulation results show that the method is capable of controlling the system effectively, in both regulation and tracking tasks. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

A new analytical method for characterizing nonlinear visual processes with stimuli of arbitrary distribution: Theory and applications.

PubMed

Hayashi, Ryusuke; Watanabe, Osamu; Yokoyama, Hiroki; Nishida, Shin'ya

2017-06-01

Characterization of the functional relationship between sensory inputs and neuronal or observers' perceptual responses is one of the fundamental goals of systems neuroscience and psychophysics. Conventional methods, such as reverse correlation and spike-triggered data analyses are limited in their ability to resolve complex and inherently nonlinear neuronal/perceptual processes because these methods require input stimuli to be Gaussian with a zero mean. Recent studies have shown that analyses based on a generalized linear model (GLM) do not require such specific input characteristics and have advantages over conventional methods. GLM, however, relies on iterative optimization algorithms and its calculation costs become very expensive when estimating the nonlinear parameters of a large-scale system using large volumes of data. In this paper, we introduce a new analytical method for identifying a nonlinear system without relying on iterative calculations and yet also not requiring any specific stimulus distribution. We demonstrate the results of numerical simulations, showing that our noniterative method is as accurate as GLM in estimating nonlinear parameters in many cases and outperforms conventional, spike-triggered data analyses. As an example of the application of our method to actual psychophysical data, we investigated how different spatiotemporal frequency channels interact in assessments of motion direction. The nonlinear interaction estimated by our method was consistent with findings from previous vision studies and supports the validity of our method for nonlinear system identification.

Situations, Interaction, Process and Affordances: An Ecological Psychology Perspective.

ERIC Educational Resources Information Center

Young, Michael F.; DePalma, Andrew; Garrett, Steven

2002-01-01

From an ecological psychology perspective, a full analysis of any learning context must acknowledge the complex nonlinear dynamics that unfold as an intentionally-driven learner interacts with a technology-based purposefully designed learning environment. A full situation model would need to incorporate constraints from the environment and also…

An individual-based process model to simulate landscape-scale forest ecosystem dynamics

Treesearch

Rupert Seidl; Werner Rammer; Robert M. Scheller; Thomas Spies

2012-01-01

Forest ecosystem dynamics emerges from nonlinear interactions between adaptive biotic agents (i.e., individual trees) and their relationship with a spatially and temporally heterogeneous abiotic environment. Understanding and predicting the dynamics resulting from these complex interactions is crucial for the sustainable stewardship of ecosystems, particularly in the...

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

NASA Astrophysics Data System (ADS)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Reconstruction of Complex Directional Networks with Group Lasso Nonlinear Conditional Granger Causality.

PubMed

Yang, Guanxue; Wang, Lin; Wang, Xiaofan

2017-06-07

Reconstruction of networks underlying complex systems is one of the most crucial problems in many areas of engineering and science. In this paper, rather than identifying parameters of complex systems governed by pre-defined models or taking some polynomial and rational functions as a prior information for subsequent model selection, we put forward a general framework for nonlinear causal network reconstruction from time-series with limited observations. With obtaining multi-source datasets based on the data-fusion strategy, we propose a novel method to handle nonlinearity and directionality of complex networked systems, namely group lasso nonlinear conditional granger causality. Specially, our method can exploit different sets of radial basis functions to approximate the nonlinear interactions between each pair of nodes and integrate sparsity into grouped variables selection. The performance characteristic of our approach is firstly assessed with two types of simulated datasets from nonlinear vector autoregressive model and nonlinear dynamic models, and then verified based on the benchmark datasets from DREAM3 Challenge4. Effects of data size and noise intensity are also discussed. All of the results demonstrate that the proposed method performs better in terms of higher area under precision-recall curve.

Efficient quantum computing using coherent photon conversion.

PubMed

Langford, N K; Ramelow, S; Prevedel, R; Munro, W J; Milburn, G J; Zeilinger, A

2011-10-12

Single photons are excellent quantum information carriers: they were used in the earliest demonstrations of entanglement and in the production of the highest-quality entanglement reported so far. However, current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed, single photons, and linear optics gates are inherently probabilistic. Here we introduce a deterministic process--coherent photon conversion (CPC)--that provides a new way to generate and process complex, multiquanta states for photonic quantum information applications. The technique uses classically pumped nonlinearities to induce coherent oscillations between orthogonal states of multiple quantum excitations. One example of CPC, based on a pumped four-wave-mixing interaction, is shown to yield a single, versatile process that provides a full set of photonic quantum processing tools. This set satisfies the DiVincenzo criteria for a scalable quantum computing architecture, including deterministic multiqubit entanglement gates (based on a novel form of photon-photon interaction), high-quality heralded single- and multiphoton states free from higher-order imperfections, and robust, high-efficiency detection. It can also be used to produce heralded multiphoton entanglement, create optically switchable quantum circuits and implement an improved form of down-conversion with reduced higher-order effects. Such tools are valuable building blocks for many quantum-enabled technologies. Finally, using photonic crystal fibres we experimentally demonstrate quantum correlations arising from a four-colour nonlinear process suitable for CPC and use these measurements to study the feasibility of reaching the deterministic regime with current technology. Our scheme, which is based on interacting bosonic fields, is not restricted to optical systems but could also be implemented in optomechanical, electromechanical and superconducting systems with extremely strong intrinsic nonlinearities. Furthermore, exploiting higher-order nonlinearities with multiple pump fields yields a mechanism for multiparty mediation of the complex, coherent dynamics.

Determination of nonlinear nanomechanical resonator-qubit coupling coefficient in a hybrid quantum system.

PubMed

Geng, Qi; Zhu, Ka-Di

2016-07-10

We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.

Selective two-photon absorption in carbon dots: a piece of the photoluminescence emission puzzle.

PubMed

Santos, Carla I M; Mariz, Inês F A; Pinto, Sandra N; Gonçalves, Gil; Bdikin, Igor; Marques, Paula A A P; Neves, Maria Graça P M S; Martinho, José M G; Maçôas, Ermelinda M S

2018-06-22

Carbon nanodots (Cdots) are now emerging as promising nonlinear fluorophores for applications in biological environments. A thorough and systematic approach to the two-photon induced emission of Cdots that could provide design guidelines to control their nonlinear emission properties is still missing. In this work, we address the nonlinear optical spectroscopy of Cdots prepared by controlled chemical cutting of graphene oxide (GO). The two-photon absorption in the 700-1000 nm region and the corresponding emission spectrum are carefully investigated. The highest two-photon absorption cross-section estimated was 130 GM at 720 nm. This value is comparable with the one reported for graphene nanoribbons with push-pull architecture. The emission spectrum depends on the excitation mode. At the same excitation energy, nonlinear excitation results in excitation-wavelength independent emission, while upon linear excitation the emission is excitation-wavelength dependent. The biphotonic interaction seems to be selective towards sp2 clusters bearing electron donor and acceptor groups found in push-pull architectures. Both linear and nonlinear emission can be understood based on the existence of isolated sp2 clusters involved in π-π stacking interactions with clusters in adjacent layers.

A Nonlinear Model for Gene-Based Gene-Environment Interaction.

PubMed

Sa, Jian; Liu, Xu; He, Tao; Liu, Guifen; Cui, Yuehua

2016-06-04

A vast amount of literature has confirmed the role of gene-environment (G×E) interaction in the etiology of complex human diseases. Traditional methods are predominantly focused on the analysis of interaction between a single nucleotide polymorphism (SNP) and an environmental variable. Given that genes are the functional units, it is crucial to understand how gene effects (rather than single SNP effects) are influenced by an environmental variable to affect disease risk. Motivated by the increasing awareness of the power of gene-based association analysis over single variant based approach, in this work, we proposed a sparse principle component regression (sPCR) model to understand the gene-based G×E interaction effect on complex disease. We first extracted the sparse principal components for SNPs in a gene, then the effect of each principal component was modeled by a varying-coefficient (VC) model. The model can jointly model variants in a gene in which their effects are nonlinearly influenced by an environmental variable. In addition, the varying-coefficient sPCR (VC-sPCR) model has nice interpretation property since the sparsity on the principal component loadings can tell the relative importance of the corresponding SNPs in each component. We applied our method to a human birth weight dataset in Thai population. We analyzed 12,005 genes across 22 chromosomes and found one significant interaction effect using the Bonferroni correction method and one suggestive interaction. The model performance was further evaluated through simulation studies. Our model provides a system approach to evaluate gene-based G×E interaction.

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Nondestructive Evaluation of Metal Fatigue Using Nonlinear Acoustics

NASA Technical Reports Server (NTRS)

Cantrell, John H., Jr.

2008-01-01

Safe-life and damage-tolerant design philosophies of high performance structures have driven the development of various methods to evaluate nondestructively the accumulation of damage in such structures resulting from cyclic loading. Although many techniques have proven useful, none has been able to provide an unambiguous, quantitative assessment of damage accumulation at each stage of fatigue from the virgin state to fracture. A method based on nonlinear acoustics is shown to provide such a means to assess the state of metal fatigue. The salient features of an analytical model are presented of the microelastic-plastic nonlinearities resulting from the interaction of an acoustic wave with fatigue-generated dislocation substructures and cracks that predictably evolve during the metal fatigue process. The interaction is quantified by the material (acoustic) nonlinearity parameter extracted from acoustic harmonic generation measurements. The parameters typically increase monotonically by several hundred percent over the fatigue life of the metal, thus providing a unique measure of the state of fatigue. Application of the model to aluminum alloy 2024-T4, 410Cb stainless steel, and IN100 nickel-base superalloy specimens fatigued using different loading conditions yields good agreement between theory and experiment. Application of the model and measurement technique to the on-site inspection of steam turbine blades is discussed.

Optical pulse generation in a transistor laser via intra-cavity photon-assisted tunneling and excess base carrier redistribution

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

Feng, M.; Iverson, E. W.; Wang, C. Y.

2015-11-02

For a direct-gap semiconductor (e.g., a p-n junction), photon-assisted tunneling is known to exhibit a high nonlinear absorption. In a transistor laser, as discussed here, the coherent photons generated at the quantum well interact with the collector junction field and “assist” electron tunneling from base to collector, thus resulting in the nonlinear modulation of the laser and the realization of optical pulse generation. 1 and 2 GHz optical pulses are demonstrated in the transistor laser using collector voltage control.

A Critical Look at Entropy-Based Gene-Gene Interaction Measures.

PubMed

Lee, Woojoo; Sjölander, Arvid; Pawitan, Yudi

2016-07-01

Several entropy-based measures for detecting gene-gene interaction have been proposed recently. It has been argued that the entropy-based measures are preferred because entropy can better capture the nonlinear relationships between genotypes and traits, so they can be useful to detect gene-gene interactions for complex diseases. These suggested measures look reasonable at intuitive level, but so far there has been no detailed characterization of the interactions captured by them. Here we study analytically the properties of some entropy-based measures for detecting gene-gene interactions in detail. The relationship between interactions captured by the entropy-based measures and those of logistic regression models is clarified. In general we find that the entropy-based measures can suffer from a lack of specificity in terms of target parameters, i.e., they can detect uninteresting signals as interactions. Numerical studies are carried out to confirm theoretical findings. © 2016 WILEY PERIODICALS, INC.

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.

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

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

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

Tide-surge Interaction Intensified by the Taiwan Strait

NASA Astrophysics Data System (ADS)

Zhang, Wen-Zhou; Shi, Fengyan; Hong, Hua-Sheng; Shang, Shao-Ping; Kirby, James T.

2010-06-01

The Taiwan Strait is a long and wide shelf-channel where the hydrodynamics is extremely complex, being characterized by strong tides, and where storm surges frequently occur during the typhoon season. Obvious oscillations due to tide-surge interaction were observed by tide gauges along the northern Fujian coast, the west bank of the Taiwan Strait, during Typhoon Dan (1999). Numerical experiments indicate that nonlinear bottom friction (described by the quadratic formula) is a major factor to predict these oscillations while the nonlinear advective terms and the shallow water effect have little contribution. It is found that the tide-surge interaction in the northern portion of the Taiwan Strait is intensified by the strait. Simulations based on simplified topographies with and without the island of Taiwan show that, in the presence of the island, the channel effect strengthens tidal currents and tends to align the major axes of tidal ellipses along the channel direction. Storm-induced currents are also strengthened by the channel. The pattern of strong tidal currents and storm-induced currents along the channel direction enhances tide-surge interaction via the nonlinear bottom friction, resulting in the obvious oscillations along the northern Fujian coast.

Ensemble survival tree models to reveal pairwise interactions of variables with time-to-events outcomes in low-dimensional setting

PubMed Central

Dazard, Jean-Eudes; Ishwaran, Hemant; Mehlotra, Rajeev; Weinberg, Aaron; Zimmerman, Peter

2018-01-01

Unraveling interactions among variables such as genetic, clinical, demographic and environmental factors is essential to understand the development of common and complex diseases. To increase the power to detect such variables interactions associated with clinical time-to-events outcomes, we borrowed established concepts from random survival forest (RSF) models. We introduce a novel RSF-based pairwise interaction estimator and derive a randomization method with bootstrap confidence intervals for inferring interaction significance. Using various linear and nonlinear time-to-events survival models in simulation studies, we first show the efficiency of our approach: true pairwise interaction-effects between variables are uncovered, while they may not be accompanied with their corresponding main-effects, and may not be detected by standard semi-parametric regression modeling and test statistics used in survival analysis. Moreover, using a RSF-based cross-validation scheme for generating prediction estimators, we show that informative predictors may be inferred. We applied our approach to an HIV cohort study recording key host gene polymorphisms and their association with HIV change of tropism or AIDS progression. Altogether, this shows how linear or nonlinear pairwise statistical interactions of variables may be efficiently detected with a predictive value in observational studies with time-to-event outcomes. PMID:29453930

Ensemble survival tree models to reveal pairwise interactions of variables with time-to-events outcomes in low-dimensional setting.

PubMed

Dazard, Jean-Eudes; Ishwaran, Hemant; Mehlotra, Rajeev; Weinberg, Aaron; Zimmerman, Peter

2018-02-17

Unraveling interactions among variables such as genetic, clinical, demographic and environmental factors is essential to understand the development of common and complex diseases. To increase the power to detect such variables interactions associated with clinical time-to-events outcomes, we borrowed established concepts from random survival forest (RSF) models. We introduce a novel RSF-based pairwise interaction estimator and derive a randomization method with bootstrap confidence intervals for inferring interaction significance. Using various linear and nonlinear time-to-events survival models in simulation studies, we first show the efficiency of our approach: true pairwise interaction-effects between variables are uncovered, while they may not be accompanied with their corresponding main-effects, and may not be detected by standard semi-parametric regression modeling and test statistics used in survival analysis. Moreover, using a RSF-based cross-validation scheme for generating prediction estimators, we show that informative predictors may be inferred. We applied our approach to an HIV cohort study recording key host gene polymorphisms and their association with HIV change of tropism or AIDS progression. Altogether, this shows how linear or nonlinear pairwise statistical interactions of variables may be efficiently detected with a predictive value in observational studies with time-to-event outcomes.

On quantum integrable models related to nonlinear quantum optics. An algebraic Bethe ansatz approach

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-08-01

A unified approach based on Bethe ansatz in a large variety of integrable models in quantum optics is given. Second harmonics generation, three-boson interaction, the Dicke model, and some cases of four-boson interaction as special cases of su(2)⊕su(1,1)-Gaudin models are included.

Solitons in a nonlinear model of spin transport in helical molecules

NASA Astrophysics Data System (ADS)

Albares, P.; Díaz, E.; Cerveró, Jose M.; Domínguez-Adame, F.; Diez, E.; Estévez, P. G.

2018-02-01

We study an effective integrable nonlinear model describing an electron moving along the axis of a deformable helical molecule. The helical conformation of dipoles in the molecular backbone induces an unconventional Rashba-like interaction that couples the electron spin with its linear momentum. In addition, a focusing nonlinearity arises from the electron-lattice interaction, enabling the formation of a variety of stable solitons such as bright solitons, breathers, and rogue waves. A thorough study of the soliton solutions for both focusing and defocusing nonlinear interaction is presented and discussed.

The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave

DOE PAGES

TenCate, J. A.; Malcolm, A. E.; Feng, X.; ...

2016-06-06

Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less

Learning Petri net models of non-linear gene interactions.

PubMed

Mayo, Michael

2005-10-01

Understanding how an individual's genetic make-up influences their risk of disease is a problem of paramount importance. Although machine-learning techniques are able to uncover the relationships between genotype and disease, the problem of automatically building the best biochemical model or "explanation" of the relationship has received less attention. In this paper, I describe a method based on random hill climbing that automatically builds Petri net models of non-linear (or multi-factorial) disease-causing gene-gene interactions. Petri nets are a suitable formalism for this problem, because they are used to model concurrent, dynamic processes analogous to biochemical reaction networks. I show that this method is routinely able to identify perfect Petri net models for three disease-causing gene-gene interactions recently reported in the literature.

Conservation laws, bilinear forms and solitons for a fifth-order nonlinear Schrödinger equation for the attosecond pulses in an optical fiber

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

Chai, Jun; Tian, Bo, E-mail: tian_bupt@163.com; Zhen, Hui-Ling

Under investigation in this paper is a fifth-order nonlinear Schrödinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on the Lax pair, infinitely-many conservation laws are derived. With the aid of auxiliary functions, bilinear forms, one-, two- and three-soliton solutions in analytic forms are generated via the Hirota method and symbolic computation. Soliton velocity varies linearly with the coefficients of the high-order terms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons as well as the bound state are depicted. For the interactions among the three solitons, two head-onmore » and one overtaking interactions, three overtaking interactions, an interaction between a bound state and a single soliton and the bound state are displayed. Graphical analysis shows that the interactions between the two solitons are elastic, and interactions among the three solitons are pairwise elastic. Stability analysis yields the modulation instability condition for the soliton solutions.« less

Nonlinear silicon photonics

NASA Astrophysics Data System (ADS)

Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.

2017-09-01

Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.

Nonlinear response of unidirectional boron/aluminum

NASA Technical Reports Server (NTRS)

Pindera, M.-J.; Herakovich, C. T.; Becker, W.; Aboudi, J.

1990-01-01

Experimental results obtained for unidirectional boron/aluminum subjected to combined loading using off-axis tension, compression and Iosipescu shear specimens are correlated with a nonlinear micromechanics model. It is illustrated that the nonlinear response in the principal material directions is markedly influenced by the different loading modes and different ratios of the applied stress components. The observed nonlinear response under pure and combined loading is discussed in terms of initial yielding, subsequent hardening, stress-interaction effects and unloading-reloading characteristics. The micromechanics model is based on the concept of a repeating unit cell representative of the composite-at-large and employs the unified theory of Bodner and Partom to model the inelastic response of the matrix. It is shown that the employed micromechanics model is sufficiently general to predict the observed nonlinear response of unidirectional boron/aluminum with good accuracy.

Nonlinear complexity of random visibility graph and Lempel-Ziv on multitype range-intensity interacting financial dynamics

NASA Astrophysics Data System (ADS)

Zhang, Yali; Wang, Jun

2017-09-01

In an attempt to investigate the nonlinear complex evolution of financial dynamics, a new financial price model - the multitype range-intensity contact (MRIC) financial model, is developed based on the multitype range-intensity interacting contact system, in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading. Two new random visibility graph (VG) based analyses and Lempel-Ziv complexity (LZC) are applied to study the complex behaviors of return time series and the corresponding random sorted series. The VG method is the complex network theory, and the LZC is a non-parametric measure of complexity reflecting the rate of new pattern generation of a series. In this work, the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, the numerical empirical study shows the similar complexity behaviors between the model and the real markets, the research confirms that the financial model is reasonable to some extent.

Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

NASA Astrophysics Data System (ADS)

Kraczek, Brent; Kanp, Jaroslaw

Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.

A quadrature based method of moments for nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin L.; Vedula, Prakash

2011-09-01

Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Amplitude Equations

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented. In this part of the analysis, the system of partial differential critical-layer equations derived in Part I is solved analytically to yield the amplitude equations which are analyzed using a combination of asymptotic and numerical methods. Numerical solutions of the inviscid non-equilibrium oblique-mode amplitude equations show that the frequency-detuned self-interaction enhances the growth of the lower-frequency oblique modes more than the higher-frequency ones. All amplitudes become singular at the same finite downstream position. The frequency detuning delays the occurrence of the singularity. The spanwise-periodic mean-flow distortion and low-frequency nonlinear modes are generated by the critical-layer interaction between frequency-detuned oblique modes. The nonlinear mean flow and higher harmonics as well as the primary instabilities become as large as the base mean flow in the inviscid wall layer in the downstream region where the distance from the singularity is of the order of the wavelength scale.

Foundations for a Post-Modern Curriculum.

ERIC Educational Resources Information Center

Doll, William E., Jr.

This paper suggests that present-day curriculum, based on Newtonian thought, has been rendered obsolete by the holistic and interactive "post-modern" world view based on quantum physics, nonlinear mathematics, general systems theory, and Ilya Prigogine's nonequilibrium thermodynamics. The Newtonian world view, which is linear and…

Numerical calculation of nonlinear ultrashort laser pulse propagation in transparent Kerr media

NASA Astrophysics Data System (ADS)

Arnold, Cord L.; Heisterkamp, Alexander; Ertmer, Wolfgang; Lubatschowski, Holger

2005-03-01

In the focal region of tightly focused ultrashort laser pulses, sufficient high intensities to initialize nonlinear ionization processes are easily achieved. Due to these nonlinear ionization processes, mainly multiphoton ionization and cascade ionization, free electrons are generated in the focus resulting in optical breakdown. A model including both nonlinear pulse propagation and plasma generation is used to calculate numerically the interaction of ultrashort pulses with their self-induced plasma in the vicinity of the focus. The model is based on a (3+1)-dimensional nonlinear Schroedinger equation describing the pulse propagation coupled to a system of rate equations covering the generation of free electrons. It is applicable to any transparent Kerr medium, whose linear and nonlinear optical parameters are known. Numerical calculations based on this model are used to understand nonlinear side effects, such as streak formation, occurring in addition to optical breakdown during short pulse refractive eye surgeries like fs-LASIK. Since the optical parameters of water are a good first-order approximation to those of corneal tissue, water is used as model substance. The free electron density distribution induced by focused ultrashort pulses as well as the pulses spatio-temporal behavior are studied in the low-power regime around the critical power for self-focusing.

Modal analysis and nonlinear characterization of an airborne power ultrasonic transducer with rectangular plate radiator.

PubMed

Andrés, R R; Acosta, V M; Lucas, M; Riera, E

2018-01-01

Some industrial processes like particle agglomeration or food dehydration among others can be enhanced by the use of power ultrasonic technologies. These technologies are based on an airborne power ultrasonic transducer (APUT) constituted by a pre-stressed Langevin-type transducer, a mechanical amplifier and an extensive plate radiator. In order to produce the desired effects in industrial processing, the transducer has to vibrate in an extensional mode driving an extensive radiator in the desired flexural mode with high amplitude displacements. Due to the generation of these high amplitude displacements in the radiator surfaces, non-linear effects like frequency shifts, hysteresis or modal interactions, among others, may be produced in the transducer behavior. When any nonlinear effect appears, when applying power, the stability and efficiency of this ultrasonic technology decreases, and the transducer may be damaged depending on the excitation power level and the nature of the nonlinearity. In this paper, an APUT with flat rectangular radiator is presented, as the active part of an innovative system with stepped reflectors. The nonlinear behavior of the APUT has been characterized numerically and experimentally in case of the modal analysis and experimentally in the case of dynamic analysis. According to the results obtained after the experiments, no modal interactions are expected, nor do other nonlinear effects. Copyright © 2017 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2009-07-01

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

Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality

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

Dai, Zhiping; Yang, Zhenjun, E-mail: zjyang@vip.163.com; Ling, Xiaohui

2016-03-15

The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and themore » oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.« less

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

NASA Technical Reports Server (NTRS)

Smith, F. T.

1988-01-01

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

Structural health monitoring based on sensitivity vector fields and attractor morphing.

PubMed

Yin, Shih-Hsun; Epureanu, Bogdan I

2006-09-15

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

NASA Astrophysics Data System (ADS)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.

A rocket-borne experiment called 'MINIX' was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction eXperiment and was carried out on August 29, 1983. The objective of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere, such as the ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no ohmic heating effects were detected.

Transport equations for subdiffusion with nonlinear particle interaction.

PubMed

Straka, P; Fedotov, S

2015-02-07

We show how the nonlinear interaction effects 'volume filling' and 'adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent. Copyright © 2014 Elsevier Ltd. All rights reserved.

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

HAARP-based Investigations of Lightning-induced Nonlinearities within the D-Region Ionosphere

NASA Astrophysics Data System (ADS)

Moore, R. C.

2015-12-01

It is well-documented that energetic lightning can produce fantastical events with the lower ionosphere. Although the High-frequency Active Auroral Research Program (HAARP) transmitter is not as powerful as lightning, it can be used to investigate the nonlinear interactions that occur within the lower ionosphere, many of which also occur during lightning-induced ionospheric events. This paper presents the best experimental results obtained during D-region modification experiments performed by the University of Florida at the HAARP observatory between 2007 and 2014, including ELF/VLF wave generation experiments, wave-wave mixing experiments, and cross-modulation experiments. We emphasize the physical processes important for lightning-ionosphere interactions that can be directly investigated using HAARP.

Dark-dark solitons for a coupled variable-coefficient higher-order nonlinear Schrödinger system in an inhomogeneous optical fiber

NASA Astrophysics Data System (ADS)

Li, Ming-Zhen; Tian, Bo; Qu, Qi-Xing; Chai, Han-Peng; Liu, Lei; Du, Zhong

2017-12-01

In this paper, under investigation is a coupled variable-coefficient higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the Lax pair and binary Darboux transformation, we present the nondegenerate N-dark-dark soliton solutions. With the graphical simulation, soliton propagation and interaction are discussed with the group velocity dispersion and fourth-order dispersion effects, which affect the velocity but have no effect on the amplitude. Linear, parabolic and periodic one dark-dark solitons are displayed. Interactions between the two solitons are presented as well, which are all elastic.

Experimental evidence of phase coherence of magnetohydrodynamic turbulence in the solar wind: GEOTAIL satellite data.

PubMed

Koga, D; Chian, A C-L; Hada, T; Rempel, E L

2008-02-13

Magnetohydrodynamic (MHD) turbulence is commonly observed in the solar wind. Nonlinear interactions among MHD waves are likely to produce finite correlation of the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in the quasi-linear theory) or have a finite coherence. Using a method based on the surrogate data technique, we analysed the GEOTAIL magnetic field data to evaluate the phase coherence in MHD turbulence in the Earth's foreshock region. The results demonstrate the existence of finite phase correlation, indicating that nonlinear wave-wave interactions are in progress.

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

NASA Astrophysics Data System (ADS)

Gupta, Samit Kumar

2018-03-01

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

Mutual information and phase dependencies: measures of reduced nonlinear cardiorespiratory interactions after myocardial infarction.

PubMed

Hoyer, Dirk; Leder, Uwe; Hoyer, Heike; Pompe, Bernd; Sommer, Michael; Zwiener, Ulrich

2002-01-01

The heart rate variability (HRV) is related to several mechanisms of the complex autonomic functioning such as respiratory heart rate modulation and phase dependencies between heart beat cycles and breathing cycles. The underlying processes are basically nonlinear. In order to understand and quantitatively assess those physiological interactions an adequate coupling analysis is necessary. We hypothesized that nonlinear measures of HRV and cardiorespiratory interdependencies are superior to the standard HRV measures in classifying patients after acute myocardial infarction. We introduced mutual information measures which provide access to nonlinear interdependencies as counterpart to the classically linear correlation analysis. The nonlinear statistical autodependencies of HRV were quantified by auto mutual information, the respiratory heart rate modulation by cardiorespiratory cross mutual information, respectively. The phase interdependencies between heart beat cycles and breathing cycles were assessed basing on the histograms of the frequency ratios of the instantaneous heart beat and respiratory cycles. Furthermore, the relative duration of phase synchronized intervals was acquired. We investigated 39 patients after acute myocardial infarction versus 24 controls. The discrimination of these groups was improved by cardiorespiratory cross mutual information measures and phase interdependencies measures in comparison to the linear standard HRV measures. This result was statistically confirmed by means of logistic regression models of particular variable subsets and their receiver operating characteristics.

Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver

NASA Technical Reports Server (NTRS)

Scott, Matthew T.; Mccune, James E.

1988-01-01

This paper presents a nonlinear theory of forces and moment acting on a two-dimensional airfoil in unsteady potential flow. Results are obtained for cases of both large and small amplitude motion. The analysis, which is based on an extension of Wagner's integral equation to the nonlinear regime, takes full advantage of the trailing wake's tendency to deform under local velocities. Interactive computational results are presented that show examples of wake-induced lift and moment augmentation on the order of 20 percent of quasi-static values. The expandability and flexibility of the present computational method are noted, as well as the relative speed with which solutions are obtained.

Excitations of breathers and rogue wave in the Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Qi, Jian-Wen; Duan, Liang; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We study the excitations of breathers and rogue wave in a classical Heisenberg spin chain with twist interaction, which is governed by a fourth-order integrable nonlinear Schrödinger equation. The dynamics of these waves have been extracted from an exact solution. In particular, the corresponding existence conditions based on the parameters of perturbation wave number K, magnon number N, background wave vector ks and amplitude c are presented explicitly. Furthermore, the characteristics of magnetic moment distribution corresponding to these nonlinear waves are also investigated in detail. Finally, we discussed the state transition of three types nonlinear localized waves under the different excitation conditions.

Non-linear molecular pattern classification using molecular beacons with multiple targets.

PubMed

Lee, In-Hee; Lee, Seung Hwan; Park, Tai Hyun; Zhang, Byoung-Tak

2013-12-01

In vitro pattern classification has been highlighted as an important future application of DNA computing. Previous work has demonstrated the feasibility of linear classifiers using DNA-based molecular computing. However, complex tasks require non-linear classification capability. Here we design a molecular beacon that can interact with multiple targets and experimentally shows that its fluorescent signals form a complex radial-basis function, enabling it to be used as a building block for non-linear molecular classification in vitro. The proposed method was successfully applied to solving artificial and real-world classification problems: XOR and microRNA expression patterns. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Does Hooke's law work in helical nanosprings?

PubMed

Ben, Sudong; Zhao, Junhua; Rabczuk, Timon

2015-08-28

Hooke's law is a principle of physics that states that the force needed to extend a spring by some distance is proportional to that distance. The law is always valid for an initial portion of the elastic range for nearly all helical macrosprings. Here we report the sharp nonlinear force-displacement relation of tightly wound helical carbon nanotubes at even small displacement via a molecular mechanics model. We demonstrate that the van der Waals (vdW) interaction between the intertube walls dominates the nonlinear relation based on our analytical expressions. This study provides physical insights into the origin of huge nonlinearity of the helical nanosprings.

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).

Observation of Quasi-Two-Dimensional Nonlinear Interactions in a Drift-Wave Streamer

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

Yamada, T.; Nagashima, Y.; Itoh, S.-I.

2010-11-26

A streamer, which is a bunching of drift-wave fluctuations, and its mediator, which generates the streamer by coupling with other fluctuations, have been observed in a cylindrical magnetized plasma. Their radial structures were investigated in detail by using the biphase analysis. Their quasi-two-dimensional structures were revealed to be equivalent with a pair of fast and slow modes predicted by a nonlinear Schroedinger equation based on the Hasegawa-Mima model.

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.

Phenomenal enhancement of optical nonlinearity in PTZ-I based ZnS/ZnSe nanocomposites

NASA Astrophysics Data System (ADS)

Divyasree, M. C.; Shiju, E.; Vijisha, M. V.; Ramesan, M. T.; Chandrasekharan, K.

2018-05-01

The enhanced nonlinear optical properties of phenothiazine-iodine (PTZ-I) charge transfer complex (CTC) on composite formation with ZnS/ZnSe nanostructures are reported. The interaction between the components was confirmed by the FTIR spectra. Structural and morphological changes on nanocomposite formation were analyzed by scanning electron microscopy and X-ray diffraction spectra. The absorption and emission features of both the nanocomposites and their constituent components were studied. Nonlinear optical properties of all the samples in nanosecond regime were investigated by the Z-scan technique using Nd: YAG laser with 532 nm wavelength and 7 ns pulse width. The optical nonlinearity of PTZ-I CTC was found to be improved considerably on composite formation and the new systems can be proposed as excellent candidates for photonic devices. Enhanced optical nonlinearity of the composites could be attributed to charge/energy transfer mechanism between PTZ-I CTC and the nanostructures.

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

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

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

2011-01-15

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

Quantum state detection and state preparation based on cavity-enhanced nonlinear interaction of atoms with single photon

NASA Astrophysics Data System (ADS)

Hosseini, Mahdi

Our ability to engineer quantum states of light and matter has significantly advanced over the past two decades, resulting in the production of both Gaussian and non-Gaussian optical states. The resulting tailored quantum states enable quantum technologies such as quantum optical communication, quantum sensing as well as quantum photonic computation. The strong nonlinear light-atom interaction is the key to deterministic quantum state preparation and quantum photonic processing. One route to enhancing the usually weak nonlinear light-atom interactions is to approach the regime of cavity quantum electrodynamics (cQED) interaction by means of high finesse optical resonators. I present results from the MIT experiment of large conditional cross-phase modulation between a signal photon, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. I also present a scheme to probabilistically change the amplitude and phase of a signal photon qubit to, in principle, arbitrary values by postselection on a control photon that has interacted with that state. Notably, small changes of the control photon polarization measurement basis by few degrees can substantially change the amplitude and phase of the signal state. Finally, I present our ongoing effort at Purdue to realize similar peculiar quantum phenomena at the single photon level on chip scale photonic systems.

The Multiple Correspondence Analysis Method and Brain Functional Connectivity: Its Application to the Study of the Non-linear Relationships of Motor Cortex and Basal Ganglia.

PubMed

Rodriguez-Sabate, Clara; Morales, Ingrid; Sanchez, Alberto; Rodriguez, Manuel

2017-01-01

The complexity of basal ganglia (BG) interactions is often condensed into simple models mainly based on animal data and that present BG in closed-loop cortico-subcortical circuits of excitatory/inhibitory pathways which analyze the incoming cortical data and return the processed information to the cortex. This study was aimed at identifying functional relationships in the BG motor-loop of 24 healthy-subjects who provided written, informed consent and whose BOLD-activity was recorded by MRI methods. The analysis of the functional interaction between these centers by correlation techniques and multiple linear regression showed non-linear relationships which cannot be suitably addressed with these methods. The multiple correspondence analysis (MCA), an unsupervised multivariable procedure which can identify non-linear interactions, was used to study the functional connectivity of BG when subjects were at rest. Linear methods showed different functional interactions expected according to current BG models. MCA showed additional functional interactions which were not evident when using lineal methods. Seven functional configurations of BG were identified with MCA, two involving the primary motor and somatosensory cortex, one involving the deepest BG (external-internal globus pallidum, subthalamic nucleus and substantia nigral), one with the input-output BG centers (putamen and motor thalamus), two linking the input-output centers with other BG (external pallidum and subthalamic nucleus), and one linking the external pallidum and the substantia nigral. The results provide evidence that the non-linear MCA and linear methods are complementary and should be best used in conjunction to more fully understand the nature of functional connectivity of brain centers.

State estimation of stochastic non-linear hybrid dynamic system using an interacting multiple model algorithm.

PubMed

Elenchezhiyan, M; Prakash, J

2015-09-01

In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Modal analysis of graphene-based structures for large deformations, contact and material nonlinearities

NASA Astrophysics Data System (ADS)

Ghaffari, Reza; Sauer, Roger A.

2018-06-01

The nonlinear frequencies of pre-stressed graphene-based structures, such as flat graphene sheets and carbon nanotubes, are calculated. These structures are modeled with a nonlinear hyperelastic shell model. The model is calibrated with quantum mechanics data and is valid for high strains. Analytical solutions of the natural frequencies of various plates are obtained for the Canham bending model by assuming infinitesimal strains. These solutions are used for the verification of the numerical results. The performance of the model is illustrated by means of several examples. Modal analysis is performed for square plates under pure dilatation or uniaxial stretch, circular plates under pure dilatation or under the effects of an adhesive substrate, and carbon nanotubes under uniaxial compression or stretch. The adhesive substrate is modeled with van der Waals interaction (based on the Lennard-Jones potential) and a coarse grained contact model. It is shown that the analytical natural frequencies underestimate the real ones, and this should be considered in the design of devices based on graphene structures.

From synthetic modeling of social interaction to dynamic theories of brain-body-environment-body-brain systems.

PubMed

Froese, Tom; Iizuka, Hiroyuki; Ikegami, Takashi

2013-08-01

Synthetic approaches to social interaction support the development of a second-person neuroscience. Agent-based models and psychological experiments can be related in a mutually informing manner. Models have the advantage of making the nonlinear brain-body-environment-body-brain system as a whole accessible to analysis by dynamical systems theory. We highlight some general principles of how social interaction can partially constitute an individual's behavior.

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.

Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1988-01-01

The nonlinear reaction between two oblique 3-D Tollmein-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an imcompressible boundary layer. The same theory applies to the destabilization of an incident vortex motion by subharmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlionear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial differential system for the vortex flow coupled with an ordinary-differential one for the TS pressure. The solution properties found sometimes produce a breakup within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasi-parallel ones governed by the full nonlinear triple-deck response.

Linear spreading speeds from nonlinear resonant interaction

NASA Astrophysics Data System (ADS)

Faye, Grégory; Holzer, Matt; Scheel, Arnd

2017-06-01

We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on the complex linear dispersion relation at the unstable equilibrium, but rely on the presence of a nonlinear term that facilitates the resonant coupling. We prove that these resonant speeds give the correct invasion speed in a simple example, we show that fronts with speeds slower than the resonant speed are unstable, and corroborate our speed criterion numerically in a variety of model equations, including a nonlocal scalar neural field model. GF received support from the project NONLOCAL (ANR-14-CE25-0013) funded by the French National Research Agency. MH was partially supported by the National Science Foundation through grant NSF-DMS-1516155. AS was partially supported by the National Science Foundation through grant NSF-DMS-1311740 and through a DAAD Fellowship.

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

NASA Astrophysics Data System (ADS)

Laurie, Jason; L'Vov, Victor S.; Nazarenko, Sergey; Rudenko, Oleksii

2010-03-01

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

Analysis and gyrokinetic simulation of MHD Alfven wave interactions

NASA Astrophysics Data System (ADS)

Nielson, Kevin Derek

The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the effect of wave amplitude upon the validity of our analytic solution, exploring the nature of strong turbulence. In the kinetic limit where k⊥ rhoi ≳ 1 where incompressible MHD is no longer a valid description, we illustrate how the nonlinear evolution departs from our analytic expression. The analytic theory we develop provides a framework from which more sophisticated of weak and strong inertial-range turbulence theories may be developed. Characterization of the limits of this theory may provide guidance in the development of kinetic Alfven wave turbulence.

Vector breather-to-soliton transitions and nonlinear wave interactions induced by higher-order effects in an erbium-doped fiber

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Wang, Lei; Xie, Xi-Yang

2018-06-01

Vector breather-to-soliton transitions for the higher-order nonlinear Schrödinger-Maxwell-Bloch (NLS-MB) system with sextic terms are investigated. The Lax pair and Darboux transformation (DT) of such system are constructed. With the DT, analytic vector breather solutions up to the second order are obtained. With appropriate choices of the spectra parameters, vector breather-to-soliton transitions happen. Interaction mechanisms of vector nonlinear waves (breather-soliton or soliton-soliton interactions) are displayed.

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.

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

NASA Technical Reports Server (NTRS)

Debussche, A.; Dubois, T.; Temam, R.

1993-01-01

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing

NASA Astrophysics Data System (ADS)

Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng

2017-05-01

Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.

Electrostatic interaction between stereocilia: II. Influence on the mechanical properties of the hair bundle.

PubMed

Dolgobrodov, S G; Lukashkin, A N; Russell, I J

2000-12-01

This paper is based on our model [Dolgobrodov et al., 2000. Hear. Res., submitted for publication] in which we examine the significance of the polyanionic surface layers of stereocilia for electrostatic interaction between them. We analyse how electrostatic forces modify the mechanical properties of the sensory hair bundle. Different charge distribution profiles within the glycocalyx are considered. When modelling a typical experiment on bundle stiffness measurements, applying an external force to the tallest row of stereocilia shows that the asymptotic stiffness of the hair bundle for negative displacements is always larger than the asymptotic stiffness for positive displacements. This increase in stiffness is monotonic for even charge distribution and shows local minima when the negative charge is concentrated in a thinner layer within the cell coat. The minima can also originate from the co-operative effect of electrostatic repulsion and inter-ciliary links with non-linear mechanical properties. Existing experimental observations are compared with the predictions of the model. We conclude that the forces of electrostatic interaction between stereocilia may influence the mechanical properties of the hair bundle and, being strongly non-linear, contribute to the non-linear phenomena, which have been recorded from the auditory periphery.

Rate and timing cues associated with the cochlear amplifier: level discrimination based on monaural cross-frequency coincidence detection.

PubMed

Heinz, M G; Colburn, H S; Carney, L H

2001-10-01

The perceptual significance of the cochlear amplifier was evaluated by predicting level-discrimination performance based on stochastic auditory-nerve (AN) activity. Performance was calculated for three models of processing: the optimal all-information processor (based on discharge times), the optimal rate-place processor (based on discharge counts), and a monaural coincidence-based processor that uses a non-optimal combination of rate and temporal information. An analytical AN model included compressive magnitude and level-dependent-phase responses associated with the cochlear amplifier, and high-, medium-, and low-spontaneous-rate (SR) fibers with characteristic frequencies (CFs) spanning the AN population. The relative contributions of nonlinear magnitude and nonlinear phase responses to level encoding were compared by using four versions of the model, which included and excluded the nonlinear gain and phase responses in all possible combinations. Nonlinear basilar-membrane (BM) phase responses are robustly encoded in near-CF AN fibers at low frequencies. Strongly compressive BM responses at high frequencies near CF interact with the high thresholds of low-SR AN fibers to produce large dynamic ranges. Coincidence performance based on a narrow range of AN CFs was robust across a wide dynamic range at both low and high frequencies, and matched human performance levels. Coincidence performance based on all CFs demonstrated the "near-miss" to Weber's law at low frequencies and the high-frequency "mid-level bump." Monaural coincidence detection is a physiologically realistic mechanism that is extremely general in that it can utilize AN information (average-rate, synchrony, and nonlinear-phase cues) from all SR groups.

N-soliton interactions: Effects of linear and nonlinear gain and loss

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Gerdjikov, V. S.; Todorov, M. D.

2017-10-01

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.

Enhanced energy transport owing to nonlinear interface interaction

PubMed Central

Su, Ruixia; Yuan, Zongqiang; Wang, Jun; Zheng, Zhigang

2016-01-01

It is generally expected that the interface coupling leads to the suppression of thermal transport through coupled nanostructures due to the additional interface phonon-phonon scattering. However, recent experiments demonstrated that the interface van der Waals interactions can significantly enhance the thermal transfer of bonding boron nanoribbons compared to a single freestanding nanoribbon. To obtain a more in-depth understanding on the important role of the nonlinear interface coupling in the heat transports, in the present paper, we explore the effect of nonlinearity in the interface interaction on the phonon transport by studying the coupled one-dimensional (1D) Frenkel-Kontorova lattices. It is found that the thermal conductivity increases with increasing interface nonlinear intensity for weak inter-chain nonlinearity. By developing the effective phonon theory of coupled systems, we calculate the dependence of heat conductivity on interfacial nonlinearity in weak inter-chain couplings regime which is qualitatively in good agreement with the result obtained from molecular dynamics simulations. Moreover, we demonstrate that, with increasing interface nonlinear intensity, the system dimensionless nonlinearity strength is reduced, which in turn gives rise to the enhancement of thermal conductivity. Our results pave the way for manipulating the energy transport through coupled nanostructures for future emerging applications. PMID:26787363

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

NASA Astrophysics Data System (ADS)

Guo, Xin; Wang, Qiang

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

Spectral long-range interaction of temporal incoherent solitons.

PubMed

Xu, Gang; Garnier, Josselin; Picozzi, Antonio

2014-02-01

We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.

Using surface lattice resonances to engineer nonlinear optical processes in metal nanoparticle arrays

NASA Astrophysics Data System (ADS)

Huttunen, Mikko J.; Rasekh, Payman; Boyd, Robert W.; Dolgaleva, Ksenia

2018-05-01

Collective responses of localized surface plasmon resonances, known as surface lattice resonances (SLRs) in metal nanoparticle arrays, can lead to high quality factors (˜100 ), large local-field enhancements, and strong light-matter interactions. SLRs have found many applications in linear optics, but little work of the influence of SLRs on nonlinear optics has been reported. Here we show how SLRs could be utilized to enhance nonlinear optical interactions. We devote special attention to the sum-frequency, difference-frequency, and third-harmonic generation processes because of their potential for the realization of novel sources of light. We also demonstrate how such arrays could be engineered to enhance higher-order nonlinear optical interactions through cascaded nonlinear processes. In particular, we demonstrate how the efficiency of third-harmonic generation could be engineered via cascaded second-order responses.

Stochastic modeling of mode interactions via linear parabolized stability equations

NASA Astrophysics Data System (ADS)

Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

2017-11-01

Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

Shot noise limited characterization of ultraweak femtosecond pulse trains.

PubMed

Schwartz, Osip; Raz, Oren; Katz, Ori; Dudovich, Nirit; Oron, Dan

2011-01-17

Ultrafast science is inherently, due to the lack of fast enough detectors and electronics, based on nonlinear interactions. Typically, however, nonlinear measurements require significant powers and often operate in a limited spectral range. Here we overcome the difficulties of ultraweak ultrafast measurements by precision time-domain localization of spectral components. We utilize this for linear self-referenced characterization of pulse trains having ∼ 1 photon per pulse, a regime in which nonlinear techniques are impractical, at a temporal resolution of ∼ 10 fs. This technique does not only set a new scale of sensitivity in ultrashort pulse characterization, but is also applicable in any spectral range from the near-infrared to the deep UV.

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

Controlling Second Harmonic Efficiency of Laser Beam Interactions

NASA Technical Reports Server (NTRS)

Barnes, Norman P. (Inventor); Walsh, Brian M. (Inventor); Reichle, Donald J. (Inventor)

2011-01-01

A method is provided for controlling second harmonic efficiency of laser beam interactions. A laser system generates two laser beams (e.g., a laser beam with two polarizations) for incidence on a nonlinear crystal having a preferred direction of propagation. Prior to incidence on the crystal, the beams are optically processed based on the crystal's beam separation characteristics to thereby control a position in the crystal along the preferred direction of propagation at which the beams interact.

Constrained State Estimation for Individual Localization in Wireless Body Sensor Networks

PubMed Central

Feng, Xiaoxue; Snoussi, Hichem; Liang, Yan; Jiao, Lianmeng

2014-01-01

Wireless body sensor networks based on ultra-wideband radio have recently received much research attention due to its wide applications in health-care, security, sports and entertainment. Accurate localization is a fundamental problem to realize the development of effective location-aware applications above. In this paper the problem of constrained state estimation for individual localization in wireless body sensor networks is addressed. Priori knowledge about geometry among the on-body nodes as additional constraint is incorporated into the traditional filtering system. The analytical expression of state estimation with linear constraint to exploit the additional information is derived. Furthermore, for nonlinear constraint, first-order and second-order linearizations via Taylor series expansion are proposed to transform the nonlinear constraint to the linear case. Examples between the first-order and second-order nonlinear constrained filters based on interacting multiple model extended kalman filter (IMM-EKF) show that the second-order solution for higher order nonlinearity as present in this paper outperforms the first-order solution, and constrained IMM-EKF obtains superior estimation than IMM-EKF without constraint. Another brownian motion individual localization example also illustrates the effectiveness of constrained nonlinear iterative least square (NILS), which gets better filtering performance than NILS without constraint. PMID:25390408

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.

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.

Nonscanning Moiré deflectometry for measurement of nonlinear refractive index and absorption coefficient of liquids.

PubMed

Farahani, Shahrzad Shahrabi; Madanipour, Khosro; Koohian, Ata

2017-05-01

In this work, a nonscanning measurement technique is presented for determining the nonlinear refractive index and absorption coefficient of liquid media based on Moiré deflectometry. In the proposed method two lasers are used: a low power, wide beam as probe and a high power with specific wavelength as a pump. Interaction of the pump laser beam with the nonlinear sample changes the refractive index, which leads to change in convergence/divergence of the collimated incident probe laser beam. The induced deflection is monitored by Moiré deflectometry. If the pump laser has a Gaussian intensity profile, the refractive index profile of the sample is Gaussian, too. Measuring the deflection angle of the probe beam by Moiré fringes deflection, and by using the inverse Abel transform integral, the refractive index profile and nonlinear refractive index can be determined. This method is fast, easy, and insensitive to environmental noise and allows real-time measurement. Also, the refractive index profile of the interacted medium with pump laser can be achieved by this technique. As a liquid sample, a DCJ dye in water solution was studied. The value of nonlinear refractive index, n₂, and absorption coefficient, α, were obtained -2.54×10^-4  cm² w^-1 and 1.368  cm^-1, respectively.

Uniform strongly interacting soliton gas in the frame of the Nonlinear Schrodinger Equation

NASA Astrophysics Data System (ADS)

Gelash, Andrey; Agafontsev, Dmitry

2017-04-01

The statistical properties of many soliton systems play the key role in the fundamental studies of integrable turbulence and extreme sea wave formation. It is well known that separated solitons are stable nonlinear coherent structures moving with constant velocity. After collisions with each other they restore the original shape and only acquire an additional phase shift. However, at the moment of strong nonlinear soliton interaction (i.e. when solitons are located close) the wave field are highly complicated and should be described by the theory of inverse scattering transform (IST), which allows to integrate the KdV equation, the NLSE and many other important nonlinear models. The usual approach of studying the dynamics and statistics of soliton wave field is based on relatively rarefied gas of solitons [1,2] or restricted by only two-soliton interactions [3]. From the other hand, the exceptional role of interacting solitons and similar coherent structures - breathers in the formation of rogue waves statistics was reported in several recent papers [4,5]. In this work we study the NLSE and use the most straightforward and general way to create many soliton initial condition - the exact N-soliton formulas obtained in the theory of the IST [6]. We propose the recursive numerical scheme for Zakharov-Mikhailov variant of the dressing method [7,8] and discuss its stability with respect to increasing the number of solitons. We show that the pivoting, i.e. the finding of an appropriate order for recursive operations, has a significant impact on the numerical accuracy. We use the developed scheme to generate statistical ensembles of 32 strongly interacting solitons, i.e. solve the inverse scattering problem for the high number of discrete eigenvalues. Then we use this ensembles as initial conditions for numerical simulations in the box with periodic boundary conditions and study statics of obtained uniform strongly interacting gas of NLSE solitons. Author thanks the support of the Russian Science Foundation (Grand No. 14-22-00174) [1] D. Dutykh, E. Pelinovsky, Numerical simulation of a solitonic gas in kdv and kdv-bbm equations, Physics Letters A 378 (42) (2014) 3102-3110. [2] E. Shurgalina, E. Pelinovsky, Nonlinear dynamics of a soliton gas: Modified korteweg-de vries equation framework, Physics Letters A 380 (24) (2016) 2049-2053. [3] E. N. Pelinovsky, E. Shurgalina, A. Sergeeva, T. G. Talipova, G. El, R. H. Grimshaw, Two-soliton interaction as an elementary act of soliton turbulence in integrable systems, Physics Letters A 377 (3) (2013) 272-275 [4] J. Soto-Crespo, N. Devine, N. Akhmediev, Integrable turbulence and rogue waves: Breathers or solitons?, Physical review letters 116 (10) (2016) 103901. [5] D. S. Agafontsev, V. E. Zakharov, Integrable turbulence and formation of rogue waves, Nonlinearity 28 (8) (2015) 2791. [6] V. E. Zakharov, A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics JETP 34 (1) (1972) 62. [7] V. Zakharov, A. Mikhailov, Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method, Sov. Phys.-JETP (Engl. Transl.) 47 (6) (1978). [8] A. A. Gelash, V. E. Zakharov, Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability, Nonlinearity 27 (4) (2014) R1.

Monte Carlo Simulation of THz Multipliers

NASA Technical Reports Server (NTRS)

East, J.; Blakey, P.

1997-01-01

Schottky Barrier diode frequency multipliers are critical components in submillimeter and Thz space based earth observation systems. As the operating frequency of these multipliers has increased, the agreement between design predictions and experimental results has become poorer. The multiplier design is usually based on a nonlinear model using a form of harmonic balance and a model for the Schottky barrier diode. Conventional voltage dependent lumped element models do a poor job of predicting THz frequency performance. This paper will describe a large signal Monte Carlo simulation of Schottky barrier multipliers. The simulation is a time dependent particle field Monte Carlo simulation with ohmic and Schottky barrier boundary conditions included that has been combined with a fixed point solution for the nonlinear circuit interaction. The results in the paper will point out some important time constants in varactor operation and will describe the effects of current saturation and nonlinear resistances on multiplier operation.

Refined Models for an Analysis of Internal and External Buckling Modes of a Monolayer in a Layered Composite

NASA Astrophysics Data System (ADS)

Paimushin, V. N.

2017-11-01

For an analysis of internal and external buckling modes of a monolayer inside or at the periphery of a layered composite, refined geometrically nonlinear equations are constructed. They are based on modeling the monolayer as a thin plate interacting with binder layers at the points of boundary surfaces. The binder layer is modeled as a transversely soft foundation. It is assumed the foundations, previously compressed in the transverse direction (the first loading stage), have zero displacements of its external boundary surfaces at the second loading stage, but the contact interaction of the plate with foundations occurs without slippage or delamination. The deformation of the plate at a medium flexure is described by geometrically nonlinear relations of the classical plate theory based on the Kirchhoff-Love hypothesis (the first variant) or the refined Timoshenko model with account of the transverse shear and compression (the second variant). The foundation is described by linearized 3D equations of elasticity theory, which are simplified within the framework of the model of a transversely soft layer. Integrating the linearized equations along the transverse coordinate and satisfying the kinematic joining conditions of the plate with foundations, with account of their initial compression in the thickness direction, a system of 2D geometrically nonlinear equations and appropriate boundary conditions are derived. These equations describe the contact interaction between elements of the deformable system. The relations obtained are simplified for the case of a symmetric stacking sequence.

Lagrangian methods in nonlinear plasma wave interaction

NASA Technical Reports Server (NTRS)

Crawford, F. W.

1980-01-01

Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-Lagrangian methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable Lagrangian densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.

Optimisation of the vibrational response of ultrasonic cutting systems

NASA Astrophysics Data System (ADS)

Cartmell, M. P.; Lim, F. C. N.; Cardoni, A.; Lucas, M.

2005-10-01

This paper provides an account of an investigation into possible dynamic interactions between two coupled non-linear sub-systems, each possessing opposing non-linear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two-degree-of-freedom Duffing oscillator in which certain non-linear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently non-linear, and which is coupled to a bar- or block-horn, and to one or more material cutting blades, for example. The horn/blade configurations are also non-linear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two-degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall non-linear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also been shown experimentally that coupling of ultrasonic components with different non-linear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice. Further experiments have shown that a multiple horn/blade configuration can, under certain circumstances, display autoparametric responses based on the forced response of the desired longitudinal mode parametrically exciting an undesired lateral mode. Typical autoparametric response phenomena have been observed and are presented at the end of the paper.

Physics of Alfvén waves and energetic particles in burning plasmas

NASA Astrophysics Data System (ADS)

Chen, Liu; Zonca, Fulvio

2016-01-01

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

Ghost Dark Energy with Non-Linear Interaction Term

NASA Astrophysics Data System (ADS)

Ebrahimi, E.

2016-06-01

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

Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

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

Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com; Singh, Navpreet, E-mail: navpreet.nit@gmail.com

2015-11-15

This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on amore » numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.« less

Micro-/nanoscale multi-field coupling in nonlinear photonic devices

NASA Astrophysics Data System (ADS)

Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu

2017-08-01

The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.

Giant nonlinear interaction between two optical beams via a quantum dot embedded in a photonic wire

NASA Astrophysics Data System (ADS)

Nguyen, H. A.; Grange, T.; Reznychenko, B.; Yeo, I.; de Assis, P.-L.; Tumanov, D.; Fratini, F.; Malik, N. S.; Dupuy, E.; Gregersen, N.; Auffèves, A.; Gérard, J.-M.; Claudon, J.; Poizat, J.-Ph.

2018-05-01

Optical nonlinearities usually appear for large intensities, but discrete transitions allow for giant nonlinearities operating at the single-photon level. This has been demonstrated in the last decade for a single optical mode with cold atomic gases, or single two-level systems coupled to light via a tailored photonic environment. Here, we demonstrate a two-mode giant nonlinearity with a single semiconductor quantum dot (QD) embedded in a photonic wire antenna. We exploit two detuned optical transitions associated with the exciton-biexciton QD level scheme. Owing to the broadband waveguide antenna, the two transitions are efficiently interfaced with two free-space laser beams. The reflection of one laser beam is then controlled by the other beam, with a threshold power as low as 10 photons per exciton lifetime (1.6 nW ). Such a two-color nonlinearity opens appealing perspectives for the realization of ultralow-power logical gates and optical quantum gates, and could also be implemented in an integrated photonic circuit based on planar waveguides.

Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality

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

Kong Qian; Department of Physics, Shanghai University, Shanghai 200444; Wang, Q.

2010-07-15

We investigate theoretically the interaction of dark solitons in materials with a spatially nonlocal nonlinearity. In particular we do this analytically and for arbitrary degree of nonlocality. We employ the variational technique to show that nonlocality induces an attractive force in the otherwise repulsive soliton interaction.

Single-cycle high-intensity electromagnetic pulse generation in the interaction of a plasma wakefield with regular nonlinear structures.

PubMed

Bulanov, S S; Esirkepov, T Zh; Kamenets, F F; Pegoraro, F

2006-03-01

The interaction of regular nonlinear structures (such as subcycle solitons, electron vortices, and wake Langmuir waves) with a strong wake wave in a collisionless plasma can be exploited in order to produce ultrashort electromagnetic pulses. The electromagnetic field of the nonlinear structure is partially reflected by the electron density modulations of the incident wake wave and a single-cycle high-intensity electromagnetic pulse is formed. Due to the Doppler effect the length of this pulse is much shorter than that of the nonlinear structure. This process is illustrated with two-dimensional particle-in-cell simulations. The considered laser-plasma interaction regimes can be achieved in present day experiments and can be used for plasma diagnostics.

Localization of intense electromagnetic waves in a relativistically hot plasma.

PubMed

Shukla, P K; Eliasson, B

2005-02-18

We consider nonlinear interactions between intense short electromagnetic waves (EMWs) and a relativistically hot electron plasma that supports relativistic electron holes (REHs). It is shown that such EMW-REH interactions are governed by a coupled nonlinear system of equations composed of a nonlinear Schro dinger equation describing the dynamics of the EMWs and the Poisson-relativistic Vlasov system describing the dynamics of driven REHs. The present nonlinear system of equations admits both a linearly trapped discrete number of eigenmodes of the EMWs in a quasistationary REH and a modification of the REH by large-amplitude trapped EMWs. Computer simulations of the relativistic Vlasov and Maxwell-Poisson system of equations show complex interactions between REHs loaded with localized EMWs.

Evaluation of the interaction between hydroxyapatite and bisphosphonate by nonlinear capillary electrochromatography.

PubMed

Kong, Deying; Chen, Zilin

2017-05-01

Bisphosphonates are a class of chemical compounds used to treat diseases caused by increased bone resorption. Zoledronate is a third-generation bisphosphonate drug. Hydroxyapatite is main mineral constituent of bones, which can be bound by bisphosphonates in vivo. In this work, we report a method of nonlinear capillary electrochromatography for study on the interaction between hydroxyapatite and bisphosphonate. Hydroxyapatite was modified on the inner wall of capillary by a biomimetic-mineralization method. Then nonlinear chromatography was used to fit and analyze the interaction between zoledronate and hydroxyapatite. The association rate constants of zoledronate in hydroxyapatite-modified capillary and bare capillary are 642.3 and 195/M/min, respectively. This indicates that there is strong binding interactions and affinity between zoledronate and hydroxyapatite. Besides, the interaction between zoledronate and hydroxyapatite was confirmed further by ultraviolet spectroscopy. The method of nonlinear capillary electrochromatography provides a fast and effect approach for studying of bone metabolism disease by evaluation of interaction between hydroxyapatite and bisphosphonates. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

CMOS-compatible 2-bit optical spectral quantization scheme using a silicon-nanocrystal-based horizontal slot waveguide

PubMed Central

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Wu, Qiang; Sang, Xinzhu; Farrell, Gerald; Yu, Chongxiu; Li, Feng; Tam, Hwa Yaw; Wai, P. K. A.

2014-01-01

All-optical analog-to-digital converters based on the third-order nonlinear effects in silicon waveguide are a promising candidate to overcome the limitation of electronic devices and are suitable for photonic integration. In this paper, a 2-bit optical spectral quantization scheme for on-chip all-optical analog-to-digital conversion is proposed. The proposed scheme is realized by filtering the broadened and split spectrum induced by the self-phase modulation effect in a silicon horizontal slot waveguide filled with silicon-nanocrystal. Nonlinear coefficient as high as 8708 W−1/m is obtained because of the tight mode confinement of the horizontal slot waveguide and the high nonlinear refractive index of the silicon-nanocrystal, which provides the enhanced nonlinear interaction and accordingly low power threshold. The results show that a required input peak power level less than 0.4 W can be achieved, along with the 1.98-bit effective-number-of-bit and Gray code output. The proposed scheme can find important applications in on-chip all-optical digital signal processing systems. PMID:25417847

Nonlinear Lamb waves for fatigue damage identification in FRP-reinforced steel plates.

PubMed

Wang, Yikuan; Guan, Ruiqi; Lu, Ye

2017-09-01

A nonlinear Lamb-wave-based method for fatigue crack detection in steel plates with and without carbon fibre reinforcement polymer (CFRP) reinforcement is presented in this study. Both numerical simulation and experimental evaluation were performed for Lamb wave propagation and its interaction with a fatigue crack on these two steel plate types. With the generation of the second harmonic, the damage-induced wave nonlinearities were identified by surface-bonded piezoelectric sensors. Numerical simulation revealed that the damage-induced wave component at the second harmonic was slightly affected by the existence of CFRP laminate, although the total wave energy was decreased because of wave leakage into the CFRP laminate. Due to unavoidable nonlinearity from the experimental environments, it was impractical to directly extract the time-of-flight of the second harmonic for locating the crack. To this end, the correlation coefficient of benchmark and signal with damage at double frequency in the time domain was calculated, based on which an imaging method was introduced to locate the fatigue crack in steel plates with and without CFRP laminates. Copyright © 2017 Elsevier B.V. All rights reserved.

CMOS-compatible 2-bit optical spectral quantization scheme using a silicon-nanocrystal-based horizontal slot waveguide.

PubMed

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Wu, Qiang; Sang, Xinzhu; Farrell, Gerald; Yu, Chongxiu; Li, Feng; Tam, Hwa Yaw; Wai, P K A

2014-11-24

All-optical analog-to-digital converters based on the third-order nonlinear effects in silicon waveguide are a promising candidate to overcome the limitation of electronic devices and are suitable for photonic integration. In this paper, a 2-bit optical spectral quantization scheme for on-chip all-optical analog-to-digital conversion is proposed. The proposed scheme is realized by filtering the broadened and split spectrum induced by the self-phase modulation effect in a silicon horizontal slot waveguide filled with silicon-nanocrystal. Nonlinear coefficient as high as 8708 W(-1)/m is obtained because of the tight mode confinement of the horizontal slot waveguide and the high nonlinear refractive index of the silicon-nanocrystal, which provides the enhanced nonlinear interaction and accordingly low power threshold. The results show that a required input peak power level less than 0.4 W can be achieved, along with the 1.98-bit effective-number-of-bit and Gray code output. The proposed scheme can find important applications in on-chip all-optical digital signal processing systems.

Nonlinear Coherent Structures, Microbursts and Turbulence

NASA Astrophysics Data System (ADS)

Lakhina, G. S.

2015-12-01

Nonlinear waves are found everywhere, in fluids, atmosphere, laboratory, space and astrophysical plasmas. The interplay of nonlinear effects, dispersion and dissipation in the medium can lead to a variety of nonlinear waves and turbulence. Two cases of coherent nonlinear waves: chorus and electrostatic solitary waves (ESWs) and their impact on modifying the plasma medium are discussed. Chorus is a right-hand, circularly-polarized electromagnetic plane wave. Dayside chorus is a bursty emission composed of rising frequency "elements" with duration of ~0.1 to 1.0 s. Each element is composed of coherent subelements with durations of ~1 to 100 ms or more. The cyclotron resonant interaction between energetic electrons and the coherent chorus waves is studied. An expression for the pitch angle transport due to this interaction is derived considering a Gaussian distribution for the time duration of the chorus elements. The rapid pitch scattering can provide an explanation for the ionospheric microbursts of ~0.1 to 0.5 s in bremsstrahlung x-rays formed by ~10-100 keV precipitating electrons. On the other hand, the ESWs are observed in the electric field component parallel to the background magnetic field, and are usually bipolar or tripolar. Generation of coherent ESWs has been explained in terms of nonlinear fluid models of ion- and electron-acoustic solitons and double layers (DLs) based on Sagdeev pseudopotential technique. Fast Fourier transform of electron- and ion-acoustic solitons/DLs produces broadband wave spectra which can explain the properties of the electrostatic turbulence observed in the magnetosheath and plasma sheet boundary layer, and in the solar wind, respectively.

Interaction Solutions for Lump-line Solitons and Lump-kink Waves of the Dimensionally Reduced Generalised KP Equation

NASA Astrophysics Data System (ADS)

Ahmed, Iftikhar

2017-09-01

In this work, we investigate dimensionally reduced generalised Kadomtsev-Petviashvili equation, which can describe many nonlinear phenomena in fluid dynamics. Based on the bilinear formalism, direct Maple symbolic computations are used with an ansätz function to construct three classes of interaction solutions between lump and line solitons. Furthermore, the dynamics of interaction phenomena is explained with 3D plots and 2D contour plots. For the first class of interaction solutions, lump appeared at t=0, and there was a normal interaction between lump and line solitons at t=1, 2, 5, and 10. For the second class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving downward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. By contrast, for the third class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving upward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. Furthermore, interaction solutions between lump solutions and kink wave are also investigated. These results might be helpful to understand the propagation processes for nonlinear waves in fluid mechanics.

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.

Laser cutting of ultra-thin glasses based on a nonlinear laser interaction effect

NASA Astrophysics Data System (ADS)

Chen, Jian; Wu, Zhouling

2013-07-01

Glass panel substrates have been widely used in consumer electronics such as in flat panel TVs, laptops, and cell phones. With the advancement in the industry, the glass substrates are becoming thinner and stronger for reduced weight and volume, which brings great challenges for traditional mechanical processes in terms of cut quality, yield, and throughput. Laser glass cutting provides a non-contact process with minimum impact and superior quality compared to the mechanical counterparts. In this paper, we presented recent progresses in advanced laser processing of ultra-thin glass substrates, especially laser-cutting of ultra-thin glasses by a high power laser through a nonlinear interaction effect. Our results indicate that this technique has great potential of application for mass production of ultra-thin glass substrates.

Helicity coherence in binary neutron star mergers and nonlinear feedback

NASA Astrophysics Data System (ADS)

Chatelain, Amélie; Volpe, Cristina

2017-02-01

Neutrino flavor conversion studies based on astrophysical environments usually implement neutrino mixings, neutrino interactions with matter, and neutrino self-interactions. In anisotropic media, the most general mean-field treatment includes neutrino mass contributions as well, which introduce a coupling between neutrinos and antineutrinos termed helicity or spin coherence. We discuss resonance conditions for helicity coherence for Dirac and Majorana neutrinos. We explore the role of these mean-field contributions on flavor evolution in the context of a binary neutron star merger remnant. We find that resonance conditions can be satisfied in neutron star merger scenarios while adiabaticity is not sufficient for efficient flavor conversion. We analyze our numerical findings by discussing general conditions to have multiple Mikheyev-Smirnov-Wolfenstein-like resonances, in the presence of nonlinear feedback, in astrophysical environments.

Nonlinear interaction in differential mode delay managed mode-division multiplexed transmission systems.

PubMed

Rademacher, Georg; Warm, Stefan; Petermann, Klaus

2015-01-12

We analyze the impact of Differential Mode Delay (DMD) Management on the nonlinear impairments in mode-division multiplexed transmission systems. It is found out that DMD Management can lead to a degraded performance, due to enhanced intermodal nonlinear interaction. This can be attributed to an increased correlation of co-propagating channels, similar to the effects that show up in dispersion managed single-mode systems.

Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction

NASA Astrophysics Data System (ADS)

Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.

2005-03-01

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

Nonlinearities in Behavioral Macroeconomics.

PubMed

Gomes, Orlando

2017-07-01

This article undertakes a journey across the literature on behavioral macroeconomics, with attention concentrated on the nonlinearities that the behavioral approach typically suggests or implies. The emphasis is placed on thinking the macro economy as a living organism, composed of many interacting parts, each one having a will of its own, which is in sharp contrast with the mechanism of the orthodox view (well represented by the neoclassical or new Keynesian dynamic stochastic general equilibrium - DSGE - model). The paper advocates that a thorough understanding of individual behavior in collective contexts is the only possible avenue to further explore macroeconomic phenomena and the often observed 'anomalies' that the benchmark DSGE macro framework is unable to explain or justify. After a reflection on the role of behavioral traits as a fundamental component of a new way of thinking the economy, the article proceeds with a debate on some of the most relevant frameworks in the literature that somehow link macro behavior and nonlinearities; covered subjects include macro models with disequilibrium rules, agent-based models that highlight interaction and complexity, evolutionary switching frameworks, and inattention based decision problems. These subjects have, as a fundamental point in common, the use of behavioral elements to transform existing interpretations of the economic reality, making it more evident how irregular fluctuations emerge and unfold on the aggregate.

An object-oriented computational model to study cardiopulmonary hemodynamic interactions in humans.

PubMed

Ngo, Chuong; Dahlmanns, Stephan; Vollmer, Thomas; Misgeld, Berno; Leonhardt, Steffen

2018-06-01

This work introduces an object-oriented computational model to study cardiopulmonary interactions in humans. Modeling was performed in object-oriented programing language Matlab Simscape, where model components are connected with each other through physical connections. Constitutive and phenomenological equations of model elements are implemented based on their non-linear pressure-volume or pressure-flow relationship. The model includes more than 30 physiological compartments, which belong either to the cardiovascular or respiratory system. The model considers non-linear behaviors of veins, pulmonary capillaries, collapsible airways, alveoli, and the chest wall. Model parameters were derisved based on literature values. Model validation was performed by comparing simulation results with clinical and animal data reported in literature. The model is able to provide quantitative values of alveolar, pleural, interstitial, aortic and ventricular pressures, as well as heart and lung volumes during spontaneous breathing and mechanical ventilation. Results of baseline simulation demonstrate the consistency of the assigned parameters. Simulation results during mechanical ventilation with PEEP trials can be directly compared with animal and clinical data given in literature. Object-oriented programming languages can be used to model interconnected systems including model non-linearities. The model provides a useful tool to investigate cardiopulmonary activity during spontaneous breathing and mechanical ventilation. Copyright © 2018 Elsevier B.V. All rights reserved.

Thermal conductance of suspended nanoribbons: interplay between strain and interatomic potential nonlinearity

NASA Astrophysics Data System (ADS)

Barreto, Roberto; Florencia Carusela, M.; Monastra, Alejandro G.

2017-10-01

We investigate the role that nonlinearity in the interatomic potential has on the thermal conductance of a suspended nanoribbon when it is subjected to a longitudinal strain. To focus on the first cubic and quartic nonlinear terms of a general potential, we propose an atomic system based on an α-β Fermi-Pasta-Ulam nearest neighbor interaction. We perform classical molecular dynamics simulations to investigate the contribution of longitudinal, transversal and flexural modes to the thermal conductance as a function of the α-β parameters and the applied strain. We compare the cases where atoms are allowed to vibrate only in plane (2D) with the case of vibrations in and out of plane (3D). We find that the dependence of conductance on α and β relies on a crossover phenomenon between linear/nonlinear delocalized/localized flexural and transversal modes, driven by an on/off switch of the strain.

Experimental study of isolas in nonlinear systems featuring modal interactions

PubMed Central

Noël, Jean-Philippe; Virgin, Lawrence N.; Kerschen, Gaëtan

2018-01-01

The objective of the present paper is to provide experimental evidence of isolated resonances in the frequency response of nonlinear mechanical systems. More specifically, this work explores the presence of isolas, which are periodic solutions detached from the main frequency response, in the case of a nonlinear set-up consisting of two masses sliding on a horizontal guide. A careful experimental investigation of isolas is carried out using responses to swept-sine and stepped-sine excitations. The experimental findings are validated with advanced numerical simulations combining nonlinear modal analysis and bifurcation monitoring. In particular, the interactions between two nonlinear normal modes are shown to be responsible for the creation of the isolas. PMID:29584758

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.

Shoaling of nonlinear internal waves in Massachusetts Bay

USGS Publications Warehouse

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

2008-01-01

The shoaling of the nonlinear internal tide in Massachusetts Bay is studied with a fully nonlinear and nonhydrostatic model. The results are compared with current and temperature observations obtained during the August 1998 Massachusetts Bay Internal Wave Experiment and observations from a shorter experiment which took place in September 2001. The model shows how the approaching nonlinear undular bore interacts strongly with a shoaling bottom, offshore of where KdV theory predicts polarity switching should occur. It is shown that the shoaling process is dominated by nonlinearity, and the model results are interpreted with the aid of a two-layer nonlinear but hydrostatic model. After interacting with the shoaling bottom, the undular bore emerges on the shallow shelf inshore of the 30-m isobath as a nonlinear internal tide with a range of possible shapes, all of which are found in the available observational record. Copyright 2008 by the American Geophysical Union.

Nonlinear robust control of hypersonic aircrafts with interactions between flight dynamics and propulsion systems.

PubMed

Li, Zhaoying; Zhou, Wenjie; Liu, Hao

2016-09-01

This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Design of a 6 TeV muon collider

DOE PAGES

Wang, M-H.; Nosochkov, Y.; Cai, Y.; ...

2016-09-09

Here, a preliminary design of a muon collider ring with the center of mass (CM) energy of 6 TeV is presented. The ring circumference is 6.3 km, and themore » $$\\beta$$ functions at collision point are 1 cm in each plane. The ring linear optics, the non-linear chromaticity compensation in the Interaction Region (IR), and the additional non-linear orthogonal correcting knobs are described. Magnet specifications are based on the maximum pole-tip field of 20T in dipoles and 15T in quadrupoles. Careful compensation of the non-linear chromatic and amplitude dependent effects provide a sufficiently large dynamic aperture for the momentum range of up to $$\\pm$$0.5% without considering magnet errors.« less

A nonlinear high temperature fracture mechanics basis for strainrange partitioning

NASA Technical Reports Server (NTRS)

Kitamura, Takayuki; Halford, Gary R.

1989-01-01

A direct link was established between Strainrange Partitioning (SRP) and high temperature fracture mechanics by deriving the general SRP inelastic strain range versus cyclic life relationships from high temperature, nonlinear, fracture mechanics considerations. The derived SRP life relationships are in reasonable agreement based on the experience of the SRP behavior of many high temperature alloys. In addition, fracture mechanics has served as a basis for derivation of the Ductility-Normalized SRP life equations, as well as for examination of SRP relations that are applicable to thermal fatigue life prediction. Areas of additional links between nonlinear fracture mechanics and SRP were identified for future exploration. These include effects of multiaxiality as well as low strain, nominally elastic, long life creep fatigue interaction.

Nonlinear quantum Langevin equations for bosonic modes in solid-state systems

NASA Astrophysics Data System (ADS)

Manninen, Juuso; Agasti, Souvik; Massel, Francesco

2017-12-01

Based on the experimental evidence that impurities contribute to the dissipation properties of solid-state open quantum systems, we provide here a description in terms of nonlinear quantum Langevin equations of the role played by two-level systems in the dynamics of a bosonic degree of freedom. Our starting point is represented by the description of the system-environment coupling in terms of coupling to two separate reservoirs, modeling the interaction with external bosonic modes and two-level systems, respectively. Furthermore, we show how this model represents a specific example of a class of open quantum systems that can be described by nonlinear quantum Langevin equations. Our analysis offers a potential explanation of the parametric effects recently observed in circuit-QED cavity optomechanics experiments.

The strong nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flow

NASA Technical Reports Server (NTRS)

Bennett, J.; Hall, P.; Smith, F. T.

1988-01-01

Viscous fluid flows with curved streamlines can support both centrifugal and viscous traveling wave instabilities. Here the interaction of these instabilities in the context of the fully developed flow in a curved channel is discussed. The viscous (Tollmein-Schlichting) instability is described asymptotically at high Reynolds numbers and it is found that it can induce a Taylor-Goertler flow even at extremely small amplitudes. In this interaction, the Tollmein-Schlichting wave can drive a vortex state with wavelength either comparable with the channel width or the wavelength of lower branch viscous modes. The nonlinear equations which describe these interactions are solved for nonlinear equilibrium states.

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

NASA Astrophysics Data System (ADS)

Zhou, Lei; Li, Aming; Wang, Long

2015-06-01

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

Getting off the Straight and Narrow: Exploiting Non-Linear, Interactive Narrative Structures in Digital Stories for Language Teaching

ERIC Educational Resources Information Center

Prosser, Andrew

2014-01-01

Digital storytelling is already used extensively in language education. Web documentaries, particularly in terms of design and narrative structure, provide an extension of the digital storytelling concept, specifically in terms of increased interactivity. Using a model of interactive, non-linear storytelling, originally derived from computer game…

Efficient nonlinear metasurface based on nonplanar plasmonic nanocavities

DOE PAGES

Wang, Feng; Martinson, Alex B. F.; Harutyunyan, Hayk

2017-04-03

Since their discovery in the 1960s, nonlinear optical effects have revolutionized optical technologies and laser industry. Development of efficient nanoscale nonlinear sources will pave the way for new applications in photonic circuitry, quantum optics and biosensing. However, nonlinear signal generation at dimensions smaller than the wavelength of light brings new challenges. The fundamental difficulty of designing an efficient nonlinear source is that some of the contributing factors involved in nonlinear wave-mixing at the nanoscale are often hard to satisfy simultaneously. Here, we overcome these limitations by developing a new type of nonplanar plasmonic metasurfaces, which can greatly enhance the secondmore » harmonic generation (SHG) at visible frequencies and achieve conversion efficiency of ~6 × 10 -5 at a peak pump intensity of ~0.5 GW/cm 2. This is 4-5 orders of magnitude larger than the efficiencies observed for nonlinear thin films and doubly resonant plasmonic antennas. The proposed metasurface consists of an array of metal-dielectric-metal (MDM) nanocavities formed by conformally cross-linked nanowires separated by an ultrathin nonlinear material layer. The nonplanar MDM geometry minimizes the destructive interference of nonlinear emission into the far-field, provides strongly enhanced independently tunable resonances both for fundamental and harmonic frequencies, a good mutual overlap of the modes and a strong interaction with the nonlinear spacer. Lastly, our findings enable the development of efficient nanoscale single photon sources, integrated frequency converters, and other nonlinear devices.« less

Interharmonic modulation products as a means to quantify nonlinear D-region interactions

NASA Astrophysics Data System (ADS)

Moore, Robert

Experimental observations performed during dual beam ionospheric HF heating experiments at the High frequency Active Auroral Research Program (HAARP) HF transmitter in Gakona, Alaska are used to quantify the relative importance of specific nonlinear interactions that occur within the D region ionosphere. During these experiments, HAARP broadcast two amplitude modulated HF beams whose center frequencies were separated by less than 20 kHz. One beam was sinusoidally modulated at 500 Hz while the second beam was sinusoidally modulated using a 1-7 kHz linear frequency-time chirp. ELF/VLF observations performed at two different locations (3 and 98 km from HAARP) provide clear evidence of strong interactions between all field components of the two HF beams in the form of low and high order interharmonic modulation products. From a theoretical standpoint, the observed interharmonic modulation products could be produced by several different nonlinearities. The two primary nonlinearities take the form of wave-medium interactions (i.e., cross modulation), wherein the ionospheric conductivity modulation produced by one signal crosses onto the other signal via collision frequency modification, and wave-wave interactions, wherein the conduction current associated with one wave mixes with the electric field of the other wave to produce electron temperature oscillations. We are able to separate and quantify these two different nonlinearities, and we conclude that the wave-wave interactions dominate the wave-medium interactions by a factor of two. These results are of great importance for the modeling of transioinospheric radio wave propagation, in that both the wave-wave and the wave-medium interactions could be responsible for a significant amount of anomalous absorption.

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong

2013-02-01

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

Squeezed-light generation in a nonlinear planar waveguide with a periodic corrugation

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

Perina, Jan Jr.; Haderka, Ondrej; Sibilia, Concita

Two-mode nonlinear interaction (second-harmonic and second-subharmonic generation) in a planar waveguide with a small periodic corrugation at the surface is studied. Scattering of the interacting fields on the corrugation leads to constructive interference that enhances the nonlinear process provided that all the interactions are phase matched. Conditions for the overall phase matching are found. Compared with a perfectly quasi-phase-matched waveguide, better values of squeezing as well as higher intensities are reached under these conditions. Procedure for finding optimum values of parameters for squeezed-light generation is described.

Synchronization and Cardio-pulmonary feedback in Sleep Apnea

NASA Astrophysics Data System (ADS)

Xu, Limei; Ivanov, Plamen Ch.; Chen, Zhi; Hu, Kun; Paydarfar, David; Stanley, H. Eugene

2004-03-01

Findings indicate a dynamical coupling between respiratory and cardiac function. However, the nature of this nonlinear interaction remains not well understood. We investigate transient patterns in the cardio-pulmonary interaction under healthy conditions by means of cross-correlation and nonlinear synchronization techniques, and we compare how these patterns change under pathologic conditions such as obstructive sleep apnea --- a periodic cessation of breathing during sleep. We find that during apnea episodes the nonlinear features of cardio-pulmonary interaction change intermittently, and can exhibit variations characterized by different time delays in the phase synchronization between breathing and heartbeat dynamics.

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas.

PubMed

Shukla, P K; Eliasson, B

2007-08-31

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.

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.

Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor.

PubMed

Spillane, S M; Pati, G S; Salit, K; Hall, M; Kumar, P; Beausoleil, R G; Shahriar, M S

2008-06-13

We report the observation of low-light level optical interactions in a tapered optical nanofiber (TNF) embedded in a hot rubidium vapor. The small optical mode area plays a significant role in the optical properties of the hot vapor Rb-TNF system, allowing nonlinear optical interactions with nW level powers even in the presence of transit-time dephasing rates much larger than the intrinsic linewidth. We demonstrate nonlinear absorption and V-type electromagnetically induced transparency with cw powers below 10 nW, comparable to the best results in any Rb-optical waveguide system. The good performance and flexibility of the Rb-TNF system makes it a very promising candidate for ultralow power resonant nonlinear optical applications.

Ytterbium-doped fiber laser passively mode locked by few-layer Molybdenum Disulfide (MoS2) saturable absorber functioned with evanescent field interaction

PubMed Central

Du, Juan; Wang, Qingkai; Jiang, Guobao; Xu, Changwen; Zhao, Chujun; Xiang, Yuanjiang; Chen, Yu; Wen, Shuangchun; Zhang, Han

2014-01-01

By coupling few-layer Molybdenum Disulfide (MoS2) with fiber-taper evanescent light field, a new type of MoS2 based nonlinear optical modulating element had been successfully fabricated as a two-dimensional layered saturable absorber with strong light-matter interaction. This MoS2-taper-fiber device is not only capable of passively mode-locking an all-normal-dispersion ytterbium-doped fiber laser and enduring high power laser excitation (up to 1 W), but also functions as a polarization sensitive optical modulating component (that is, different polarized light can induce different nonlinear optical response). Thanks to the combined advantages from the strong nonlinear optical response in MoS2 together with the sufficiently-long-range interaction between light and MoS2, this device allows for the generation of high power stable dissipative solitons at 1042.6 nm with pulse duration of 656 ps and a repetition rate of 6.74 MHz at a pump power of 210 mW. Our work may also constitute the first example of MoS2-enabled wave-guiding photonic device, and potentially give some new insights into two-dimensional layered materials related photonics. PMID:25213108

Phase-space topography characterization of nonlinear ultrasound waveforms.

PubMed

Dehghan-Niri, Ehsan; Al-Beer, Helem

2018-03-01

Fundamental understanding of ultrasound interaction with material discontinuities having closed interfaces has many engineering applications such as nondestructive evaluation of defects like kissing bonds and cracks in critical structural and mechanical components. In this paper, to analyze the acoustic field nonlinearities due to defects with closed interfaces, the use of a common technique in nonlinear physics, based on a phase-space topography construction of ultrasound waveform, is proposed. The central idea is to complement the "time" and "frequency" domain analyses with the "phase-space" domain analysis of nonlinear ultrasound waveforms. A nonlinear time series method known as pseudo phase-space topography construction is used to construct equivalent phase-space portrait of measured ultrasound waveforms. Several nonlinear models are considered to numerically simulate nonlinear ultrasound waveforms. The phase-space response of the simulated waveforms is shown to provide different topographic information, while the frequency domain shows similar spectral behavior. Thus, model classification can be substantially enhanced in the phase-space domain. Experimental results on high strength aluminum samples show that the phase-space transformation provides a unique detection and classification capabilities. The Poincaré map of the phase-space domain is also used to better understand the nonlinear behavior of ultrasound waveforms. It is shown that the analysis of ultrasound nonlinearities is more convenient and informative in the phase-space domain than in the frequency domain. Copyright © 2017 Elsevier B.V. All rights reserved.

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

DTIC Science & Technology

2015-09-30

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

Circuit transients due to negative bias arcs-II. [on solar cell power systems in low earth orbit

NASA Technical Reports Server (NTRS)

Metz, R. N.

1986-01-01

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report

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

Cai, Xiao-Chuan; Keyes, David; Yang, Chao

2014-09-29

The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementationmore » since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.« less

Polarization chaos and random bit generation in nonlinear fiber optics induced by a time-delayed counter-propagating feedback loop.

PubMed

Morosi, J; Berti, N; Akrout, A; Picozzi, A; Guasoni, M; Fatome, J

2018-01-22

In this manuscript, we experimentally and numerically investigate the chaotic dynamics of the state-of-polarization in a nonlinear optical fiber due to the cross-interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop. Thanks to the cross-polarization interaction between the two-delayed counter-propagating waves, the output polarization exhibits fast temporal chaotic dynamics, which enable a powerful scrambling process with moving speeds up to 600-krad/s. The performance of this all-optical scrambler was then evaluated on a 10-Gbit/s On/Off Keying telecom signal achieving an error-free transmission. We also describe how these temporal and chaotic polarization fluctuations can be exploited as an all-optical random number generator. To this aim, a billion-bit sequence was experimentally generated and successfully confronted to the dieharder benchmarking statistic tools. Our experimental analysis are supported by numerical simulations based on the resolution of counter-propagating coupled nonlinear propagation equations that confirm the observed behaviors.

A fluid-structure interaction model of soft robotics using an active strain approach

NASA Astrophysics Data System (ADS)

Hess, Andrew; Lin, Zhaowu; Gao, Tong

2017-11-01

Soft robotic swimmers exhibit rich dynamics that stem from the non-linear interplay of the fluid and immersed soft elastic body. Due to the difficulty of handling the nonlinear two-way coupling of hydrodynamic flow and deforming elastic body, studies of flexible swimmers often employ either one-way coupling strategies with imposed motions of the solid body or some simplified elasticity models. To explore the nonlinear dynamics of soft robots powered by smart soft materials, we develop a computational model to deal with the two-way fluid/elastic structure interactions using the fictitious domain method. To mimic the dynamic response of the functional soft material under external actuations, we assume the solid phase to be neo-Hookean, and employ an active strain approach to incorporate actuation, which is based on the multiplicative decomposition of the deformation gradient tensor. We demonstrate the capability of our algorithm by performing a series of numerical explorations that manipulate an elastic structure with finite thickness, starting from simple rectangular or circular plates to soft robot prototypes such as stingrays and jellyfish.

Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks

PubMed Central

Mangussi, Franco

2016-01-01

In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined. PMID:27648829

APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission.

PubMed

Temprana, E; Myslivets, E; Kuo, B P-P; Liu, L; Ataie, V; Alic, N; Radic, S

2015-06-26

Nonlinear optical response of silica imposes a fundamental limit on the information transfer capacity in optical fibers. Communication beyond this limit requires higher signal power and suppression of nonlinear distortions to prevent irreversible information loss. The nonlinear interaction in silica is a deterministic phenomenon that can, in principle, be completely reversed. However, attempts to remove the effects of nonlinear propagation have led to only modest improvements, and the precise physical mechanism preventing nonlinear cancellation remains unknown. We demonstrate that optical carrier stability plays a critical role in canceling Kerr-induced distortions and that nonlinear wave interaction in silica can be substantially reverted if optical carriers possess a sufficient degree of mutual coherence. These measurements indicate that fiber information capacity can be notably increased over previous estimates. Copyright © 2015, American Association for the Advancement of Science.

Uranium(IV) Interaction with Aqueous/Solid Interfaces Studied by Nonlinear Optics

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

Geiger, Franz

2015-03-27

This is the Final Technical Report for "Uranium(IV) Interaction with Aqueous/Solid Interfaces Studied by Nonlinear Optics", by Franz M. Geiger, PI, from Northwestern University, IL, USA, Grant Number SC0004101 and/or DE-PS02-ER09-07.

Coupling fluid-structure interaction with phase-field fracture

NASA Astrophysics Data System (ADS)

Wick, Thomas

2016-12-01

In this work, a concept for coupling fluid-structure interaction with brittle fracture in elasticity is proposed. The fluid-structure interaction problem is modeled in terms of the arbitrary Lagrangian-Eulerian technique and couples the isothermal, incompressible Navier-Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The brittle fracture model is based on a phase-field approach for cracks in elasticity and pressurized elastic solids. In order to derive a common framework, the phase-field approach is re-formulated in Lagrangian coordinates to combine it with fluid-structure interaction. A crack irreversibility condition, that is mathematically characterized as an inequality constraint in time, is enforced with the help of an augmented Lagrangian iteration. The resulting problem is highly nonlinear and solved with a modified Newton method (e.g., error-oriented) that specifically allows for a temporary increase of the residuals. The proposed framework is substantiated with several numerical tests. In these examples, computational stability in space and time is shown for several goal functionals, which demonstrates reliability of numerical modeling and algorithmic techniques. But also current limitations such as the necessity of using solid damping are addressed.

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

Nonlinear modeling of wave-topography interactions, shear instabilities and shear induced wave breaking using vortex method

NASA Astrophysics Data System (ADS)

Guha, Anirban

2017-11-01

Theoretical studies on linear shear instabilities as well as different kinds of wave interactions often use simple velocity and/or density profiles (e.g. constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Moreover, such simple profiles provide a minimal model to obtain a mechanistic understanding of shear instabilities. Here we have extended this minimal paradigm into nonlinear domain using vortex method. Making use of unsteady Bernoulli's equation in presence of linear shear, and extending Birkhoff-Rott equation to multiple interfaces, we have numerically simulated the interaction between multiple fully nonlinear waves. This methodology is quite general, and has allowed us to simulate diverse problems that can be essentially reduced to the minimal system with interacting waves, e.g. spilling and plunging breakers, stratified shear instabilities (Holmboe, Taylor-Caulfield, stratified Rayleigh), jet flows, and even wave-topography interaction problem like Bragg resonance. We found that the minimal models capture key nonlinear features (e.g. wave breaking features like cusp formation and roll-ups) which are observed in experiments and/or extensive simulations with smooth, realistic profiles.

A quantum description of linear, and non-linear optical interactions in arrays of plasmonic nanoparticles

NASA Astrophysics Data System (ADS)

Arabahmadi, Ehsan; Ahmadi, Zabihollah; Rashidian, Bizhan

2018-06-01

A quantum theory for describing the interaction of photons and plasmons, in one- and two-dimensional arrays is presented. Ohmic losses and inter-band transitions are not considered. We use macroscopic approach, and quantum field theory methods including S-matrix expansion, and Feynman diagrams for this purpose. Non-linear interactions are also studied, and increasing the probability of such interactions, and its application are also discussed.

Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information

NASA Astrophysics Data System (ADS)

Li, Songting; Xiao, Yanyang; Zhou, Douglas; Cai, David

2018-05-01

The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems—it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.

Relativistic laser-plasma interactions in the quantum regime.

PubMed

Eliasson, Bengt; Shukla, P K

2011-04-01

We consider nonlinear interactions between a relativistically strong laser beam and a plasma in the quantum regime. The collective behavior of electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the electromagnetic wave through the Maxwell and Poisson equations. This allows us to study nonlinear interactions between arbitrarily large-amplitude electromagnetic waves and a quantum plasma. We have used our system of nonlinear equations to study theoretically the parametric instabilities involving stimulated Raman scattering and modulational instabilities. A model for quasi-steady-state propagating electromagnetic wave packets is also derived, and which shows possibility of localized solitary structures in a quantum plasma. Numerical simulations demonstrate collapse and acceleration of electrons in the nonlinear stage of the modulational instability, as well as possibility of the wake-field acceleration of electrons to relativistic speeds by short laser pulses at nanometer length scales. Our study is relevant for understanding the localization of intense electromagnetic pulses in a quantum plasma with extremely high electron densities and relatively low temperature.

Studies of central interactions of Si ions at 14.5 x A GeV/c in Au and Cu

NASA Astrophysics Data System (ADS)

Eiseman, S. E.; Etkin, A.; Foley, K. J.; Hackenburg, R. W.; Longacre, R. S.; Love, W. A.; Morris, T. W.; Platner, E. D.; Saulys, A. C.; Lindenbaum, S. J.

Understanding the growth and saturation of parametric instabilities in laser-produced plasmas requires knowledge of the nonlinear properties of the instabilities and their interaction with each other. Nonlinear behavior of parametric instabilities, which are usually associated with unique optical features, were evidenced in numerous experiments on a variety of laser facilities. Four examples of nonlinear behavior in laser-produced plasmas are discussed: nonlinear stimulated Brillouin scattering spectra, suppression of stimulated Raman scattering by stimulated Brillouin scattering, the parametric decay instability and the onset of turbulence, and the transition to bursting behavior of the two-plasmon decay instability. Experiments are discussed that demonstrate the nonlinear effects which occur as a consequence.

Single pion production in neutrino-nucleon interactions

NASA Astrophysics Data System (ADS)

Kabirnezhad, M.

2018-01-01

This work represents an extension of the single pion production model proposed by Rein [Z. Phys. C 35, 43 (1987)., 10.1007/BF01561054]. The model consists of resonant pion production and nonresonant background contributions coming from three Born diagrams in the helicity basis. The new work includes lepton mass effects, and nonresonance interaction is described by five diagrams based on a nonlinear σ model. This work provides a full kinematic description of single pion production in the neutrino-nucleon interactions, including resonant and nonresonant interactions in the helicity basis, in order to study the interference effect.

Polyspectral signal analysis techniques for condition based maintenance of helicopter drive-train system

NASA Astrophysics Data System (ADS)

Hassan Mohammed, Mohammed Ahmed

For an efficient maintenance of a diverse fleet of air- and rotorcraft, effective condition based maintenance (CBM) must be established based on rotating components monitored vibration signals. In this dissertation, we present theory and applications of polyspectral signal processing techniques for condition monitoring of critical components in the AH-64D helicopter tail rotor drive train system. Currently available vibration-monitoring tools are mostly built around auto- and cross-power spectral analysis which have limited performance in detecting frequency correlations higher than second order. Studying higher order correlations and their Fourier transforms, higher order spectra, provides more information about the vibration signals which helps in building more accurate diagnostic models of the mechanical system. Based on higher order spectral analysis, different signal processing techniques are developed to assess health conditions of different critical rotating-components in the AH-64D helicopter drive-train. Based on cross-bispectrum, quadratic nonlinear transfer function is presented to model second order nonlinearity in a drive-shaft running between the two hanger bearings. Then, quadratic-nonlinearity coupling coefficient between frequency harmonics of the rotating shaft is used as condition metric to study different seeded shaft faults compared to baseline case, namely: shaft misalignment, shaft imbalance, and combination of shaft misalignment and imbalance. The proposed quadratic-nonlinearity metric shows better capabilities in distinguishing the four studied shaft settings than the conventional linear coupling based on cross-power spectrum. We also develop a new concept of Quadratic-Nonlinearity Power-Index spectrum, QNLPI(f), that can be used in signal detection and classification, based on bicoherence spectrum. The proposed QNLPI(f) is derived as a projection of the three-dimensional bicoherence spectrum into two-dimensional spectrum that quantitatively describes how much of the mean square power at certain frequency f is generated due to nonlinear quadratic interaction between different frequency components. The proposed index, QNLPI(f), can be used to simplify the study of bispectrum and bicoherence signal spectra. It also inherits useful characteristics from the bicoherence such as high immunity to additive Gaussian noise, high capability of nonlinear-systems identifications, and amplification invariance. The quadratic-nonlinear power spectral density PQNL(f) and percentage of quadratic nonlinear power PQNLP are also introduced based on the QNLPI(f). Concept of the proposed indices and their computational considerations are discussed first using computer generated data, and then applied to real-world vibration data to assess health conditions of different rotating components in the drive train including drive-shaft, gearbox, and hanger bearing faults. The QNLPI(f) spectrum enables us to gain more details about nonlinear harmonic generation patterns that can be used to distinguish between different cases of mechanical faults, which in turn helps to gaining more diagnostic/prognostic capabilities.

The existence of electron-acoustic shock waves and their interactions in a non-Maxwellian plasma with q-nonextensive distributed electrons

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

Han, Jiu-Ning; He, Yong-Lin; Han, Zhen-Hai

2013-07-15

We present a theoretical investigation for the nonlinear interaction between electron-acoustic shock waves in a nonextensive two-electron plasma. The interaction is governed by a pair of Korteweg-de Vries-Burgers equations. We focus on studying the colliding effects on the propagation of shock waves, more specifically, we have studied the effects of plasma parameters, i.e., the nonextensive parameter q, the “hot” to “cold” electron number density ratio α, and the normalized electron kinematic viscosity η{sub 0} on the trajectory changes (phase shifts) of shock waves. It is found that there are trajectory changes (phase shifts) for both colliding shock waves in themore » present plasma system. We also noted that the nonlinearity has no decisive effect on the trajectory changes, the occurrence of trajectory changes may be due to the combined role played by the dispersion and dissipation of the nonlinear structure. Our theoretical study may be beneficial to understand the propagation and interaction of nonlinear electrostatic waves and may brings a possibility to develop the nonlinear theory of electron-acoustic waves in astrophysical plasma systems.« less

Enhancing light-atom interactions via atomic bunching

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie L.; Gauthier, Daniel J.

2014-07-01

There is a broad interest in enhancing the strength of light-atom interactions to the point where injecting a single photon induces a nonlinear material response. Here we show theoretically that sub-Doppler-cooled two-level atoms that are spatially organized by weak optical fields give rise to a nonlinear material response that is greatly enhanced beyond that attainable in a homogeneous gas. Specifically, in the regime where the intensity of the applied optical fields is much less than the off-resonance saturation intensity, we show that the third-order nonlinear susceptibility scales inversely with atomic temperature and, due to this scaling, can be two orders of magnitude larger than that of a homogeneous gas for typical experimental parameters. As a result, we predict that spatially bunched two-level atoms can exhibit single-photon nonlinearities. Our model is valid for all regimes of atomic bunching and simultaneously accounts for the backaction of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only limited regimes of atomic bunching. For lattice beams tuned to the low-frequency side of the atomic transition, we find that the nonlinearity transitions from a self-focusing type to a self-defocusing type at a critical intensity. We also show that higher than third-order nonlinear optical susceptibilities are significant in the regime where the dipole potential energy is on the order of the atomic thermal energy. We therefore find that it is crucial to retain high-order nonlinearities to accurately predict interactions of laser fields with spatially organized ultracold atoms. The model presented here is a foundation for modeling low-light-level nonlinear optical processes for ultracold atoms in optical lattices.

Calibrating Nonlinear Soil Material Properties for Seismic Analysis Using Soil Material Properties Intended for Linear Analysis

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

Spears, Robert Edward; Coleman, Justin Leigh

2015-08-01

Seismic analysis of nuclear structures is routinely performed using guidance provided in “Seismic Analysis of Safety-Related Nuclear Structures and Commentary (ASCE 4, 1998).” This document, which is currently under revision, provides detailed guidance on linear seismic soil-structure-interaction (SSI) analysis of nuclear structures. To accommodate the linear analysis, soil material properties are typically developed as shear modulus and damping ratio versus cyclic shear strain amplitude. A new Appendix in ASCE 4-2014 (draft) is being added to provide guidance for nonlinear time domain SSI analysis. To accommodate the nonlinear analysis, a more appropriate form of the soil material properties includes shear stressmore » and energy absorbed per cycle versus shear strain. Ideally, nonlinear soil model material properties would be established with soil testing appropriate for the nonlinear constitutive model being used. However, much of the soil testing done for SSI analysis is performed for use with linear analysis techniques. Consequently, a method is described in this paper that uses soil test data intended for linear analysis to develop nonlinear soil material properties. To produce nonlinear material properties that are equivalent to the linear material properties, the linear and nonlinear model hysteresis loops are considered. For equivalent material properties, the shear stress at peak shear strain and energy absorbed per cycle should match when comparing the linear and nonlinear model hysteresis loops. Consequently, nonlinear material properties are selected based on these criteria.« less

Unilateral contact induced blade/casing vibratory interactions in impellers: Analysis for rigid casings

NASA Astrophysics Data System (ADS)

Batailly, Alain; Meingast, Markus; Legrand, Mathias

2015-02-01

This contribution addresses the vibratory analysis of unilateral-contact induced structural interactions between a bladed impeller and its surrounding rigid casing. Such assemblies can be found in helicopter or small aircraft engines for instance and the interactions of interest shall arise due to the always tighter operating clearances between the rotating and stationary components. The investigation is conducted by extending to cyclically symmetric structures an in-house time-marching based tool dedicated to unilateral contact occurrences in turbomachines. The main components of the considered impeller together with the associated assumptions and modelling principles considered in this work are detailed. Typical dynamical features of cyclically symmetric structures, such as the aliasing effect and frequency clustering are explored in this nonlinear framework by means of thorough frequency-domain analyses and harmonic trackings of the numerically predicted impeller displacements. Additional contact maps highlight the existence of critical rotational velocities at which displacements potentially reach high amplitudes due to the synchronization of the bladed assembly vibratory pattern with the shape of the rigid casing. The proposed numerical investigations are also compared to a simpler and (almost) empirical criterion: it is suggested, based on nonlinear numerical simulations with a linear reduced order model of the impeller and a rigid casing, that this criterion may miss important critical velocities emanating from the unfavorable combination of aliasing and contact-induced higher harmonics in the vibratory response of the impeller. Overall, this work suggests a way to enhance guidelines to improve the design of impellers in the context of nonlinear and nonsmooth dynamics.

Persistence and long-term memories of daily maximum and minimum temperatures in southern South America

NASA Astrophysics Data System (ADS)

Naumann, Gustavo; Vargas, Walter M.; Minetti, Juan L.

2011-10-01

The persistence and long-term memories in daily maximum and minimum temperature series during the instrumental period in southern South America were analysed. Here, we found a markedly seasonal pattern both for short- and long-term memories that can lead to enhanced predictability on intraseasonal timescales. In addition, well-defined spatial patterns of these properties were found in the region. Throughout the entire region, the strongest dependence was observed in autumn and early winter. In the Patagonia region only, the temperatures exhibited more memory during the spring. In general, these elements indicate that nonlinear interactions exist between the annual cycles of temperature and its anomalies. Knowledge of the spatiotemporal behaviour of these long-term memories can be used in the building of stochastic models that only use persistence. It is possible to propose two objective forecast models based on linear interactions associated with persistence and one that allows for the use of information from nonlinear interactions that are manifested in the form of forerunners.

First report of resonant interactions between whistler mode waves in the Earth's magnetosphere

NASA Astrophysics Data System (ADS)

Gao, Xinliang; Lu, Quanming; Wang, Shui

2017-06-01

Nonlinear physics related to whistler mode waves in the Earth's magnetosphere are now becoming a hot topic. In this letter, based on Time History of Events and Macroscale Interactions during Substorms waveform data, we report several interesting whistler mode wave events, where the upper band whistler mode waves are believed to be generated through the nonlinear wave-wave coupling between two lower band waves. This is the first report on resonant interactions between whistler mode waves in the Earth's magnetosphere. In these events, the two lower band whistler mode waves are observed to have oppositely propagating directions, while the generated upper band wave has the same propagating direction as the lower band wave with the relatively higher frequency. Moreover, the wave normal angle of the excited upper band wave is usually larger than those of two lower band whistler mode waves. Our results reveal the large diversity of the evolution of whistler mode waves in the Earth's magnetosphere.

A Workflow for Global Sensitivity Analysis of PBPK Models

PubMed Central

McNally, Kevin; Cotton, Richard; Loizou, George D.

2011-01-01

Physiologically based pharmacokinetic (PBPK) models have a potentially significant role in the development of a reliable predictive toxicity testing strategy. The structure of PBPK models are ideal frameworks into which disparate in vitro and in vivo data can be integrated and utilized to translate information generated, using alternative to animal measures of toxicity and human biological monitoring data, into plausible corresponding exposures. However, these models invariably include the description of well known non-linear biological processes such as, enzyme saturation and interactions between parameters such as, organ mass and body mass. Therefore, an appropriate sensitivity analysis (SA) technique is required which can quantify the influences associated with individual parameters, interactions between parameters and any non-linear processes. In this report we have defined the elements of a workflow for SA of PBPK models that is computationally feasible, accounts for interactions between parameters, and can be displayed in the form of a bar chart and cumulative sum line (Lowry plot), which we believe is intuitive and appropriate for toxicologists, risk assessors, and regulators. PMID:21772819

On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

NASA Technical Reports Server (NTRS)

Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Huang; Peng, Chung Kang;

On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data

PubMed Central

Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Hung; Peng, Chung Kang; Meijer, Johanna H.; Wang, Yung-Hung; Long, Steven R.; Wu, Zhauhua

2016-01-01

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time–frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities. PMID:26953180

Transfer of dipolar gas through the discrete localized mode.

PubMed

Bai, Xiao-Dong; Zhang, Ai-Xia; Xue, Ju-Kui

2013-12-01

By considering the discrete nonlinear Schrödinger model with dipole-dipole interactions for dipolar condensate, the existence, the types, the stability, and the dynamics of the localized modes in a nonlinear lattice are discussed. It is found that the contact interaction and the dipole-dipole interactions play important roles in determining the existence, the type, and the stability of the localized modes. Because of the coupled effects of the contact interaction and the dipole-dipole interactions, rich localized modes and their stability nature can exist: when the contact interaction is larger and the dipole-dipole interactions is smaller, a discrete bright breather occurs. In this case, while the on-site interaction can stabilize the discrete breather, the dipole-dipole interactions will destabilize the discrete breather; when both the contact interaction and the dipole-dipole interactions are larger, a discrete kink appears. In this case, both the on-site interaction and the dipole-dipole interactions can stabilize the discrete kink, but the discrete kink is more unstable than the ordinary discrete breather. The predicted results provide a deep insight into the dynamics of blocking, filtering, and transfer of the norm in nonlinear lattices for dipolar condensates.

Experimental and numerical investigations of temporally and spatially periodic modulated wave trains

NASA Astrophysics Data System (ADS)

Houtani, H.; Waseda, T.; Tanizawa, K.

2018-03-01

A number of studies on steep nonlinear waves were conducted experimentally with the temporally periodic and spatially evolving (TPSE) wave trains and numerically with the spatially periodic and temporally evolving (SPTE) ones. The present study revealed that, in the vicinity of their maximum crest height, the wave profiles of TPSE and SPTE modulated wave trains resemble each other. From the investigation of the Akhmediev-breather solution of the nonlinear Schrödinger equation (NLSE), it is revealed that the dispersion relation deviated from the quadratic dependence of frequency on wavenumber and became linearly dependent instead. Accordingly, the wave profiles of TPSE and SPTE breathers agree. The range of this agreement is within the order of one wave group of the maximum crest height and persists during the long-term evolution. The findings extend well beyond the NLSE regime and can be applied to modulated wave trains that are highly nonlinear and broad-banded. This was demonstrated from the numerical wave tank simulations with a fully nonlinear potential flow solver based on the boundary element method, in combination with the nonlinear wave generation method based on the prior simulation with the higher-order spectral model. The numerical wave tank results were confirmed experimentally in a physical wave tank. The findings of this study unravel the fundamental nature of the nonlinear wave evolution. The deviation of the dispersion relation of the modulated wave trains occurs because of the nonlinear phase variation due to quasi-resonant interaction, and consequently, the wave geometry of temporally and spatially periodic modulated wave trains coincides.

Digital backpropagation accounting for polarization-mode dispersion.

PubMed

Czegledi, Cristian B; Liga, Gabriele; Lavery, Domaniç; Karlsson, Magnus; Agrell, Erik; Savory, Seb J; Bayvel, Polina

2017-02-06

Digital backpropagation (DBP) is a promising digital-domain technique to mitigate Kerr-induced nonlinear interference. While it successfully removes deterministic signal-signal interactions, the performance of ideal DBP is limited by stochastic effects, such as polarization-mode dispersion (PMD). In this paper, we consider an ideal full-field DBP implementation and modify it to additionally account for PMD; reversing the PMD effects in the backward propagation by passing the reverse propagated signal also through PMD sections, which concatenated equal the inverse of the PMD in the forward propagation. These PMD sections are calculated analytically at the receiver based on the total accumulated PMD of the link estimated from channel equalizers. Numerical simulations show that, accounting for nonlinear polarization-related interactions in the modified DBP algorithm, additional signal-to-noise ratio gains of 1.1 dB are obtained for transmission over 1000 km.

Nonlinear complexity behaviors of agent-based 3D Potts financial dynamics with random environments

NASA Astrophysics Data System (ADS)

Xing, Yani; Wang, Jun

2018-02-01

A new microscopic 3D Potts interaction financial price model is established in this work, to investigate the nonlinear complexity behaviors of stock markets. 3D Potts model, which extends the 2D Potts model to three-dimensional, is a cubic lattice model to explain the interaction behavior among the agents. In order to explore the complexity of real financial markets and the 3D Potts financial model, a new random coarse-grained Lempel-Ziv complexity is proposed to certain series, such as the price returns, the price volatilities, and the random time d-returns. Then the composite multiscale entropy (CMSE) method is applied to the intrinsic mode functions (IMFs) and the corresponding shuffled data to study the complexity behaviors. The empirical results indicate that the 3D financial model is feasible.

Modelization of highly nonlinear waves in coastal regions

NASA Astrophysics Data System (ADS)

Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre

2015-04-01

The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.

A Lattice-Boltzmann model to simulate diffractive nonlinear ultrasound beam propagation in a dissipative fluid medium

NASA Astrophysics Data System (ADS)

Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan

2012-12-01

Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.

Controlling modal interactions in lasers for frequency selection and power enhancement

NASA Astrophysics Data System (ADS)

Ge, Li

2015-03-01

The laser is an out-of-equilibrium non-linear wave system where the interplay of the cavity geometry and non-linear wave interactions determines the self-organized oscillation frequencies and the associated spatial field patterns. Using the correspondence between nonlinear and linear systems, we propose a simple and systematic method to achieve selective excitation of lasing modes that would have been dwarfed by more dominant ones. The key idea is incorporating the control of modal interaction into the spatial pump profile. Our proposal is most valuable in the regime of spatially and spectrally overlapping modes, which can lead to a significant enhancement of laser power as well.

A Web Tool for Research in Nonlinear Optics

NASA Astrophysics Data System (ADS)

Prikhod'ko, Nikolay V.; Abramovsky, Viktor A.; Abramovskaya, Natalia V.; Demichev, Andrey P.; Kryukov, Alexandr P.; Polyakov, Stanislav P.

2016-02-01

This paper presents a project of developing the web platform called WebNLO for computer modeling of nonlinear optics phenomena. We discuss a general scheme of the platform and a model for interaction between the platform modules. The platform is built as a set of interacting RESTful web services (SaaS approach). Users can interact with the platform through a web browser or command line interface. Such a resource has no analogues in the field of nonlinear optics and will be created for the first time therefore allowing researchers to access high-performance computing resources that will significantly reduce the cost of the research and development process.

Vortex-induced vibrations mitigation through a nonlinear energy sink

NASA Astrophysics Data System (ADS)

Dai, H. L.; Abdelkefi, A.; Wang, L.

2017-01-01

The passive suppression mechanism of the vortex-induced vibrations (VIV) of the cylinder by means of an essentially nonlinear element, the nonlinear energy sink (NES) is investigated. The flow-induced loads on the cylinder are modeled using a prevalent van der Pol oscillator which is experimentally validated, coupling to the structural vibrations in the presence of the NES structure. Based on the coupled nonlinear governing equations of motion, the performed analysis indicates that the mass and damping of NES have significant effects on the coupled frequency and damping of the aero-elastic system, leading to the shift of synchronization region and mitigation of vibration responses. It is demonstrated that the coupled system of flow-cylinder-NES behaves resonant interactions, showing periodic, aperiodic, and multiple stable responses which depend on the values of the NES parameters. In addition, it is found that the occurrence of multiple stable responses can enhance the nonlinear energy pumping effect, resulting in the increment of transferring energy from the flow via the cylinder to the NES, which is related to the essential nonlinearity of the sink stiffness. This results in a significant reduction in the VIV amplitudes of the primary circular cylinder for appropriate NES parameter values.

Features of the Paired Soliton Interactions Within the Framework of the Gardner Equation

NASA Astrophysics Data System (ADS)

Shurgalina, E. G.

2018-02-01

We study the dynamics of the two-soliton interaction within the framework of a completely integrable model, namely, the Gardner equation with negative cubic nonlinearity, which admits the existence of a limiting soliton. The features of the soliton interaction with participation of a thick soliton are demonstrated. Special attention is paid to the nonlinear-interaction influence on the wave-field moments, which determine the skewness and the kurtosis in the theory of turbulence.

Problems in nonlinear acoustics: Pulsed finite amplitude sound beams, nonlinear acoustic wave propagation in a liquid layer, nonlinear effects in asymmetric cylindrical sound beams, effects of absorption on the interaction of sound beams, and parametric receiving arrays

NASA Astrophysics Data System (ADS)

Hamilton, Mark F.

1990-12-01

This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.

Nonlinear Internal Wave Interaction in the China Seas

NASA Technical Reports Server (NTRS)

Liu, Antony K.; Hsu, Ming-K.

1998-01-01

This project researched the nonlinear wave interactions in the East China Sea, and the South China Sea, using Synthetic Aperture Radar (SAR) images. The complicated nature of the internal wave field, including the generation mechanisms, was studied, and is discussed. Discussion of wave-wave interactions in the East China Sea, the area of the China Sea northeast of Taiwan, and the Yellow Sea is included.

Spectra of Baroclinic Inertia-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, Roman E.

1996-01-01

Baroclinic inertia-gravity (IG) waves form a persistent background of thermocline depth and sea surface height oscillations. They also contribute to the kinetic energy of horizontal motions in the subsurface layer. Measured by the ratio of water particle velocity to wave phase speed, the wave nonlinearity may be rather high. Given a continuous supply of energy from external sources, nonlinear wave-wave interactions among IG waves would result in inertial cascades of energy, momentum, and wave action. Based on a recently developed theory of wave turbulence in scale-dependent systems, these cascades are investigated and IG wave spectra are derived for an arbitrary degree of wave nonlinearity. Comparisons with satellite-altimetry-based spectra of surface height variations and with energy spectra of horizontal velocity fluctuations show good agreement. The well-known spectral peak at the inertial frequency is thus explained as a result of the inverse cascade. Finally, we discuss a possibility of inferring the internal Rossby radius of deformation and other dynamical properties of the upper thermocline from the spectra of SSH (sea surface height) variations based on altimeter measurements.

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.

Resonant Triad in Boundary-Layer Stability. Part 2; Composite Solution and Comparison with Observations

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

All-optical tunable dual Fano resonance in nonlinear metamaterials in optical communication range

NASA Astrophysics Data System (ADS)

Zhou, Yi; Hu, Xiaoyong; Li, Chong; Yang, Hong; Gong, Qihuang

2018-01-01

Low-power, ultra-fast all-optical tunable dual Fano resonance was realized in a metamaterial coated with a non-linear nanocomposite layer composed of gold nanoparticle-doped polycrystalline barium strontium titanate and multilayer tungsten disulphide microsheets. A high non-linear refractive index of -2.148 × 10-11 m2/W was achieved in the nanocomposite material that originated in the non-linearity enhancement associated with the quantum confinement effect, the local-field enhancement effect, and reinforced interactions between photons and the multilayer tungsten disulphide microsheets. An ultra-low threshold pump intensity of 600 kW/cm2 was obtained. An ultra-fast response time of 25.4 ps was maintained because of the fast relaxation dynamics of the bound electrons in the nanoscale polycrystalline barium strontium titanate grains. The large third-order non-linear responses of the metamaterial were confirmed with a high third harmonic generation conversion efficiency of 5.4 × 10-5. This work may help to pave the way towards realization of ultra-high-speed information processing chips and multifunctional integrated photonic devices based on metamaterials.

Adaptive Fault-Tolerant Control of Uncertain Nonlinear Large-Scale Systems With Unknown Dead Zone.

PubMed

Chen, Mou; Tao, Gang

2016-08-01

In this paper, an adaptive neural fault-tolerant control scheme is proposed and analyzed for a class of uncertain nonlinear large-scale systems with unknown dead zone and external disturbances. To tackle the unknown nonlinear interaction functions in the large-scale system, the radial basis function neural network (RBFNN) is employed to approximate them. To further handle the unknown approximation errors and the effects of the unknown dead zone and external disturbances, integrated as the compounded disturbances, the corresponding disturbance observers are developed for their estimations. Based on the outputs of the RBFNN and the disturbance observer, the adaptive neural fault-tolerant control scheme is designed for uncertain nonlinear large-scale systems by using a decentralized backstepping technique. The closed-loop stability of the adaptive control system is rigorously proved via Lyapunov analysis and the satisfactory tracking performance is achieved under the integrated effects of unknown dead zone, actuator fault, and unknown external disturbances. Simulation results of a mass-spring-damper system are given to illustrate the effectiveness of the proposed adaptive neural fault-tolerant control scheme for uncertain nonlinear large-scale systems.

Modifying patch-scale connectivity to initiate landscape change: An experimental approach to link scale

USDA-ARS?s Scientific Manuscript database

Nonlinear interactions and feedbacks across spatial and temporal scales are common features of biological and physical systems. These emergent behaviors often result in surprises that challenge the ability of scientists to understand and predict system behavior at one scale based on information at f...

An Anisotropic Multiphysics Model for Intervertebral Disk

PubMed Central

Gao, Xin; Zhu, Qiaoqiao; Gu, Weiyong

2016-01-01

Intervertebral disk (IVD) is the largest avascular structure in human body, consisting of three types of charged hydrated soft tissues. Its mechanical behavior is nonlinear and anisotropic, due mainly to nonlinear interactions among different constituents within tissues. In this study, a more realistic anisotropic multiphysics model was developed based on the continuum mixture theory and employed to characterize the couplings of multiple physical fields in the IVD. Numerical simulations demonstrate that this model is capable of systematically predicting the mechanical and electrochemical signals within the disk under various loading conditions, which is essential in understanding the mechanobiology of IVD. PMID:27099402

Cardiovascular oscillations: in search of a nonlinear parametric model

NASA Astrophysics Data System (ADS)

Bandrivskyy, Andriy; Luchinsky, Dmitry; McClintock, Peter V.; Smelyanskiy, Vadim; Stefanovska, Aneta; Timucin, Dogan

2003-05-01

We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.

Nonlinear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.

1972-01-01

Two particular cases of nonlinear wave interaction in a plasma column were investigated. The frequencies of the waves were on the order of magnitude of the electron plasma frequency, and ion motion was neglected. The nonlinear coupling of slow waves on a plasma column was studied by means of cold plasma theory, and the case of a plasma column surrounded by an infinite dielectric in the absence of a magnetic field was also examined. Nonlinear scattering from a plasma column in an electromagnetic field having it's magnetic field parallel to the axis of the column was investigated. Some experimental results on mode conversion in the presence of loss are presented along with some observations of nonlinear scattering, The effect of the earth's magnetic field and of discharge symmetry on the radiation pattern are discussed.

Bright-dark and dark-dark solitons for the coupled cubic-quintic nonlinear Schrödinger equations in a twin-core nonlinear optical fiber

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Liu, Lei; Chai, Han-Peng

2017-11-01

In this paper, we investigate the coupled cubic-quintic nonlinear Schrödinger equations, which can describe the effects of quintic nonlinearity on the ultrashort optical soliton pulse propagation in a twin-core nonlinear optical fiber. Through the Kadomtsev-Petviashvili hierarchy reduction, we present the bright-dark and dark-dark soliton solutions in terms of the Grammian for such equations. With the help of analytic and graphic analysis, head-on and overtaking elastic interactions between the two solitons are presented, as well as the bound-state solitons. Particularly, we find the inelastic interaction between the bright-dark two solitons. One of the electromagnetic fields presents the V-shape profile, while the other one presents the Y-shape profile.

Current interactions from the one-form sector of nonlinear higher-spin equations

NASA Astrophysics Data System (ADS)

Gelfond, O. A.; Vasiliev, M. A.

2018-06-01

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp ⁡ iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.

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.

Threshold effect under nonlinear limitation of the intensity of high-power light

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

Tereshchenko, S A; Podgaetskii, V M; Gerasimenko, A Yu

2015-04-30

A model is proposed to describe the properties of limiters of high-power laser radiation, which takes into account the threshold character of nonlinear interaction of radiation with the working medium of the limiter. The generally accepted non-threshold model is a particular case of the threshold model if the threshold radiation intensity is zero. Experimental z-scan data are used to determine the nonlinear optical characteristics of media with carbon nanotubes, polymethine and pyran dyes, zinc selenide, porphyrin-graphene and fullerene-graphene. A threshold effect of nonlinear interaction between laser radiation and some of investigated working media of limiters is revealed. It is shownmore » that the threshold model more adequately describes experimental z-scan data. (nonlinear optical phenomena)« less

On the tidal interaction between protoplanets and the primordial solar nebula. II - Self-consistent nonlinear interaction

NASA Technical Reports Server (NTRS)

Lin, D. N. C.; Papaloizou, J.

1986-01-01

A method to analyze the full nonlinear response and physical processes associated with the tidal interaction between a binary system and a thin disk in the steady state is presented. Using this approach, density wave propagation, induced by tidal interaction, may be studied for a wide range of sound speeds and viscosities. The effect of self-gravity may also be incorporated. The results of several calculations relevant to the tidal interaction between a protoplanet and the primordial solar nebula are also presented.

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.

Enhancement of laser power-efficiency by control of spatial hole burning interactions

NASA Astrophysics Data System (ADS)

Ge, Li; Malik, Omer; Türeci, Hakan E.

2014-11-01

The laser is an out-of-equilibrium nonlinear wave system where the interplay of the cavity geometry and nonlinear wave interactions mediated by the gain medium determines the self-organized oscillation frequencies and the associated spatial field patterns. In the steady state, a constant energy flux flows through the laser from the pump to the far field, with the ratio of the total output power to the input power determining the power-efficiency. Although nonlinear wave interactions have been modelled and well understood since the early days of laser theory, their impact on the power-efficiency of a laser system is poorly understood. Here, we show that spatial hole burning interactions generally decrease the power-efficiency. We then demonstrate how spatial hole burning interactions can be controlled by a spatially tailored pump profile, thereby boosting the power-efficiency, in some cases by orders of magnitude.

Non-destructive testing techniques based on nonlinear methods for assessment of debonding in single lap joints

NASA Astrophysics Data System (ADS)

Scarselli, G.; Ciampa, F.; Ginzburg, D.; Meo, M.

2015-04-01

Nonlinear ultrasonic non-destructive evaluation (NDE) methods can be used for the identification of defects within adhesive bonds as they rely on the detection of nonlinear elastic features for the evaluation of the bond strength. In this paper the nonlinear content of the structural response of a single lap joint subjected to ultrasonic harmonic excitation is both numerically and experimentally evaluated to identify and characterize the defects within the bonded region. Different metallic samples with the same geometry were experimentally tested in order to characterize the debonding between two plates by using two surface bonded piezoelectric transducers in pitch-catch mode. The dynamic response of the damaged samples acquired by the single receiver sensor showed the presence of higher harmonics (2nd and 3rd) and subharmonics of the fundamental frequencies. These nonlinear elastic phenomena are clearly due to nonlinear effects induced by the poor adhesion between the two plates. A new constitutive model aimed at representing the nonlinear material response generated by the interaction of the ultrasonic waves with the adhesive joint is also presented. Such a model is implemented in an explicit FE software and uses a nonlinear user defined traction-displacement relationship implemented by means of a cohesive material user model interface. The developed model is verified for the different geometrical and material configurations. Good agreement between the experimental and numerical nonlinear response showed that this model can be used as a simple and useful tool for understanding the quality of the adhesive joint.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Numerical Simulation of the Interaction of a Vortex with Stationary Airfoil in Transonic Flow,

DTIC Science & Technology

1984-01-12

Goorjian, P. M., "Implicit Vortex Wakes ," AIAA Journal, Vol. 15, No. 4, April Finite- Difference Computations of Unsteady Transonic 1977, pp. 581-590... Difference Simulations of Three- tion of Wing- Vortex Interaction in Transonic Flow Dimensional Flow," AIAA Journal, Vol. 18, No. 2, Using Implicit...assumptions are made in p = density modeling the nonlinear vortex wake structure. Numerical algorithms based on the Euler equations p_ = free stream density

Nonlinear spin current generation in noncentrosymmetric spin-orbit coupled systems

NASA Astrophysics Data System (ADS)

Hamamoto, Keita; Ezawa, Motohiko; Kim, Kun Woo; Morimoto, Takahiro; Nagaosa, Naoto

2017-06-01

Spin current plays a central role in spintronics. In particular, finding more efficient ways to generate spin current has been an important issue and has been studied actively. For example, representative methods of spin-current generation include spin-polarized current injections from ferromagnetic metals, the spin Hall effect, and the spin battery. Here, we theoretically propose a mechanism of spin-current generation based on nonlinear phenomena. By using Boltzmann transport theory, we show that a simple application of the electric field E induces spin current proportional to E2 in noncentrosymmetric spin-orbit coupled systems. We demonstrate that the nonlinear spin current of the proposed mechanism is supported in the surface state of three-dimensional topological insulators and two-dimensional semiconductors with the Rashba and/or Dresselhaus interaction. In the latter case, the angular dependence of the nonlinear spin current can be manipulated by the direction of the electric field and by the ratio of the Rashba and Dresselhaus interactions. We find that the magnitude of the spin current largely exceeds those in the previous methods for a reasonable magnitude of the electric field. Furthermore, we show that application of ac electric fields (e.g., terahertz light) leads to the rectifying effect of the spin current, where dc spin current is generated. These findings will pave a route to manipulate the spin current in noncentrosymmetric crystals.

Azimuthal hotwire measurements in a transitional boundary layer on a flared cone in a Mach 6 quiet wind tunnel

NASA Astrophysics Data System (ADS)

Hofferth, Jerrod; Saric, William

2012-11-01

Hotwire measurements of second-mode instability waves and the early stages of nonlinear interaction are conducted on a sharp-tipped, 5°-half-angle flared cone at zero angle of attack in a low-disturbance Mach 6 wind tunnel at Re = 10 ×106 m-1. Profiles of mean and fluctuating mass flux are acquired at several axial stations along the cone with a bandwidth of over 300 kHz. Frequencies and relative amplitude growth of second-mode instability waves are characterized and compared with nonlinear parabolized stability (NPSE) computations. Additionally, an azimuthal probe-traversing mechanism is used to investigate the character of the nonlinear stages of transition occurring near the base of the cone. Recent Direct Numerical Simulations (DNS) of a sharp cone at Mach 6 have shown that a fundamental resonance (or Klebanoff-type) breakdown mechanism can arise in the late stages of transition, wherein a pair of oblique waves nonlinearly interacts with the dominant two-dimensional wave to create an azimuthal modulation in the form of Λ-vortex structures and streamwise streaks. The azimuthal measurements will identify periodicity qualitatively consistent with these computations and with ``hot streaks'' observed in temperature sensitive paints at Purdue. AFOSR/NASA National Center for Hypersonic Laminar-Turbulent Transition Research, Grant FA9550-09-1-0341.

Investigating the interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance

NASA Technical Reports Server (NTRS)

Van Dongen, Hans P A.; Dinges, David F.

2003-01-01

The two-process model of sleep regulation has been applied successfully to describe, predict, and understand sleep-wake regulation in a variety of experimental protocols such as sleep deprivation and forced desynchrony. A non-linear interaction between the homeostatic and circadian processes was reported when the model was applied to describe alertness and performance data obtained during forced desynchrony. This non-linear interaction could also be due to intrinsic non-linearity in the metrics used to measure alertness and performance, however. Distinguishing these possibilities would be of theoretical interest, but could also have important implications for the design and interpretation of experiments placing sleep at different circadian phases or varying the duration of sleep and/or wakefulness. Although to date no resolution to this controversy has been found, here we show that the issue can be addressed with existing data sets. The interaction between the homeostatic and circadian processes of sleep-wake regulation was investigated using neurobehavioural performance data from a laboratory experiment involving total sleep deprivation. The results provided evidence of an actual non-linear interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance.

Nonlinear interactions and their scaling in the logarithmic region of turbulent channels

NASA Astrophysics Data System (ADS)

Moarref, Rashad; Sharma, Ati S.; Tropp, Joel A.; McKeon, Beverley J.

2014-11-01

The nonlinear interactions in wall turbulence redistribute the turbulent kinetic energy across different scales and different wall-normal locations. To better understand these interactions in the logarithmic region of turbulent channels, we decompose the velocity into a weighted sum of resolvent modes (McKeon & Sharma, J. Fluid Mech., 2010). The resolvent modes represent the linear amplification mechanisms in the Navier-Stokes equations (NSE) and the weights represent the scaling influence of the nonlinearity. An explicit equation for the unknown weights is obtained by projecting the NSE onto the known resolvent modes (McKeon et al., Phys. Fluids, 2013). The weights of triad modes -the modes that directly interact via the quadratic nonlinearity in the NSE- are coupled via interaction coefficients that depend solely on the resolvent modes. We use the hierarchies of self-similar modes in the logarithmic region (Moarref et al., J. Fluid Mech., 2013) to extend the notion of triad modes to triad hierarchies. It is shown that the interaction coefficients for the triad modes that belong to a triad hierarchy follow an exponential function. These scalings can be used to better understand the interaction of flow structures in the logarithmic region and develop analytical results therein. The support of Air Force Office of Scientific Research under Grants FA 9550-09-1-0701 (P.M. Rengasamy Ponnappan) and FA 9550-12-1-0469 (P.M. Doug Smith) is gratefully acknowledged.

MoS2 /Carbon Nanotube Core-Shell Nanocomposites for Enhanced Nonlinear Optical Performance.

PubMed

Zhang, Xiaoyan; Selkirk, Andrew; Zhang, Saifeng; Huang, Jiawei; Li, Yuanxin; Xie, Yafeng; Dong, Ningning; Cui, Yun; Zhang, Long; Blau, Werner J; Wang, Jun

2017-03-08

Nanocomposites of layered MoS 2 and multi-walled carbon nanotubes (CNTs) with core-shell structure were prepared by a simple solvothermal method. The formation of MoS 2 nanosheets on the surface of coaxial CNTs has been confirmed by scanning electron microscopy, transmission electron microscopy, absorption spectrum, Raman spectroscopy, and X-ray photoelectron spectroscopy. Enhanced third-order nonlinear optical performances were observed for both femtosecond and nanosecond laser pulses over a broad wavelength range from the visible to the near infrared, compared to those of MoS 2 and CNTs alone. The enhancement can be ascribed to the strong coupling effect and the photoinduced charge transfer between MoS 2 and CNTs. This work affords an efficient way to fabricate novel CNTs based nanocomposites for enhanced nonlinear light-matter interaction. The versatile nonlinear properties imply a huge potential of the nanocomposites in the development of nanophotonic devices, such as mode-lockers, optical limiters, or optical switches. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.

PubMed

Mei, Jie; Ren, Wei; Li, Bing; Ma, Guangfu

2015-09-01

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Second order harmonic guided wave mutual interactions in plate: Vector analysis, numerical simulation, and experimental results

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2017-08-01

The extraordinary sensitivity of nonlinear ultrasonic waves to the early stages of material degradation makes them excellent candidates for nondestructive material characterization. However, distinguishing weak material nonlinearity from instrumentation nonlinearity remains problematic for second harmonic generation approaches. A solution to this problem is to mix waves having different frequencies and to let their mutual interaction generate sum and difference harmonics at frequencies far from those of the instrumentation. Mixing of bulk waves and surface waves has been researched for some time, but mixing of guided waves has not yet been investigated in depth. A unique aspect of guided waves is their dispersive nature, which means we need to assure that a wave can propagate at the sum or difference frequency. A wave vector analysis is conducted that enables selection of primary waves traveling in any direction that generate phase matched secondary waves. We have tabulated many sets of primary waves and phase matched sum and difference harmonics. An example wave mode triplet of two counter-propagating collinear shear horizontal waves that interact to generate a symmetric Lamb wave at the sum frequency is simulated using finite element analysis and then laboratory experiments are conducted. The finite element simulation eliminates issues associated with instrumentation nonlinearities and signal-to-noise ratio. A straightforward subtraction method is used in the experiments to identify the material nonlinearity induced mutual interaction and show that the generated Lamb wave propagates on its own and is large enough to measure. Since the Lamb wave has different polarity than the shear horizontal waves the material nonlinearity is clearly identifiable. Thus, the mutual interactions of shear horizontal waves in plates could enable volumetric characterization of material in remote regions from transducers mounted on just one side of the plate.

Electromagnetic-continuum-induced nonlinearity

NASA Astrophysics Data System (ADS)

Matsko, Andrey B.; Vyatchanin, Sergey P.

2018-05-01

A nonrelativistic Hamiltonian describing interaction between a mechanical degree of freedom and radiation pressure is commonly used as an ultimate tool for studying system behavior in optomechanics. This Hamiltonian is derived from the equation of motion of a mechanical degree of freedom and the optical wave equation with time-varying boundary conditions. We show that this approach is deficient for studying higher-order nonlinear effects in an open resonant optomechanical system. Optomechanical interaction induces a large mechanical nonlinearity resulting from a strong dependence of the power of the light confined in the optical cavity on the mechanical degrees of freedom of the cavity due to coupling with electromagnetic continuum. This dissipative nonlinearity cannot be inferred from the standard Hamiltonian formalism.

Strongly interacting photons in asymmetric quantum well via resonant tunneling.

PubMed

Sun, H; Fan, S L; Feng, X L; Wu, C F; Gong, S Q; Huang, G X; Oh, C H

2012-04-09

We propose an asymmetric quantum well structure to realize strong interaction between two slow optical pulses. The essential idea is the combination of the advantages of inverted-Y type scheme and resonant tunneling. We analytically demonstrate that giant cross-Kerr nonlinearity can be achieved with vanishing absorptions. Owing to resonant tunneling, the contributions of the probe and signal cross-Kerr nonlinearities to total nonlinear phase shift vary from destructive to constrictive, leading to nonlinear phase shift on order of π at low light level. In this structure, the scheme is inherent symmetric for the probe and signal pulses. Consequently, the condition of group velocity matching can be fulfilled with appropriate initial electron distribution.

Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.

2016-01-01

An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.

Assessment of the uncertainty and predictive power of large-scale predictors for nonlinear precipitation downscaling in the European Arctic (Invited)

NASA Astrophysics Data System (ADS)

Sauter, T.

2013-12-01

Despite the extensive research on downscaling methods there is still little consensus about the choice of useful atmospheric predictor variables. Besides the general decision of a proper statistical downscaling model, the selection of an informative predictor set is crucial for the accuracy and stability of the resulting downscaled time series. These requirements must be fullfilled by both the atmospheric variables and the predictor domains in terms of geographical location and spatial extend, to which in general not much attention is paid. However, only a limited number of studies is interested in the predictive capability of the predictor domain size or shape, and the question to what extent variability of neighboring grid points influence local-scale events. In this study we emphasized the spatial relationships between observed daily precipitation and selected number of atmospheric variables for the European Arctic. Several nonlinear regression models are used to link the large-scale predictors obtained from reanalysed Weather Research and Forecast model runs to the local-scale observed precipitation. Inferences on the sources of uncertainty are then drawn from variance based sensitivity measures, which also permit to capture interaction effects between individual predictors. The information is further used to develop more parsimonious downscaling models with only small decreases in accuracy. Individual predictors (without interactions) account for almost 2/3 of the total output variance, while the remaining fraction is solely due to interactions. Neglecting predictor interactions in the screening process will lead to some loss of information. Hence, linear screening methods are insufficient as they neither account for interactions nor for non-additivity as given by many nonlinear prediction algorithms.

Predicting radiotherapy outcomes using statistical learning techniques

NASA Astrophysics Data System (ADS)

El Naqa, Issam; Bradley, Jeffrey D.; Lindsay, Patricia E.; Hope, Andrew J.; Deasy, Joseph O.

2009-09-01

Radiotherapy outcomes are determined by complex interactions between treatment, anatomical and patient-related variables. A common obstacle to building maximally predictive outcome models for clinical practice is the failure to capture potential complexity of heterogeneous variable interactions and applicability beyond institutional data. We describe a statistical learning methodology that can automatically screen for nonlinear relations among prognostic variables and generalize to unseen data before. In this work, several types of linear and nonlinear kernels to generate interaction terms and approximate the treatment-response function are evaluated. Examples of institutional datasets of esophagitis, pneumonitis and xerostomia endpoints were used. Furthermore, an independent RTOG dataset was used for 'generalizabilty' validation. We formulated the discrimination between risk groups as a supervised learning problem. The distribution of patient groups was initially analyzed using principle components analysis (PCA) to uncover potential nonlinear behavior. The performance of the different methods was evaluated using bivariate correlations and actuarial analysis. Over-fitting was controlled via cross-validation resampling. Our results suggest that a modified support vector machine (SVM) kernel method provided superior performance on leave-one-out testing compared to logistic regression and neural networks in cases where the data exhibited nonlinear behavior on PCA. For instance, in prediction of esophagitis and pneumonitis endpoints, which exhibited nonlinear behavior on PCA, the method provided 21% and 60% improvements, respectively. Furthermore, evaluation on the independent pneumonitis RTOG dataset demonstrated good generalizabilty beyond institutional data in contrast with other models. This indicates that the prediction of treatment response can be improved by utilizing nonlinear kernel methods for discovering important nonlinear interactions among model variables. These models have the capacity to predict on unseen data. Part of this work was first presented at the Seventh International Conference on Machine Learning and Applications, San Diego, CA, USA, 11-13 December 2008.

Nonlinear Decay of Alfvén Waves Driven by Interplaying Two- and Three-dimensional Nonlinear Interactions

NASA Astrophysics Data System (ADS)

Zhao, J. S.; Voitenko, Y.; De Keyser, J.; Wu, D. J.

2018-04-01

We study the decay of Alfvén waves in the solar wind, accounting for the joint operation of two-dimensional (2D) scalar and three-dimensional (3D) vector nonlinear interactions between Alfvén and slow waves. These interactions have previously been studied separately in long- and short-wavelength limits where they lead to 2D scalar and 3D vector decays, correspondingly. The joined action of the scalar and vector interactions shifts the transition between 2D and 3D decays to significantly smaller wavenumbers than was predicted by Zhao et al. who compared separate scalar and vector decays. In application to the broadband Alfvén waves in the solar wind, this means that the vector nonlinear coupling dominates in the extended wavenumber range 5 × 10‑4 ≲ ρ i k 0⊥ ≲ 1, where the decay is essentially 3D and nonlocal, generating product Alfvén and slow waves around the ion gyroscale. Here ρ i is the ion gyroradius, and k 0⊥ is the pump Alfvén wavenumber. It appears that, except for the smallest wavenumbers at and below {ρ }i{k}0\\perp ∼ {10}-4 in Channel I, the nonlinear decay of magnetohydrodynamic Alfvén waves propagating from the Sun is nonlocal and cannot generate counter-propagating Alfvén waves with similar scales needed for the turbulent cascade. Evaluation of the nonlinear frequency shift shows that product Alfvén waves can still be approximately described as normal Alfvénic eigenmodes. On the contrary, nonlinearly driven slow waves deviate considerably from normal modes and are therefore difficult to identify on the basis of their phase velocities and/or polarization.

Scaling and interaction of self-similar modes in models of high Reynolds number wall turbulence.

PubMed

Sharma, A S; Moarref, R; McKeon, B J

2017-03-13

Previous work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the self-similarity of the resolvent arising from that of the mean velocity profile. The orthogonal modes provided by the resolvent analysis describe the wall-normal coherence of the motions and inherit that self-similarity. In this contribution, we present the implications of this similarity for the nonlinear interaction between modes with different scales and wall-normal locations. By considering the nonlinear interactions between modes, it is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane. Thus, the geometric scaling of the modes is impressed upon the nonlinear interaction between modes. Implications of these observations on the self-sustaining mechanisms of wall turbulence, modelling and simulation are outlined.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

Studies of nonlinear interactions between counter-propagating Alfv'en waves in the LAPD

NASA Astrophysics Data System (ADS)

Auerbach, D. W.; Perez, J. C.; Carter, T. A.; Boldyrev, S.

2007-11-01

From a weak turbulence point of view, nonlinear interactions between shear Alfv'en waves are fundamental to the energy cascade in low-frequency magnetic turbulence. We report here on an experimental study of counter-propagating Alfv'en wave interactions in the Large Plasma Device (LAPD) at UCLA. Colliding, orthogonally polarized kinetic Alfv'en waves are generated by two antennae, separated by 5m along the guide magnetic field. Magnetic field and langmuir probes record plasma behavior between the antennae. When each antenna is operated separately, linearly polarized Alfv'en waves propagate in opposite directions along the guide field. When two antennae simultaneously excite counter propagating waves, we observe multiple side bands in the frequency domain, whose amplitude scales quadratically with wave amplitude. In the spatial domain we observe non-linear superposition in the 2D structure of the waves and spectral broadening in the perpendicular wave-number spectrum. This indicates the presence of nonlinear interaction of the counter propagating Alfv'en waves, and opens the possiblity to investigate Alfv'enic plasma turbulence in controlled and reproducible laboratory experiments.

The influence of surface roughness on the contact stiffness and the contact filter effect in nonlinear wheel-track interaction

NASA Astrophysics Data System (ADS)

Lundberg, Oskar E.; Nordborg, Anders; Lopez Arteaga, Ines

2016-03-01

A state-dependent contact model including nonlinear contact stiffness and nonlinear contact filtering is used to calculate contact forces and rail vibrations with a time-domain wheel-track interaction model. In the proposed method, the full three-dimensional contact geometry is reduced to a point contact in order to lower the computational cost and to reduce the amount of required input roughness-data. Green's functions including the linear dynamics of the wheel and the track are coupled with a point contact model, leading to a numerically efficient model for the wheel-track interaction. Nonlinear effects due to the shape and roughness of the wheel and the rail surfaces are included in the point contact model by pre-calculation of functions for the contact stiffness and contact filters. Numerical results are compared to field measurements of rail vibrations for passenger trains running at 200 kph on a ballast track. Moreover, the influence of vehicle pre-load and different degrees of roughness excitation on the resulting wheel-track interaction is studied by means of numerical predictions.

Computational aeroelastic analysis of aircraft wings including geometry nonlinearity

NASA Astrophysics Data System (ADS)

Tian, Binyu

The objective of the present study is to show the ability of solving fluid structural interaction problems more realistically by including the geometric nonlinearity of the structure so that the aeroelastic analysis can be extended into the onset of flutter, or in the post flutter regime. A nonlinear Finite Element Analysis software is developed based on second Piola-Kirchhoff stress and Green-Lagrange strain. The second Piola-Kirchhoff stress and Green-Lagrange strain is a pair of energetically conjugated tensors that can accommodate arbitrary large structural deformations and deflection, to study the flutter phenomenon. Since both of these tensors are objective tensors, i.e., the rigid-body motion has no contribution to their components, the movement of the body, including maneuvers and deformation, can be included. The nonlinear Finite Element Analysis software developed in this study is verified with ANSYS, NASTRAN, ABAQUS, and IDEAS for the linear static, nonlinear static, linear dynamic and nonlinear dynamic structural solutions. To solve the flow problems by Euler/Navier equations, the current nonlinear structural software is then embedded into ENSAERO, which is an aeroelastic analysis software package developed at NASA Ames Research Center. The coupling of the two software, both nonlinear in their own field, is achieved by domain decomposition method first proposed by Guruswamy. A procedure has been set for the aeroelastic analysis process. The aeroelastic analysis results have been obtained for fight wing in the transonic regime for various cases. The influence dynamic pressure on flutter has been checked for a range of Mach number. Even though the current analysis matches the general aeroelastic characteristic, the numerical value not match very well with previous studies and needs farther investigations. The flutter aeroelastic analysis results have also been plotted at several time points. The influences of the deforming wing geometry can be well seen in those plots. The movement of shock changes the aerodynamic load distribution on the wing. The effect of viscous on aeroelastic analysis is also discussed. Also compared are the flutter solutions with, or without the structural nonlinearity. As can be seen, linear structural solution goes to infinite, which can not be true in reality. The nonlinear solution is more realistic and can be used to understand the fluid and structure interaction behavior, to control, or prevent disastrous events. (Abstract shortened by UMI.)

Determination of the Interaction Position of Gamma Photons in Monolithic Scintillators Using Neural Network Fitting

NASA Astrophysics Data System (ADS)

Conde, P.; Iborra, A.; González, A. J.; Hernández, L.; Bellido, P.; Moliner, L.; Rigla, J. P.; Rodríguez-Álvarez, M. J.; Sánchez, F.; Seimetz, M.; Soriano, A.; Vidal, L. F.; Benlloch, J. M.

2016-02-01

In Positron Emission Tomography (PET) detectors based on monolithic scintillators, the photon interaction position needs to be estimated from the light distribution (LD) on the photodetector pixels. Due to the finite size of the scintillator volume, the symmetry of the LD is truncated everywhere except for the crystal center. This effect produces a poor estimation of the interaction positions towards the edges, an especially critical situation when linear algorithms, such as Center of Gravity (CoG), are used. When all the crystal faces are painted black, except the one in contact with the photodetector, the LD can be assumed to behave as the inverse square law, providing a simple theoretical model. Using this LD model, the interaction coordinates can be determined by means of fitting each event to a theoretical distribution. In that sense, the use of neural networks (NNs) has been shown to be an effective alternative to more traditional fitting techniques as nonlinear least squares (LS). The multilayer perceptron is one type of NN which can model non-linear functions well and can be trained to accurately generalize when presented with new data. In this work we have shown the capability of NNs to approximate the LD and provide the interaction coordinates of γ-photons with two different photodetector setups. One experimental setup was based on analog Silicon Photomultipliers (SiPMs) and a charge division diode network, whereas the second setup was based on digital SiPMs (dSiPMs). In both experiments NNs minimized border effects. Average spatial resolutions of 1.9 ±0.2 mm and 1.7 ±0.2 mm for the entire crystal surface were obtained for the analog and dSiPMs approaches, respectively.

Good vibrations: Controlling light with sound (Conference Presentation)

NASA Astrophysics Data System (ADS)

Eggleton, Benjamin J.; Choudhary, Amol

2016-10-01

One of the surprises of nonlinear optics, is that light may interact strongly with sound. Intense laser light literally "shakes" the glass in optical fibres, exciting acoustic waves (sound) in the fibre. Under the right conditions, it leads to a positive feedback loop between light and sound termed "Stimulated Brillouin Scattering," or simply SBS. This nonlinear interaction can amplify or filter light waves with extreme precision in frequency which makes it uniquely suited to solve key problems in the fields of defence, biomedicine, wireless communications, spectroscopy and imaging. We have achieved the first demonstration of SBS in compact chip-scale structures, carefully designed so that the optical fields and the acoustic fields are simultaneously confined and guided. This new platform has opened a range of new functionalities that are being applied in communications and defence with breathtaking performance and compactness. My talk will introduce this new field and review our progress and achievements, including silicon based optical phononic processor.

Low-Dimensional Models for Physiological Systems: Nonlinear Coupling of Gas and Liquid Flows

NASA Astrophysics Data System (ADS)

Staples, A. E.; Oran, E. S.; Boris, J. P.; Kailasanath, K.

2006-11-01

Current computational models of biological organisms focus on the details of a specific component of the organism. For example, very detailed models of the human heart, an aorta, a vein, or part of the respiratory or digestive system, are considered either independently from the rest of the body, or as interacting simply with other systems and components in the body. In actual biological organisms, these components and systems are strongly coupled and interact in complex, nonlinear ways leading to complicated global behavior. Here we describe a low-order computational model of two physiological systems, based loosely on a circulatory and respiratory system. Each system is represented as a one-dimensional fluid system with an interconnected series of mass sources, pumps, valves, and other network components, as appropriate, representing different physical organs and system components. Preliminary results from a first version of this model system are presented.

Nonlinear optical detection of electron transfer adiabaticity in metal polypyridyl complexes.

PubMed

Miller, Stephen A; Moran, Andrew M

2010-02-11

Nonlinear optical signatures of electron transfer (ET) adiabaticity are investigated in a prototypical metal polypyridyl system, Os(II)(bpy)(3), known to possess large interligand couplings. Together with a theoretical model, transient absorption anisotropy (TAA) experiments show that field-matter interactions occur with diabatic basis states despite these large couplings. In addition, activated and activationless interligand ET mechanisms are distinguished with a series of TAA experiments in which the pump pulse frequency is tuned over a wide range. At lower pump frequencies, activated interligand ET, which occurs with a time constant of approximately 600 fs, is the dominant mechanism. However, an activationless mechanism becomes most prominent when the pump pulse is tuned by only 800 cm(-1) to higher frequency. This sensitivity of the ET mechanism to the pump frequency agrees with earlier experimental work that estimated an activation energy barrier of 875 cm(-1). The premise of signal interpretation in this paper is that the basis states appropriate for modeling nonradiative relaxation also govern the optical response. Model calculations suggest that optical nonlinearities corresponding to diabatic and adiabatic bases are readily distinguished with TAA experiments. In the diabatic basis, field-matter interaction sequences are restricted to terms in which the pump and probe pulses interact with the same transition dipoles, whereas the adiabatic basis imposes no such restriction and supports a class of coherent cross terms in the nonlinear response function. It is suggested that TAA should be preferred to alternative methods of studying ET adiabaticity that vary solvents and/or temperature. Altering the solvent, for example, generally also impacts solvent reorganization energies and the free energies of the donor and acceptor states. Parallels are discussed between the present work and research aimed at understanding energy transfer mechanisms in molecular aggregates.

Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series.

PubMed

Faes, Luca; Nollo, Giandomenico; Porta, Alberto

2012-03-01

The complexity of the short-term cardiovascular control prompts for the introduction of multivariate (MV) nonlinear time series analysis methods to assess directional interactions reflecting the underlying regulatory mechanisms. This study introduces a new approach for the detection of nonlinear Granger causality in MV time series, based on embedding the series by a sequential, non-uniform procedure, and on estimating the information flow from one series to another by means of the corrected conditional entropy. The approach is validated on short realizations of linear stochastic and nonlinear deterministic processes, and then evaluated on heart period, systolic arterial pressure and respiration variability series measured from healthy humans in the resting supine position and in the upright position after head-up tilt. Copyright © 2011 Elsevier Ltd. All rights reserved.

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

LINEAR AND NONLINEAR CORRECTIONS IN THE RHIC INTERACTION REGIONS.

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

PILAT,F.; CAMERON,P.; PTITSYN,V.

2002-06-02

A method has been developed to measure operationally the linear and non-linear effects of the interaction region triplets, that gives access to the multipole content through the action kick, by applying closed orbit bumps and analysing tune and orbit shifts. This technique has been extensively tested and used during the RHIC operations in 2001. Measurements were taken at 3 different interaction regions and for different focusing at the interaction point. Non-linear effects up to the dodecapole have been measured as well as the effects of linear, sextupolar and octupolar corrections. An analysis package for the data processing has been developedmore » that through a precise fit of the experimental tune shift data (measured by a phase lock loop technique to better than 10{sup -5} resolution) determines the multipole content of an IR triplet.« less

Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction

NASA Technical Reports Server (NTRS)

Parker, B. Eugene, Jr.; Cellucci, Richard L.; Abbott, Dean W.; Barron, Roger L.; Jordan, Paul R., III; Poor, H. Vincent

1993-01-01

The acoustic pressures developed in a boundary layer can interact with an aircraft panel to induce significant vibration in the panel. Such vibration is undesirable due to the aerodynamic drag and structure-borne cabin noises that result. The overall objective of this work is to develop effective and practical feedback control strategies for actively reducing this flow-induced structural vibration. This report describes the results of initial evaluations using polynomial, neural network-based, feedback control to reduce flow induced vibration in aircraft panels due to turbulent boundary layer/structural interaction. Computer simulations are used to develop and analyze feedback control strategies to reduce vibration in a beam as a first step. The key differences between this work and that going on elsewhere are as follows: that turbulent and transitional boundary layers represent broadband excitation and thus present a more complex stochastic control scenario than that of narrow band (e.g., laminar boundary layer) excitation; and secondly, that the proposed controller structures are adaptive nonlinear infinite impulse response (IIR) polynomial neural network, as opposed to the traditional adaptive linear finite impulse response (FIR) filters used in most studies to date. The controllers implemented in this study achieved vibration attenuation of 27 to 60 dB depending on the type of boundary layer established by laminar, turbulent, and intermittent laminar-to-turbulent transitional flows. Application of multi-input, multi-output, adaptive, nonlinear feedback control of vibration in aircraft panels based on polynomial neural networks appears to be feasible today. Plans are outlined for Phase 2 of this study, which will include extending the theoretical investigation conducted in Phase 2 and verifying the results in a series of laboratory experiments involving both bum and plate models.

Adaptive nodes enrich nonlinear cooperative learning beyond traditional adaptation by links.

PubMed

Sardi, Shira; Vardi, Roni; Goldental, Amir; Sheinin, Anton; Uzan, Herut; Kanter, Ido

2018-03-23

Physical models typically assume time-independent interactions, whereas neural networks and machine learning incorporate interactions that function as adjustable parameters. Here we demonstrate a new type of abundant cooperative nonlinear dynamics where learning is attributed solely to the nodes, instead of the network links which their number is significantly larger. The nodal, neuronal, fast adaptation follows its relative anisotropic (dendritic) input timings, as indicated experimentally, similarly to the slow learning mechanism currently attributed to the links, synapses. It represents a non-local learning rule, where effectively many incoming links to a node concurrently undergo the same adaptation. The network dynamics is now counterintuitively governed by the weak links, which previously were assumed to be insignificant. This cooperative nonlinear dynamic adaptation presents a self-controlled mechanism to prevent divergence or vanishing of the learning parameters, as opposed to learning by links, and also supports self-oscillations of the effective learning parameters. It hints on a hierarchical computational complexity of nodes, following their number of anisotropic inputs and opens new horizons for advanced deep learning algorithms and artificial intelligence based applications, as well as a new mechanism for enhanced and fast learning by neural networks.

Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems

NASA Astrophysics Data System (ADS)

Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau, Bernard

2014-02-01

Three-dimensional fluid-structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration.

Fluid–structure interaction involving large deformations: 3D simulations and applications to biological systems

PubMed Central

Tian, Fang-Bao; Dai, Hu; Luo, Haoxiang; Doyle, James F.; Rousseau, Bernard

2013-01-01

Three-dimensional fluid–structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration. PMID:24415796

Polarization domain wall pulses in a microfiber-based topological insulator fiber laser

PubMed Central

Liu, Jingmin; Li, Xingliang; Zhang, Shumin; Zhang, Han; Yan, Peiguang; Han, Mengmeng; Pang, Zhaoguang; Yang, Zhenjun

2016-01-01

Topological insulators (TIs), are novel two-dimension materials, which can act as effective saturable absorbers (SAs) in a fiber laser. Moreover, based on the evanescent wave interaction, deposition of the TI on microfiber would create an effective SA, which has combined advantages from the strong nonlinear optical response in TI material together with the sufficiently-long-range interaction length in fiber taper. By using this type of TI SA, various scalar solitons have been obtained in fiber lasers. However, a single mode fiber always exhibits birefringence, and hence can support two orthogonal degenerate modes. Here we investigate experimentally the vector characters of a TI SA fiber laser. Using the saturated absorption and the high nonlinearity of the TI SA, a rich variety of dynamic states, including polarization-locked dark pulses and their harmonic mode locked counterparts, polarization-locked noise-like pulses and their harmonic mode locked counterparts, incoherently coupled polarization domain wall pulses, including bright square pulses, bright-dark pulse pairs, dark pulses and bright square pulse-dark pulse pairs are all observed with different pump powers and polarization states. PMID:27381942

Polarization domain wall pulses in a microfiber-based topological insulator fiber laser

NASA Astrophysics Data System (ADS)

Liu, Jingmin; Li, Xingliang; Zhang, Shumin; Zhang, Han; Yan, Peiguang; Han, Mengmeng; Pang, Zhaoguang; Yang, Zhenjun

2016-07-01

Topological insulators (TIs), are novel two-dimension materials, which can act as effective saturable absorbers (SAs) in a fiber laser. Moreover, based on the evanescent wave interaction, deposition of the TI on microfiber would create an effective SA, which has combined advantages from the strong nonlinear optical response in TI material together with the sufficiently-long-range interaction length in fiber taper. By using this type of TI SA, various scalar solitons have been obtained in fiber lasers. However, a single mode fiber always exhibits birefringence, and hence can support two orthogonal degenerate modes. Here we investigate experimentally the vector characters of a TI SA fiber laser. Using the saturated absorption and the high nonlinearity of the TI SA, a rich variety of dynamic states, including polarization-locked dark pulses and their harmonic mode locked counterparts, polarization-locked noise-like pulses and their harmonic mode locked counterparts, incoherently coupled polarization domain wall pulses, including bright square pulses, bright-dark pulse pairs, dark pulses and bright square pulse-dark pulse pairs are all observed with different pump powers and polarization states.

Optimization of non-linear gradient in hydrophobic interaction chromatography for the analytical characterization of antibody-drug conjugates.

PubMed

Bobály, Balázs; Randazzo, Giuseppe Marco; Rudaz, Serge; Guillarme, Davy; Fekete, Szabolcs

2017-01-20

The goal of this work was to evaluate the potential of non-linear gradients in hydrophobic interaction chromatography (HIC), to improve the separation between the different homologous species (drug-to-antibody, DAR) of commercial antibody-drug conjugates (ADC). The selectivities between Brentuximab Vedotin species were measured using three different gradient profiles, namely linear, power function based and logarithmic ones. The logarithmic gradient provides the most equidistant retention distribution for the DAR species and offers the best overall separation of cysteine linked ADC in HIC. Another important advantage of the logarithmic gradient, is its peak focusing effect for the DAR0 species, which is particularly useful to improve the quantitation limit of DAR0. Finally, the logarithmic behavior of DAR species of ADC in HIC was modelled using two different approaches, based on i) the linear solvent strength theory (LSS) and two scouting linear gradients and ii) a new derived equation and two logarithmic scouting gradients. In both cases, the retention predictions were excellent and systematically below 3% compared to the experimental values. Copyright © 2016 Elsevier B.V. All rights reserved.

Data based identification and prediction of nonlinear and complex dynamical systems

NASA Astrophysics Data System (ADS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods outlined in this Review are principled on various concepts in complexity science and engineering such as phase transitions, bifurcations, stabilities, and robustness. The methodologies have the potential to significantly improve our ability to understand a variety of complex dynamical systems ranging from gene regulatory systems to social networks toward the ultimate goal of controlling such systems.

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1987-01-01

It is known that a viscous fluid flow with curved streamlines can support both Tollmien-Schlichting and Taylor-Goertler instabilities. In a situation where both modes are possible on the basis of linear theory a nonlinear theory must be used to determine the effect of the interaction of the instabilities. The details of this interaction are of practical importance because of its possible catastrophic effects on mechanisms used for laminar flow control. This interaction is studied in the context of fully developed flows in curved channels. A part form technical differences associated with boundary layer growth the structures of the instabilities in this flow are very similar to those in the practically more important external boundary layer situation. The interaction is shown to have two distinct phases depending on the size of the disturbances. At very low amplitudes two oblique Tollmein-Schlichting waves interact with a Goertler vortex in such a manner that the amplitudes become infinite at a finite time. This type of interaction is described by ordinary differential amplitude equations with quadratic nonlinearities.

Modelling vortex-induced fluid-structure interaction.

PubMed

Benaroya, Haym; Gabbai, Rene D

2008-04-13

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails-formulating generalized equations of motion, as a superset of the flow-oscillator models; and-developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

An Artificial Neural Network-Based Algorithm for Evaluation of Fatigue Crack Propagation Considering Nonlinear Damage Accumulation

PubMed Central

Zhang, Wei; Bao, Zhangmin; Jiang, Shan; He, Jingjing

2016-01-01

In the aerospace and aviation sectors, the damage tolerance concept has been applied widely so that the modeling analysis of fatigue crack growth has become more and more significant. Since the process of crack propagation is highly nonlinear and determined by many factors, such as applied stress, plastic zone in the crack tip, length of the crack, etc., it is difficult to build up a general and flexible explicit function to accurately quantify this complicated relationship. Fortunately, the artificial neural network (ANN) is considered a powerful tool for establishing the nonlinear multivariate projection which shows potential in handling the fatigue crack problem. In this paper, a novel fatigue crack calculation algorithm based on a radial basis function (RBF)-ANN is proposed to study this relationship from the experimental data. In addition, a parameter called the equivalent stress intensity factor is also employed as training data to account for loading interaction effects. The testing data is then placed under constant amplitude loading with different stress ratios or overloads used for model validation. Moreover, the Forman and Wheeler equations are also adopted to compare with our proposed algorithm. The current investigation shows that the ANN-based approach can deliver a better agreement with the experimental data than the other two models, which supports that the RBF-ANN has nontrivial advantages in handling the fatigue crack growth problem. Furthermore, it implies that the proposed algorithm is possibly a sophisticated and promising method to compute fatigue crack growth in terms of loading interaction effects. PMID:28773606

An Artificial Neural Network-Based Algorithm for Evaluation of Fatigue Crack Propagation Considering Nonlinear Damage Accumulation.

PubMed

Zhang, Wei; Bao, Zhangmin; Jiang, Shan; He, Jingjing

2016-06-17

In the aerospace and aviation sectors, the damage tolerance concept has been applied widely so that the modeling analysis of fatigue crack growth has become more and more significant. Since the process of crack propagation is highly nonlinear and determined by many factors, such as applied stress, plastic zone in the crack tip, length of the crack, etc. , it is difficult to build up a general and flexible explicit function to accurately quantify this complicated relationship. Fortunately, the artificial neural network (ANN) is considered a powerful tool for establishing the nonlinear multivariate projection which shows potential in handling the fatigue crack problem. In this paper, a novel fatigue crack calculation algorithm based on a radial basis function (RBF)-ANN is proposed to study this relationship from the experimental data. In addition, a parameter called the equivalent stress intensity factor is also employed as training data to account for loading interaction effects. The testing data is then placed under constant amplitude loading with different stress ratios or overloads used for model validation. Moreover, the Forman and Wheeler equations are also adopted to compare with our proposed algorithm. The current investigation shows that the ANN-based approach can deliver a better agreement with the experimental data than the other two models, which supports that the RBF-ANN has nontrivial advantages in handling the fatigue crack growth problem. Furthermore, it implies that the proposed algorithm is possibly a sophisticated and promising method to compute fatigue crack growth in terms of loading interaction effects.

Inferring genetic interactions via a nonlinear model and an optimization algorithm.

PubMed

Chen, Chung-Ming; Lee, Chih; Chuang, Cheng-Long; Wang, Chia-Chang; Shieh, Grace S

2010-02-26

Biochemical pathways are gradually becoming recognized as central to complex human diseases and recently genetic/transcriptional interactions have been shown to be able to predict partial pathways. With the abundant information made available by microarray gene expression data (MGED), nonlinear modeling of these interactions is now feasible. Two of the latest advances in nonlinear modeling used sigmoid models to depict transcriptional interaction of a transcription factor (TF) for a target gene, but do not model cooperative or competitive interactions of several TFs for a target. An S-shape model and an optimization algorithm (GASA) were developed to infer genetic interactions/transcriptional regulation of several genes simultaneously using MGED. GASA consists of a genetic algorithm (GA) and a simulated annealing (SA) algorithm, which is enhanced by a steepest gradient descent algorithm to avoid being trapped in local minimum. Using simulated data with various degrees of noise, we studied how GASA with two model selection criteria and two search spaces performed. Furthermore, GASA was shown to outperform network component analysis, the time series network inference algorithm (TSNI), GA with regular GA (GAGA) and GA with regular SA. Two applications are demonstrated. First, GASA is applied to infer a subnetwork of human T-cell apoptosis. Several of the predicted interactions are supported by the literature. Second, GASA was applied to infer the transcriptional factors of 34 cell cycle regulated targets in S. cerevisiae, and GASA performed better than one of the latest advances in nonlinear modeling, GAGA and TSNI. Moreover, GASA is able to predict multiple transcription factors for certain targets, and these results coincide with experiments confirmed data in YEASTRACT. GASA is shown to infer both genetic interactions and transcriptional regulatory interactions well. In particular, GASA seems able to characterize the nonlinear mechanism of transcriptional regulatory interactions (TIs) in yeast, and may be applied to infer TIs in other organisms. The predicted genetic interactions of a subnetwork of human T-cell apoptosis coincide with existing partial pathways, suggesting the potential of GASA on inferring biochemical pathways.

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

Rapid Frequency Chirps of TAE mode due to Finite Orbit Energetic Particles

NASA Astrophysics Data System (ADS)

Berk, Herb; Wang, Ge

2013-10-01

The tip model for the TAE mode in the large aspect ratio limit, conceived by Rosenbluth et al. in the frequency domain, together with an interaction term in the frequency domain based on a map model, has been extended into the time domain. We present the formal basis for the model, starting with the Lagrangian for the particle wave interaction. We shall discuss the formal nonlinear time domain problem and the procedure that needs to obtain solutions in the adiabatic limit.

Acoustic Analysis of a Sandwich Non Metallic Panel for Roofs by FEM and Experimental Validation

NASA Astrophysics Data System (ADS)

Nieto, P. J. García; del Coz Díaz, J. J.; Vilán, J. A. Vilán; Rabanal, F. P. Alvarez

2007-12-01

In this paper we have studied the acoustic behavior of a sandwich non metallic panel for roofs by the finite element method (FEM). This new field of analysis is the fully coupled solution of fluid flows with structural interactions, commonly referred to as fluid-structure interaction (FSI). It is the natural next step to take in the simulation of mechanical systems. The finite element analysis of acoustic-fluid/structure interactions using potential-based or displacement-based Lagrangian formulations is now well established. The non-linearity is due to the `fluid-structure interaction' (FSI) that governs the problem. In a very considerable range of problems the fluid displacement remains small while interaction is substantial. In this category falls our problem, in which the structural motion influence and react with the generation of pressures in two reverberation rooms. The characteristic of acoustic insulation of the panel is calculated basing on the pressures for different frequencies and points in the transmission rooms. Finally the conclusions reached are shown.

Modeling the cardiovascular system using a nonlinear additive autoregressive model with exogenous input

NASA Astrophysics Data System (ADS)

Riedl, M.; Suhrbier, A.; Malberg, H.; Penzel, T.; Bretthauer, G.; Kurths, J.; Wessel, N.

2008-07-01

The parameters of heart rate variability and blood pressure variability have proved to be useful analytical tools in cardiovascular physics and medicine. Model-based analysis of these variabilities additionally leads to new prognostic information about mechanisms behind regulations in the cardiovascular system. In this paper, we analyze the complex interaction between heart rate, systolic blood pressure, and respiration by nonparametric fitted nonlinear additive autoregressive models with external inputs. Therefore, we consider measurements of healthy persons and patients suffering from obstructive sleep apnea syndrome (OSAS), with and without hypertension. It is shown that the proposed nonlinear models are capable of describing short-term fluctuations in heart rate as well as systolic blood pressure significantly better than similar linear ones, which confirms the assumption of nonlinear controlled heart rate and blood pressure. Furthermore, the comparison of the nonlinear and linear approaches reveals that the heart rate and blood pressure variability in healthy subjects is caused by a higher level of noise as well as nonlinearity than in patients suffering from OSAS. The residue analysis points at a further source of heart rate and blood pressure variability in healthy subjects, in addition to heart rate, systolic blood pressure, and respiration. Comparison of the nonlinear models within and among the different groups of subjects suggests the ability to discriminate the cohorts that could lead to a stratification of hypertension risk in OSAS patients.

Microscopic Lagrangian description of warm plasmas. III - Nonlinear wave-particle interaction

NASA Technical Reports Server (NTRS)

Galloway, J. J.; Crawford, F. W.

1977-01-01

The averaged-Lagrangian method is applied to nonlinear wave-particle interactions in an infinite, homogeneous, magnetic-field-free plasma. The specific example of Langmuir waves is considered, and the combined effects of four-wave interactions and wave-particle interactions are treated. It is demonstrated how the latter lead to diffusion in velocity space, and the quasilinear diffusion equation is derived. The analysis is generalized to the random phase approximation. The paper concludes with a summary of the method as applied in Parts 1-3 of the paper.

Blackbody emission from light interacting with an effective moving dispersive medium.

PubMed

Petev, M; Westerberg, N; Moss, D; Rubino, E; Rimoldi, C; Cacciatori, S L; Belgiorno, F; Faccio, D

2013-07-26

Intense laser pulses excite a nonlinear polarization response that may create an effective flowing medium and, under appropriate conditions, a blocking horizon for light. Here, we analyze in detail the interaction of light with such laser-induced flowing media, fully accounting for the medium dispersion properties. An analytical model based on a first Born approximation is found to be in excellent agreement with numerical simulations based on Maxwell's equations and shows that when a blocking horizon is formed, the stimulated medium scatters light with a blackbody emission spectrum. Based on these results, diamond is proposed as a promising candidate medium for future studies of Hawking emission from artificial, dispersive horizons.

Brain signal variability as a window into the bidirectionality between music and language processing: moving from a linear to a nonlinear model

PubMed Central

Hutka, Stefanie; Bidelman, Gavin M.; Moreno, Sylvain

2013-01-01

There is convincing empirical evidence for bidirectional transfer between music and language, such that experience in either domain can improve mental processes required by the other. This music-language relationship has been studied using linear models (e.g., comparing mean neural activity) that conceptualize brain activity as a static entity. The linear approach limits how we can understand the brain’s processing of music and language because the brain is a nonlinear system. Furthermore, there is evidence that the networks supporting music and language processing interact in a nonlinear manner. We therefore posit that the neural processing and transfer between the domains of language and music are best viewed through the lens of a nonlinear framework. Nonlinear analysis of neurophysiological activity may yield new insight into the commonalities, differences, and bidirectionality between these two cognitive domains not measurable in the local output of a cortical patch. We thus propose a novel application of brain signal variability (BSV) analysis, based on mutual information and signal entropy, to better understand the bidirectionality of music-to-language transfer in the context of a nonlinear framework. This approach will extend current methods by offering a nuanced, network-level understanding of the brain complexity involved in music-language transfer. PMID:24454295

Electrical control of second-harmonic generation in a WSe 2 monolayer transistor

DOE PAGES

Seyler, Kyle L.; Schaibley, John R.; Gong, Pu; ...

2015-04-20

Nonlinear optical frequency conversion, in which optical fields interact with a nonlinear medium to produce new field frequencies, is ubiquitous in modern photonic systems. However, the nonlinear electric susceptibilities that give rise to such phenomena are often challenging to tune in a given material and, so far, dynamical control of optical nonlinearities remains confined to research laboratories as a spectroscopic tool. In this paper, we report a mechanism to electrically control second-order optical nonlinearities in monolayer WSe 2, an atomically thin semiconductor. We show that the intensity of second-harmonic generation at the A-exciton resonance is tunable by over an ordermore » of magnitude at low temperature and nearly a factor of four at room temperature through electrostatic doping in a field-effect transistor. Such tunability arises from the strong exciton charging effects in monolayer semiconductors, which allow for exceptional control over the oscillator strengths at the exciton and trion resonances. The exciton-enhanced second-harmonic generation is counter-circularly polarized to the excitation laser due to the combination of the two-photon and one-photon valley selection rules, which have opposite helicity in the monolayer. Finally, our study paves the way towards a new platform for chip-scale, electrically tunable nonlinear optical devices based on two-dimensional semiconductors.« less

Brain signal variability as a window into the bidirectionality between music and language processing: moving from a linear to a nonlinear model.

PubMed

Hutka, Stefanie; Bidelman, Gavin M; Moreno, Sylvain

2013-12-30

There is convincing empirical evidence for bidirectional transfer between music and language, such that experience in either domain can improve mental processes required by the other. This music-language relationship has been studied using linear models (e.g., comparing mean neural activity) that conceptualize brain activity as a static entity. The linear approach limits how we can understand the brain's processing of music and language because the brain is a nonlinear system. Furthermore, there is evidence that the networks supporting music and language processing interact in a nonlinear manner. We therefore posit that the neural processing and transfer between the domains of language and music are best viewed through the lens of a nonlinear framework. Nonlinear analysis of neurophysiological activity may yield new insight into the commonalities, differences, and bidirectionality between these two cognitive domains not measurable in the local output of a cortical patch. We thus propose a novel application of brain signal variability (BSV) analysis, based on mutual information and signal entropy, to better understand the bidirectionality of music-to-language transfer in the context of a nonlinear framework. This approach will extend current methods by offering a nuanced, network-level understanding of the brain complexity involved in music-language transfer.

Method of performing computational aeroelastic analyses

NASA Technical Reports Server (NTRS)

Silva, Walter A. (Inventor)

2011-01-01

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

Travel Demand Modeling

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

Southworth, Frank; Garrow, Dr. Laurie

This chapter describes the principal types of both passenger and freight demand models in use today, providing a brief history of model development supported by references to a number of popular texts on the subject, and directing the reader to papers covering some of the more recent technical developments in the area. Over the past half century a variety of methods have been used to estimate and forecast travel demands, drawing concepts from economic/utility maximization theory, transportation system optimization and spatial interaction theory, using and often combining solution techniques as varied as Box-Jenkins methods, non-linear multivariate regression, non-linear mathematical programming,more » and agent-based microsimulation.« less

Using Recursive Regression to Explore Nonlinear Relationships and Interactions: A Tutorial Applied to a Multicultural Education Study

ERIC Educational Resources Information Center

Strang, Kenneth David

2009-01-01

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

Advances in nonlinear optical materials and devices

NASA Technical Reports Server (NTRS)

Byer, Robert L.

1991-01-01

The recent progress in the application of nonlinear techniques to extend the frequency of laser sources has come from the joint progress in laser sources and in nonlinear materials. A brief summary of the progress in diode pumped solid state lasers is followed by an overview of progress in nonlinear frequency extension by harmonic generation and parametric processes. Improved nonlinear materials including bulk crystals, quasiphasematched interactions, guided wave devices, and quantum well intersubband studies are discussed with the idea of identifying areas of future progress in nonlinear materials and devices.

MHD shocks in coronal mass ejections

NASA Technical Reports Server (NTRS)

Steinolfson, R. S.

1991-01-01

The primary objective of this research program is the study of the magnetohydrodynamic (MHD) shocks and nonlinear simple waves produced as a result of the interaction of ejected lower coronal plasma with the ambient corona. The types of shocks and nonlinear simple waves produced for representative coronal conditions and disturbance velocities were determined. The wave system and the interactions between the ejecta and ambient corona were studied using both analytic theory and numerical solutions of the time-dependent, nonlinear MHD equations. Observations from the SMM coronagraph/polarimeter provided both guidance and motivation and are used extensively in evaluating the results. As a natural consequence of the comparisons with the data, the simulations assisted in better understanding the physical interactions in coronal mass ejections (CME's).

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

NASA Astrophysics Data System (ADS)

Tzang, Omer; Caravaca-Aguirre, Antonio M.; Wagner, Kelvin; Piestun, Rafael

2018-06-01

Recent progress in wavefront shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibres comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibres and its applications are in their infancy, opening opportunities to take advantage of complex nonlinear modal dynamics. Here, we demonstrate a wavefront shaping approach for controlling nonlinear phenomena in multimode fibres. Using a spatial light modulator at the fibre input, real-time spectral feedback and a genetic algorithm optimization, we control a highly nonlinear multimode stimulated Raman scattering cascade and its interplay with four-wave mixing via a flexible implicit control on the superposition of modes coupled into the fibre. We show versatile spectrum manipulations including shifts, suppression, and enhancement of Stokes and anti-Stokes peaks. These demonstrations illustrate the power of wavefront shaping to control and optimize nonlinear wave propagation.

Development of a railway wagon-track interaction model: Case studies on excited tracks

NASA Astrophysics Data System (ADS)

Xu, Lei; Chen, Xianmai; Li, Xuwei; He, Xianglin

2018-02-01

In this paper, a theoretical framework for modeling the railway wagon-ballast track interactions is presented, in which the dynamic equations of motion of wagon-track systems are constructed by effectively coupling the linear and nonlinear dynamic characteristics of system components. For the linear components, the energy-variational principle is directly used to derive their dynamic matrices, while for the nonlinear components, the dynamic equilibrium method is implemented to deduce the load vectors, based on which a novel railway wagon-ballast track interaction model is developed, and being validated by comparing with the experimental data measured from a heavy haul railway and another advanced model. With this study, extensive contributions in figuring out the critical speed of instability, limits and localizations of track irregularities over derailment accidents are presented by effectively integrating the dynamic simulation model, the track irregularity probabilistic model and time-frequency analysis method. The proposed approaches can provide crucial information to guarantee the running safety and stability of the wagon-track system when considering track geometries and various running speeds.

Pattern Formation and Strong Nonlinear Interactions in Exciton-Polariton Condensates

NASA Astrophysics Data System (ADS)

Ge, Li; Nersisyan, Ani; Oztop, Baris; Tureci, Hakan

2014-03-01

Exciton-polaritons generated by light-induced potentials can spontaneously condense into macroscopic quantum states that display nontrivial spatial and temporal density modulation. While these patterns and their dynamics can be reproduced through the solution of the generalized Gross-Pitaevskii equation, a predictive theory of their thresholds, oscillation frequencies, and multi-pattern interactions has so far been lacking. Here we represent such an approach based on current-carrying quasi-modes of the non-Hermitian potential induced by the pump. The presented theory allows us to capture the patterns formed in the steady-state directly and account for nonlinearities exactly. We find a simple but powerful expression for thresholds of condensation and the associated frequencies of oscillations, quantifying the contribution of particle formation, leakage, and interactions. We also show that the evolution of the condensate with increasing pump strength is strongly geometry dependent and can display contrasting features such as enhancement or reduction of the spatial localization of the condensate. We acknowledge support by DARPA under Grant No. N66001-11-1-4162 and NSF under CAREER Grant No. DMR-1151810.

Nonlinear evolution of Mack modes in a hypersonic boundary layer

NASA Astrophysics Data System (ADS)

Chokani, Ndaona

2005-01-01

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

Numerical investigation of nonlinear interactions between multimodal guided waves and delamination in composite structures

NASA Astrophysics Data System (ADS)

Shen, Yanfeng

2017-04-01

This paper presents a numerical investigation of the nonlinear interactions between multimodal guided waves and delamination in composite structures. The elastodynamic wave equations for anisotropic composite laminate were formulated using an explicit Local Interaction Simulation Approach (LISA). The contact dynamics was modeled using the penalty method. In order to capture the stick-slip contact motion, a Coulomb friction law was integrated into the computation procedure. A random gap function was defined for the contact pairs to model distributed initial closures or openings to approximate the nature of rough delamination interfaces. The LISA procedure was coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized computation on powerful graphic cards. Several guided wave modes centered at various frequencies were investigated as the incident wave. Numerical case studies of different delamination locations across the thickness were carried out. The capability of different wave modes at various frequencies to trigger the Contact Acoustic Nonlinearity (CAN) was studied. The correlation between the delamination size and the signal nonlinearity was also investigated. Furthermore, the influence from the roughness of the delamination interfaces was discussed as well. The numerical investigation shows that the nonlinear features of wave delamination interactions can enhance the evaluation capability of guided wave Structural Health Monitoring (SHM) system. This paper finishes with discussion, concluding remarks, and suggestions for future work.

Cases Study of Nonlinear Interaction Between Near-Inertial Waves Induced by Typhoon and Diurnal Tides Near the Xisha Islands

NASA Astrophysics Data System (ADS)

Liu, Junliang; He, Yinghui; Li, Juan; Cai, Shuqun; Wang, Dongxiao; Huang, Yandan

2018-04-01

Nonlinear interaction between near-inertial waves (NIWs) and diurnal tides (DTs) after nine typhoons near the Xisha Islands of the northwestern South China Sea (SCS) were investigated using three-year in situ mooring observation data. It was found that a harmonic wave (f + D1, hereafter referred to as fD1 wave), with a frequency equal to the sum of frequencies of NIWs and DTs (hereafter referred to as f and D1, respectively), was generated via nonlinear interaction between typhoon-induced NIWs and DTs after each typhoon. The fD1 wave mainly concentrates in the subsurface layer, and is mainly induced by the first component of the vertical nonlinear momentum term, the product of the vertical velocity of DT and vertical shear of near-inertial current (hereafter referred to as Component 1), in which the vertical shear of the near-inertial current greatly affects the strength of the fD1 current. The larger the Component 1, the stronger the fD1 currents. The background preexisting mesoscale anticyclonic eddy near the mooring site may also enhance the vertical velocity of DT and thus Component 1, which subsequently facilitates the nonlinear interaction-induced energy transfer to the fD1 wave and enhances the fD1 currents after the passage of a typhoon.

Three-dimensional earthquake analysis of roller-compacted concrete dams

NASA Astrophysics Data System (ADS)

Kartal, M. E.

2012-07-01

Ground motion effect on a roller-compacted concrete (RCC) dams in the earthquake zone should be taken into account for the most critical conditions. This study presents three-dimensional earthquake response of a RCC dam considering geometrical non-linearity. Besides, material and connection non-linearity are also taken into consideration in the time-history analyses. Bilinear and multilinear kinematic hardening material models are utilized in the materially non-linear analyses for concrete and foundation rock respectively. The contraction joints inside the dam blocks and dam-foundation-reservoir interaction are modeled by the contact elements. The hydrostatic and hydrodynamic pressures of the reservoir water are modeled with the fluid finite elements based on the Lagrangian approach. The gravity and hydrostatic pressure effects are employed as initial condition before the strong ground motion. In the earthquake analyses, viscous dampers are defined in the finite element model to represent infinite boundary conditions. According to numerical solutions, horizontal displacements increase under hydrodynamic pressure. Besides, those also increase in the materially non-linear analyses of the dam. In addition, while the principle stress components by the hydrodynamic pressure effect the reservoir water, those decrease in the materially non-linear time-history analyses.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

PubMed

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

Jet formation at the interaction of localized waves on the free surface of dielectric liquid in a tangential electric field

NASA Astrophysics Data System (ADS)

Kochurin, E. A.; Zubarev, N. M.

2018-01-01

Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid into a strip, the process of interaction of counter-propagating waves is numerically simulated. The nonlinear solitary waves on the surface can separately propagate along or against the direction of electric field without distortion. At the same time, the shape of the oppositely traveling waves can be distorted as the result of their interaction. In the problem under study, the nonlinearity leads to increasing the wave amplitudes and the duration of their interaction. This effect is inversely proportional to the fluid depth. In the shallow water limit, the tendency to the formation of a vertical liquid jet is observed.

NOLM-based all-optical 40 Gbit/s format conversion through sum-frequency generation (SFG) in a PPLN waveguide

NASA Astrophysics Data System (ADS)

Wang, Jian; Sun, Junqiang

2005-11-01

A novel all-optical format conversion scheme from NRZ to RZ based on sum-frequency generation (SFG) in a periodically poled LiNbO 3 (PPLN) waveguide is proposed, using a nonlinear optical loop mirror (NOLM). The conversion mechanism relies on the combination of attenuation and nonlinear phase shift induced on the clockwise signal field during the SFG process. The SFG between pump, and co- and counter- propagating signals in the PPLN waveguide are numerically studied, showing that counter-propagating SFG can be ignored when quasi-phase matching (QPM) for SFG during co-propagating interaction. The nonlinear phase shift induced on the clockwise signal field is analyzed in detail, showing that it is more effective to yield large values for nonlinear phase shift when appropriately phase mismatched for the SFG process. Two tuning schemes are proposed depend on whether the sum-frequency wavelength is variable or fixed. It is found that the latter has a rather wide 3dB signal conversion bandwidth approximately 154nm. Finally, the influence of reversible process of SFG is discussed and the optimum arrangement of pump and signal peak powers is theoretically demonstrated. The result shows that proper power arrangement, pump width, and waveguide length are necessary for achieving a good conversion effect.

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

Robust Models for Optic Flow Coding in Natural Scenes Inspired by Insect Biology

PubMed Central

Brinkworth, Russell S. A.; O'Carroll, David C.

2009-01-01

The extraction of accurate self-motion information from the visual world is a difficult problem that has been solved very efficiently by biological organisms utilizing non-linear processing. Previous bio-inspired models for motion detection based on a correlation mechanism have been dogged by issues that arise from their sensitivity to undesired properties of the image, such as contrast, which vary widely between images. Here we present a model with multiple levels of non-linear dynamic adaptive components based directly on the known or suspected responses of neurons within the visual motion pathway of the fly brain. By testing the model under realistic high-dynamic range conditions we show that the addition of these elements makes the motion detection model robust across a large variety of images, velocities and accelerations. Furthermore the performance of the entire system is more than the incremental improvements offered by the individual components, indicating beneficial non-linear interactions between processing stages. The algorithms underlying the model can be implemented in either digital or analog hardware, including neuromorphic analog VLSI, but defy an analytical solution due to their dynamic non-linear operation. The successful application of this algorithm has applications in the development of miniature autonomous systems in defense and civilian roles, including robotics, miniature unmanned aerial vehicles and collision avoidance sensors. PMID:19893631

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.; Sharpley, Robert C.

1999-01-01

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Radical-Driven Silicon Surface Passivation for Organic-Inorganic Hybrid Photovoltaics

NASA Astrophysics Data System (ADS)

Chandra, Nitish

The advent of metamaterials has increased the complexity of possible light-matter interactions, creating gaps in knowledge and violating various commonly used approximations and rendering some common mathematical frameworks incomplete. Our forward scattering experiments on metallic shells and cavities have created a need for a rigorous geometry-based analysis of scattering problems and more rigorous current distribution descriptions in the volume of the scattering object. In order to build an accurate understanding of these interactions, we have revisited the fundamentals of Maxwell's equations, electromagnetic potentials and boundary conditions to build a bottom-up geometry-based analysis of scattering. Individual structures or meta-atoms can be designed to localize the incident electromagnetic radiation in order to create a change in local constitutive parameters and possible nonlinear responses. Hence, in next generation engineered materials, an accurate determination of current distribution on the surface and in the structure's volume play an important role in describing and designing desired properties. Multipole expansions of the exact current distribution determined using principles of differential geometry provides an elegant way to study these local interactions of meta-atoms. The dynamics of the interactions can be studied using the behavior of the polarization and magnetization densities generated by localized current densities interacting with the electromagnetic potentials associated with the incident waves. The multipole method combined with propagation of electromagnetic potentials can be used to predict a large variety of linear and nonlinear physical phenomena. This has been demonstrated in experiments that enable the analog detection of sources placed at subwavelength separation by using time reversal of observed signals. Time reversal is accomplished by reversing the direction of the magnetic dipole in bianisotropic metasurfaces while simultaneously providing a method to reduce the losses often observed when light interacts with meta-structures.

Low-loss saturable absorbers based on tapered fibers embedded in carbon nanotube/polymer composites

NASA Astrophysics Data System (ADS)

Martinez, Amos; Al Araimi, Mohammed; Dmitriev, Artemiy; Lutsyk, Petro; Li, Shen; Mou, Chengbo; Rozhin, Alexey; Sumetsky, Misha; Turitsyn, Sergei

2017-12-01

The emergence of low-dimensional materials has opened new opportunities in the fabrication of compact nonlinear photonic devices. Single-walled carbon nanotubes were among the first of those materials to attract the attention of the photonics community owing to their high third order susceptibility, broadband operation, and ultrafast response. Saturable absorption, in particular, has become a widespread application for nanotubes in the mode-locking of a fiber laser where they are used as nonlinear passive amplitude modulators to initiate pulsed operation. Numerous approaches have been proposed for the integration of nanotubes in fiber systems; these can be divided into those that rely on direct interaction (where the nanotubes are sandwiched between fiber connectors) and those that rely on lateral interaction with the evanescence field of the propagating wave. Tapered fibers, in particular, offer excellent flexibility to adjust the nonlinearity of nanotube-based devices but suffer from high losses (typically exceeding 50%) and poor saturable to non-saturable absorption ratios (typically above 1:5). In this paper, we propose a method to fabricate carbon nanotube saturable absorbers with controllable saturation power, low-losses (as low as 15%), and large saturable to non-saturable loss ratios approaching 1:1. This is achieved by optimizing the procedure of embedding tapered fibers in low-refractive index polymers. In addition, this study sheds light in the operation of these devices, highlighting a trade-off between losses and saturation power and providing guidelines for the design of saturable absorbers according to their application.

Human systems dynamics: Toward a computational model

NASA Astrophysics Data System (ADS)

Eoyang, Glenda H.

2012-09-01

A robust and reliable computational model of complex human systems dynamics could support advancements in theory and practice for social systems at all levels, from intrapersonal experience to global politics and economics. Models of human interactions have evolved from traditional, Newtonian systems assumptions, which served a variety of practical and theoretical needs of the past. Another class of models has been inspired and informed by models and methods from nonlinear dynamics, chaos, and complexity science. None of the existing models, however, is able to represent the open, high dimension, and nonlinear self-organizing dynamics of social systems. An effective model will represent interactions at multiple levels to generate emergent patterns of social and political life of individuals and groups. Existing models and modeling methods are considered and assessed against characteristic pattern-forming processes in observed and experienced phenomena of human systems. A conceptual model, CDE Model, based on the conditions for self-organizing in human systems, is explored as an alternative to existing models and methods. While the new model overcomes the limitations of previous models, it also provides an explanatory base and foundation for prospective analysis to inform real-time meaning making and action taking in response to complex conditions in the real world. An invitation is extended to readers to engage in developing a computational model that incorporates the assumptions, meta-variables, and relationships of this open, high dimension, and nonlinear conceptual model of the complex dynamics of human systems.

Characterizing Feedback Control Mechanisms in Nonlinear Microbial Models of Soil Organic Matter Decomposition by Stability Analysis

NASA Astrophysics Data System (ADS)

Georgiou, K.; Tang, J.; Riley, W. J.; Torn, M. S.

2014-12-01

Soil organic matter (SOM) decomposition is regulated by biotic and abiotic processes. Feedback interactions between such processes may act to dampen oscillatory responses to perturbations from equilibrium. Indeed, although biological oscillations have been observed in small-scale laboratory incubations, the overlying behavior at the plot-scale exhibits a relatively stable response to disturbances in input rates and temperature. Recent studies have demonstrated the ability of microbial models to capture nonlinear feedbacks in SOM decomposition that linear Century-type models are unable to reproduce, such as soil priming in response to increased carbon input. However, these microbial models often exhibit strong oscillatory behavior that is deemed unrealistic. The inherently nonlinear dynamics of SOM decomposition have important implications for global climate-carbon and carbon-concentration feedbacks. It is therefore imperative to represent these dynamics in Earth System Models (ESMs) by introducing sub-models that accurately represent microbial and abiotic processes. In the present study we explore, both analytically and numerically, four microbe-enabled model structures of varying levels of complexity. The most complex model combines microbial physiology, a non-linear mineral sorption isotherm, and enzyme dynamics. Based on detailed stability analysis of the nonlinear dynamics, we calculate the system modes as functions of model parameters. This dependence provides insight into the source of state oscillations. We find that feedback mechanisms that emerge from careful representation of enzyme and mineral interactions, with parameter values in a prescribed range, are critical for both maintaining system stability and capturing realistic responses to disturbances. Corroborating and expanding upon the results of recent studies, we explain the emergence of oscillatory responses and discuss the appropriate microbe-enabled model structure for inclusion in ESMs.

Individual Differences: Implications for Web-Based Learning Design

ERIC Educational Resources Information Center

Alomyan, Hesham

2004-01-01

In the past ten years the Web has attracted many educators for purposes of teaching and learning. The main advantage of the Web lies in its non-linear interaction. That is, students can have more control over their learning paths. However, this freedom of control may cause problems for some students, such as disorientation, cognitive overload and…

Blended Learning Approach for Enhancing Students' Learning Experiences in a Knowledge Society

ERIC Educational Resources Information Center

Suprabha, K.; Subramonian, G.

2015-01-01

Blended learning which, its name suggests, blends online learning with traditional methods of learning and development. It is a new instructional strategy, based on the non-linear and interactive features of the digital learning and instruction through the web. Exploring the literature review, the purpose of the study was to get a deeper…

Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.

2011-01-01

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

ERIC Educational Resources Information Center

Kelava, Augustin; Nagengast, Benjamin

2012-01-01

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

Solitonic and chaotic behaviors of a (3+1)-dimensional nonlinear Schrödinger equation in a magnetized electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Chai, Jun

2015-05-01

In a magnetized e-p-i plasma with two-electron temperatures, the (3+1)-dimensional nonlinear Schrödinger equation for the ion-acoustic envelope solitons is hereby investigated. Bright and dark soliton solutions are both obtained. It is found that the soliton amplitude is inversely related to P, Q and R, with P, Q and R respectively as the coefficients of the dispersive term, nonlinear term and combined effect of the transverse perturbation and magnetic field. Head-on interactions are displayed, and with Q and R decreasing, can be transferred into the overtaking ones. Bright bound-state solitons are obtained, and the interaction period decreases with Q increasing. Both the head-on and overtaking interactions between the two dark solitons are displayed, and such a head-on interaction can be transformed into the overtaking one with R increasing. Upon the introduction of the external perturbation, the developed and weak chaos are observed. Phase projections and power spectra are presented. Difference between the two chaotic motions roots in the inequality between the nonlinear and perturbed terms. Developed chaos can be weakened with Q decreasing, or with the frequency of external perturbation increasing.

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

NASA Astrophysics Data System (ADS)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Distributed source model for the full-wave electromagnetic simulation of nonlinear terahertz generation.

PubMed

Fumeaux, Christophe; Lin, Hungyen; Serita, Kazunori; Withayachumnankul, Withawat; Kaufmann, Thomas; Tonouchi, Masayoshi; Abbott, Derek

2012-07-30

The process of terahertz generation through optical rectification in a nonlinear crystal is modeled using discretized equivalent current sources. The equivalent terahertz sources are distributed in the active volume and computed based on a separately modeled near-infrared pump beam. This approach can be used to define an appropriate excitation for full-wave electromagnetic numerical simulations of the generated terahertz radiation. This enables predictive modeling of the near-field interactions of the terahertz beam with micro-structured samples, e.g. in a near-field time-resolved microscopy system. The distributed source model is described in detail, and an implementation in a particular full-wave simulation tool is presented. The numerical results are then validated through a series of measurements on square apertures. The general principle can be applied to other nonlinear processes with possible implementation in any full-wave numerical electromagnetic solver.

Nonlinear dynamics of trions under strong optical excitation in monolayer MoSe2.

PubMed

Ye, Jialiang; Yan, Tengfei; Niu, Binghui; Li, Ying; Zhang, Xinhui

2018-02-05

By employing ultrafast transient reflection measurements based on two-color pump-probe spectroscopy, the population and valley polarization dynamics of trions in monolayer MoSe 2 were investigated at relatively high excitation densities under near-resonant excitation. Both the nonlinear dynamic photobleaching of the trion resonance and the redshift of the exciton resonance were found to be responsible for the excitation-energy- and density-dependent transient reflection change as a result of many-body interactions. Furthermore, from the polarization-resolved measurements, it was revealed that the initial fast population and polarization decay process upon strong photoexcitation observed for trions was determined by trion formation, transient phase-space filling and the short valley lifetime of excitons. The results provide a basic understanding of the nonlinear dynamics of population and valley depolarization of trions, as well as exciton-trion correlation in atomically thin MoSe 2 and other transition metal dichalcogenide materials.

Investigation of the Dynamics of Coherent Structure, BBF, and Intermittent Turbulence in Earth's Magnetotail: A Study of Complexity in Nonlinear Space Plasmas

NASA Technical Reports Server (NTRS)

Chang, Tom

2005-01-01

We have achieved all the goals stated in our grant proposal. Specifically, these include: 1. The understanding of the complexity induced nonlinear spatiotemporal coherent structures and the coexisting propagating modes. 2. The understanding of the intermittent turbulence and energization process of the observed Bursty Bulk Flows (BBF's) in the Earth s magnetotail. 3. The development of "anisotropic three-dimensional complexity" in the plasma sheet due to localized merging and interactions of the magnetic coherent structures. 4. The study of fluctuation-induced nonlinear instabilities and their role in the reconfiguration of magnetic topologies in the magnetotail based on the concepts of the dynamic renormalization group. 5. The acceleration of ions due to the intermittent turbulence of propagating and nonpropagating fluctuations. In the following, we include lists of our published papers, invited talks, and professional activities. A detailed description of our accomplished research results is given..

Nonlinear Dynamic Behavior of Impact Damage in a Composite Skin-Stiffener Structure

NASA Technical Reports Server (NTRS)

Ooijevaar, T. H.; Rogge, M. D.; Loendersloot, R.; Warnet, L.; Akkerman, R.; deBoer, A.

2013-01-01

One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage, like delaminations. A wide range of technologies, comprising global vibration and local wave propagation methods can be employed for health monitoring purposes. Traditional low frequency modal analysis based methods are linear methods. The effectiveness of these methods is often limited since they rely on a stationary and linear approximation of the system. The nonlinear interaction between a low frequency wave field and a local impact induced skin-stiffener failure is experimentally demonstrated in this paper. The different mechanisms that are responsible for the nonlinearities (opening, closing and contact) of the distorted harmonic waveforms are separated with the help of phase portraits. A basic analytical model is employed to support the observations.

Nonlinear adhesion dynamics of confined lipid membranes

NASA Astrophysics Data System (ADS)

To, Tung; Le Goff, Thomas; Pierre-Louis, Olivier

Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems. Supported by the grand ANR Biolub.

Nonlinear network model analysis of vibrational energy transfer and localisation in the Fenna-Matthews-Olson complex

NASA Astrophysics Data System (ADS)

Morgan, Sarah E.; Cole, Daniel J.; Chin, Alex W.

2016-11-01

Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex of photosynthetic green sulphur bacteria, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level in large protein structures, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the entire trimeric FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes through their influence on pigment properties. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.

Air-Coupled Vibrometry

NASA Astrophysics Data System (ADS)

Döring, D.; Solodov, I.; Busse, G.

Sound and ultrasound in air are the products of a multitude of different processes and thus can be favorable or undesirable phenomena. Development of experimental tools for non-invasive measurements and imaging of airborne sound fields is of importance for linear and nonlinear nondestructive material testing as well as noise control in industrial or civil engineering applications. One possible solution is based on acousto-optic interaction, like light diffraction imaging. The diffraction approach usually requires a sophisticated setup with fine optical alignment barely applicable in industrial environment. This paper focuses on the application of the robust experimental tool of scanning laser vibrometry, which utilizes commercial off-the-shelf equipment. The imaging technique of air-coupled vibrometry (ACV) is based on the modulation of the optical path length by the acoustic pressure of the sound wave. The theoretical considerations focus on the analysis of acousto-optical phase modulation. The sensitivity of the ACV in detecting vibration velocity was estimated as ~1 mm/s. The ACV applications to imaging of linear airborne fields are demonstrated for leaky wave propagation and measurements of ultrasonic air-coupled transducers. For higher-intensity ultrasound, the classical nonlinear effect of the second harmonic generation was measured in air. Another nonlinear application includes a direct observation of the nonlinear air-coupled emission (NACE) from the damaged areas in solid materials. The source of the NACE is shown to be strongly localized around the damage and proposed as a nonlinear "tag" to discern and image the defects.

Optimization-Based Inverse Identification of the Parameters of a Concrete Cap Material Model

NASA Astrophysics Data System (ADS)

Král, Petr; Hokeš, Filip; Hušek, Martin; Kala, Jiří; Hradil, Petr

2017-10-01

Issues concerning the advanced numerical analysis of concrete building structures in sophisticated computing systems currently require the involvement of nonlinear mechanics tools. The efforts to design safer, more durable and mainly more economically efficient concrete structures are supported via the use of advanced nonlinear concrete material models and the geometrically nonlinear approach. The application of nonlinear mechanics tools undoubtedly presents another step towards the approximation of the real behaviour of concrete building structures within the framework of computer numerical simulations. However, the success rate of this application depends on having a perfect understanding of the behaviour of the concrete material models used and having a perfect understanding of the used material model parameters meaning. The effective application of nonlinear concrete material models within computer simulations often becomes very problematic because these material models very often contain parameters (material constants) whose values are difficult to obtain. However, getting of the correct values of material parameters is very important to ensure proper function of a concrete material model used. Today, one possibility, which permits successful solution of the mentioned problem, is the use of optimization algorithms for the purpose of the optimization-based inverse material parameter identification. Parameter identification goes hand in hand with experimental investigation while it trying to find parameter values of the used material model so that the resulting data obtained from the computer simulation will best approximate the experimental data. This paper is focused on the optimization-based inverse identification of the parameters of a concrete cap material model which is known under the name the Continuous Surface Cap Model. Within this paper, material parameters of the model are identified on the basis of interaction between nonlinear computer simulations, gradient based and nature inspired optimization algorithms and experimental data, the latter of which take the form of a load-extension curve obtained from the evaluation of uniaxial tensile test results. The aim of this research was to obtain material model parameters corresponding to the quasi-static tensile loading which may be further used for the research involving dynamic and high-speed tensile loading. Based on the obtained results it can be concluded that the set goal has been reached.

Reduced order modeling of fluid/structure interaction.

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

Barone, Matthew Franklin; Kalashnikova, Irina; Segalman, Daniel Joseph

2009-11-01

This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preservesmore » numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.« less

The influence of filtering and downsampling on the estimation of transfer entropy

PubMed Central

Florin, Esther; von Papen, Michael; Timmermann, Lars

2017-01-01

Transfer entropy (TE) provides a generalized and model-free framework to study Wiener-Granger causality between brain regions. Because of its nonparametric character, TE can infer directed information flow also from nonlinear systems. Despite its increasing number of applications in neuroscience, not much is known regarding the influence of common electrophysiological preprocessing on its estimation. We test the influence of filtering and downsampling on a recently proposed nearest neighborhood based TE estimator. Different filter settings and downsampling factors were tested in a simulation framework using a model with a linear coupling function and two nonlinear models with sigmoid and logistic coupling functions. For nonlinear coupling and progressively lower low-pass filter cut-off frequencies up to 72% false negative direct connections and up to 26% false positive connections were identified. In contrast, for the linear model, a monotonic increase was only observed for missed indirect connections (up to 86%). High-pass filtering (1 Hz, 2 Hz) had no impact on TE estimation. After low-pass filtering interaction delays were significantly underestimated. Downsampling the data by a factor greater than the assumed interaction delay erased most of the transmitted information and thus led to a very high percentage (67–100%) of false negative direct connections. Low-pass filtering increases the number of missed connections depending on the filters cut-off frequency. Downsampling should only be done if the sampling factor is smaller than the smallest assumed interaction delay of the analyzed network. PMID:29149201

Nonlinear Whistler Wave Physics in the Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, Chris

2016-10-01

Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data suggest that these weak turbulence processes may be playing a role in saturating the nonlinear instability.

Non-linear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.-M.; Crawford, F. W.

1979-01-01

Non-linear three-wave interaction is analysed for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field. An averaged-Lagrangian method is used, and the results are specialized to parametric interaction and mode conversion, assuming an undepleted pump wave. The theory for these two types of interactions is extended to include imperfect synchronism, and the effects of loss. Computations are presented indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma column parameters.

Response of jammed packings to thermal fluctuations

NASA Astrophysics Data System (ADS)

Wu, Qikai; Bertrand, Thibault; Shattuck, Mark D.; O'Hern, Corey S.

2017-12-01

We focus on the response of mechanically stable (MS) packings of frictionless, bidisperse disks to thermal fluctuations, with the aim of quantifying how nonlinearities affect system properties at finite temperature. In contrast, numerous prior studies characterized the structural and mechanical properties of MS packings of frictionless spherical particles at zero temperature. Packings of disks with purely repulsive contact interactions possess two main types of nonlinearities, one from the form of the interaction potential (e.g., either linear or Hertzian spring interactions) and one from the breaking (or forming) of interparticle contacts. To identify the temperature regime at which the contact-breaking nonlinearities begin to contribute, we first calculated the minimum temperatures Tc b required to break a single contact in the MS packing for both single- and multiple-eigenmode perturbations of the T =0 MS packing. We find that the temperature required to break a single contact for equal velocity-amplitude perturbations involving all eigenmodes approaches the minimum value obtained for a perturbation in the direction connecting disk pairs with the smallest overlap. We then studied deviations in the constant volume specific heat C¯V and deviations of the average disk positions Δ r from their T =0 values in the temperature regime TC ¯V100 for linear spring interactions is independent of system size. This result emphasizes that contact-breaking nonlinearities are dominant over form nonlinearities in the low-temperature range Tc b

Comparing Numerical Spall Simulations with a Nonlinear Spall Formation Model

NASA Astrophysics Data System (ADS)

Ong, L.; Melosh, H. J.

2012-12-01

Spallation accelerates lightly shocked ejecta fragments to speeds that can exceed the escape velocity of the parent body. We present high-resolution simulations of nonlinear shock interactions in the near surface. Initial results show the acceleration of near-surface material to velocities up to 1.8 times greater than the peak particle velocity in the detached shock, while experiencing little to no shock pressure. These simulations suggest a possible nonlinear spallation mechanism to produce the high-velocity, low show pressure meteorites from other planets. Here we pre-sent the numerical simulations that test the production of spall through nonlinear shock interactions in the near sur-face, and compare the results with a model proposed by Kamegai (1986 Lawrence Livermore National Laboratory Report). We simulate near-surface shock interactions using the SALES_2 hydrocode and the Murnaghan equation of state. We model the shock interactions in two geometries: rectangular and spherical. In the rectangular case, we model a planar shock approaching the surface at a constant angle phi. In the spherical case, the shock originates at a point below the surface of the domain and radiates spherically from that point. The angle of the shock front with the surface is dependent on the radial distance of the surface point from the shock origin. We model the target as a solid with a nonlinear Murnaghan equation of state. This idealized equation of state supports nonlinear shocks but is tem-perature independent. We track the maximum pressure and maximum velocity attained in every cell in our simula-tions and compare them to the Hugoniot equations that describe the material conditions in front of and behind the shock. Our simulations demonstrate that nonlinear shock interactions in the near surface produce lightly shocked high-velocity material for both planar and cylindrical shocks. The spall is the result of the free surface boundary condi-tion, which forces a pressure gradient from the peak shock pressure to the zero pressure boundary. The nonlinear shock interactions occur where the pressure contours curve to accommodate the free surface. The material within this spall zone is ejected at speeds up to 1.8 km s-1 for an imposed pulse of 1 km s-1. Where the ejection velocities are highest, the maximum pressure attained in each cell is effectively zero. We compare our simulation results with a model for nonlinear shock interactions proposed by Kamegai (1986). This model recognizes that the material behind the shock is compressed and has a higher soundspeed than the mate-rial in front of the shock. As the rarefaction wave moves behind the shock, its increased velocity through the com-pressed material combines with the residual particle velocity behind the shock to "catch up" with the shock. This occurs in the near surface where the sum of the compressed sound speed and the residual particle velocity is greater than or equal to the shock velocity. Initial results for the spherical shocks qualitatively match the volume described by this model, but differ significantly in the quantitative slope of the curve defining the region of interaction. We continue to test the Kamegai model with high-resolution numerical simulations of shock interactions to determine its potential application to planetary spallation.

Non-linear wave-particle interactions and fast ion loss induced by multiple Alfvén eigenmodes in the DIII-D tokamak

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

Chen, Xi; Kramer, Gerrit J.; Heidbrink, William W.

2014-05-21

A new non-linear feature has been observed in fast-ion loss from tokamak plasmas in the form of oscillations at the sum, difference and second harmonic frequencies of two independent Alfvén eigenmodes (AEs). Full orbit calculations and analytic theory indicate this non-linearity is due to coupling of fast-ion orbital response as it passes through each AE — a change in wave-particle phase k • r by one mode alters the force exerted by the next. Furthermore, the loss measurement is of barely confined, non-resonant particles, while similar non-linear interactions can occur between well-confined particles and multiple AEs leading to enhanced fast-ionmore » transport.« less

Influence of pump-field scattering on nonclassical-light generation in a photonic-band-gap nonlinear planar waveguide

NASA Astrophysics Data System (ADS)

Peřina, Jan, Jr.; Sibilia, Concita; Tricca, Daniela; Bertolotti, Mario

2005-04-01

Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. The properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic-band-gap structure inside the waveguide. A general quantum model of linear operator amplitude corrections to the amplitude mean values and its numerical analysis provide conditions for efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. The destructive influence of phase mismatch of the nonlinear interaction can fully be compensated using a suitable photonic-band-gap structure inside the waveguide. Also an increase of the signal-to-noise ratio of the incident optical field can be reached in the waveguide.

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Generation of terahertz radiation upon filtration of a supercontinuum produced during the propagation of a femtosecond laser pulse in a GaAs crystal

NASA Astrophysics Data System (ADS)

Vardanyan, Aleksandr O.; Oganesyan, David L.

2008-11-01

The results of a theoretical study of the formation of a supercontinuum produced due to the interaction of femtosecond laser pulses with an isotropic nonlinear medium are presented. The system of nonlinear Maxwell's equations was numerically integrated in time by the finite-difference method. The interaction of mutually orthogonal linearly-polarised 1.98-μm, 30-fs, 30-nJ pulses propagating along the normal to the 110 plane in a 1-mm-long GaAs crystal was considered. In the nonlinear part of the polarisation medium, the inertialless second-order nonlinear susceptibility was taken into account. The formation process of a terahertz pulse obtained due to the supercontinuum filtration was studied.

Complex and Nonlinear Pedagogy and the Implications for Physical Education

ERIC Educational Resources Information Center

Chow, Jia Yi; Atencio, Matthew

2014-01-01

There is increasing support to describe and examine the teaching of game skills in physical education from a complex and nonlinear perspective. The emergence of game behaviours as a consequence of the dynamic interactions of the learner, the game environment and the task constraints within the game context highlights the nonlinear and complex…

Exact multisoliton solutions of general nonlinear Schrödinger equation with derivative.

PubMed

Li, Qi; Duan, Qiu-yuan; Zhang, Jian-bing

2014-01-01

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

A Learning Progression Should Address Regression: Insights from Developing Non-Linear Reasoning in Ecology

ERIC Educational Resources Information Center

Hovardas, Tasos

2016-01-01

Although ecological systems at varying scales involve non-linear interactions, learners insist thinking in a linear fashion when they deal with ecological phenomena. The overall objective of the present contribution was to propose a hypothetical learning progression for developing non-linear reasoning in prey-predator systems and to provide…

Theory of plasmonic effects in nonlinear optics: the case of graphene

NASA Astrophysics Data System (ADS)

Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

System and method for generating 3D images of non-linear properties of rock formation using surface seismic or surface to borehole seismic or both

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

Vu, Cung Khac; Nihei, Kurt Toshimi; Johnson, Paul A.

A system and method of characterizing properties of a medium from a non-linear interaction are include generating, by first and second acoustic sources disposed on a surface of the medium on a first line, first and second acoustic waves. The first and second acoustic sources are controllable such that trajectories of the first and second acoustic waves intersect in a mixing zone within the medium. The method further includes receiving, by a receiver positioned in a plane containing the first and second acoustic sources, a third acoustic wave generated by a non-linear mixing process from the first and second acousticmore » waves in the mixing zone; and creating a first two-dimensional image of non-linear properties or a first ratio of compressional velocity and shear velocity, or both, of the medium in a first plane generally perpendicular to the surface and containing the first line, based on the received third acoustic wave.« less

Numerical study of nonlinear full wave acoustic propagation

NASA Astrophysics Data System (ADS)

Velasco-Segura, Roberto; Rendon, Pablo L.

2013-11-01

With the aim of describing nonlinear acoustic phenomena, a form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite-volume method using Roe's linearization has been implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is written for parallel execution on a GPU and improves performance by a factor of over 50 when compared to the standard CLAWPACK Fortran code. This code can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from modest models of diagnostic and therapeutic HIFU, parametric acoustic arrays, to acoustic wave guides. A couple of examples will be presented showing shock formation and oblique interaction. DGAPA PAPIIT IN110411, PAEP UNAM 2013.

Designing an ultrafast laser virtual laboratory using MATLAB GUIDE

NASA Astrophysics Data System (ADS)

Cambronero-López, F.; Gómez-Varela, A. I.; Bao-Varela, C.

2017-05-01

In this work we present a virtual simulator developed using the MATLAB GUIDE environment based on the numerical resolution of the nonlinear Schrödinger equation (NLS) and using the split step method for the study of the spatial-temporal propagation of nonlinear ultrashort laser pulses. This allows us to study the spatial-temporal propagation of ultrafast pulses as well as the influence of high-order spectral phases such as group delay dispersion and third-order dispersion on pulse compression in time. The NLS can describe several nonlinear effects, in particular in this paper we consider the Kerr effect, cross-polarized wave generation and cubic-quintic propagation in order to highlight the potential of this equation combined with the GUIDE environment. Graphical user interfaces are commonly used in science and engineering teaching due to their educational value, and have proven to be an effective way to engage and motivate students. Specifically, the interactive graphical interfaces presented provide the visualization of some of the most important nonlinear optics phenomena and allows users to vary the values of the main parameters involved.

Polarimetric Doppler spectrum of backscattered echoes from nonlinear sea surface damped by natural slicks

NASA Astrophysics Data System (ADS)

Yang, Pengju; Guo, Lixin

2016-11-01

Based on the Lombardini et al. model that can predict the hydrodynamic damping of rough sea surfaces in the presence of monomolecular slicks and the "choppy wave" model (CWM) that can describe the nonlinear interactions between ocean waves, the modeling of time-varying nonlinear sea surfaces damped by natural or organic sea slicks is presented in this paper. The polarimetric scattering model of second-order small-slope approximation (SSA-II) with tapered wave incidence is utilized for evaluating co- and cross-polarized backscattered echoes from clean and contaminated CWM nonlinear sea surfaces. The influence of natural sea slicks on Doppler shift and spectral bandwidth of radar sea echoes is investigated in detail by comparing the polarimetric Doppler spectra of contaminated sea surfaces with those of clean sea surfaces. A narrowing of Doppler spectra in the presence of oil slicks is observed for both co- and cross-polarization, which is qualitatively consistent with wave-tank measurements. Simulation results also show that the Doppler shifts in slicks can increase or decrease, depending on incidence angles and polarizations.

Phase-resolved two-dimensional terahertz spectroscopy - a probe of highly nonlinear light-matter interactions

NASA Astrophysics Data System (ADS)

Elsaesser, Thomas

Terahertz (THz) spectroscopy gives insight into low-frequency excitations and charge dynamics in condensed matter. So far, most experiments in a frequency range from 0.5 to 30 THz have focused on the linear THz response to determine linear absorption and disperion spectra, and/or electric conductivities. The generation of ultrashort THz transients with peak electric fields up to megavolts/cm has allowed for addressing nonlinear light-matter interactions and inducing excitations far from equilibrium. The novel method of two-dimensional THz (2D-THz) spectroscopy allows for mapping ultrafast dynamics and couplings of elementary excitations up to arbitrary nonlinear order in the electric field, both under resonant and nonresonant excitation conditions. In particular, different contributions to the overall nonlinear response are separated by dissecting it as a function of excitation and detection frequencies and for different waiting times after excitation. This talk gives an introduction in 2D-THz spectroscopy, including its recent extension to 3-pulse sequences and interaction schemes. To illustrate the potential of the method, recent results on two-phonon coherences and high-order interband excitations in the semiconductor InSb will be presented. Nonlinear THz excitation of two-phonon coherences exploits a resonance enhancement by the large electronic interband dipole of InSb and is, thus, far more efficient than linear excitation via resonant two-phonon absorption. As a second application, the nonlinear softmode response in a crystal consisting of aspirin molecules will be discussed. At moderate THz driving fields, the pronounced correlation of rotational modes of CH3 groups with collective oscillations of π-electrons drives the system into the regime of nonperturbative light-matter interaction. Nonlinear absorption around 1.1 THz leads to a blue-shifted coherent emission at 1.5 THz, revealing a dynamic breakup of the strong electron-phonon correlations.

Rewriting the rules governing high intensity interactions of light with matter

NASA Astrophysics Data System (ADS)

Borisov, Alex B.; McCorkindale, John C.; Poopalasingam, Sankar; Longworth, James W.; Simon, Peter; Szatmári, Sándor; Rhodes, Charles K.

2016-04-01

The trajectory of discovery associated with the study of high-intensity nonlinear radiative interactions with matter and corresponding nonlinear modes of electromagnetic propagation through material that have been conducted over the last 50 years can be presented as a landscape in the intensity/quantum energy [I-ħω] plane. Based on an extensive series of experimental and theoretical findings, a universal zone of anomalous enhanced electromagnetic coupling, designated as the fundamental nonlinear domain, can be defined. Since the lower boundaries of this region for all atomic matter correspond to ħω ~ 103 eV and I  ≈  1016 W cm-2, it heralds a future dominated by x-ray and γ-ray studies of all phases of matter including nuclear states. The augmented strength of the interaction with materials can be generally expressed as an increase in the basic electromagnetic coupling constant in which the fine structure constant α  →  Z 2 α, where Z denotes the number of electrons participating in an ordered response to the driving field. Since radiative conditions strongly favoring the development of this enhanced electromagnetic coupling are readily produced in self-trapped plasma channels, the processes associated with the generation of nonlinear interactions with materials stand in natural alliance with the nonlinear mechanisms that induce confined propagation. An experimental example involving the Xe (4d105s25p6) supershell for which Z  ≅  18 that falls in the specified anomalous nonlinear domain is described. This yields an effective coupling constant of Z 2 α  ≅  2.4  >  1, a magnitude comparable to the strong interaction and a value rendering as useless conventional perturbative analyses founded on an expansion in powers of α. This enhancement can be quantitatively understood as a direct consequence of the dominant role played by coherently driven multiply-excited states in the dynamics of the coupling. It is also conclusively demonstrated by an abundance of data that the utterly peerless champion of the experimental campaign leading to the definition of the fundamental nonlinear domain was excimer laser technology. The basis of this unique role was the ability to satisfy simultaneously a triplet (ω, I, P) of conditions stating the minimal values of the frequency ω, intensity I, and the power P necessary to enable the key physical processes to be experimentally observed and controllably combined. The historical confluence of these developments creates a solid foundation for the prediction of future advances in the fundamental understanding of ultra-high power density states of matter. The atomic findings graciously generalize to the composition of a nuclear stanza expressing the accessibility of the nuclear domain. With this basis serving as the launch platform, a cadenza of three grand challenge problems representing both new materials and new interactions is presented for future solution; they are (1) the performance of an experimental probe of the properties of the vacuum state associated with the dark energy at an intensity approaching the Schwinger/Heisenberg limit, (2) the attainment of amplification in the γ-ray region (~1 MeV) and the discovery of a nuclear excimer, and (3) the determination of a path to the projected super-heavy nuclear island of stability.

Rewriting the rules governing high intensity interactions of light with matter.

PubMed

Borisov, Alex B; McCorkindale, John C; Poopalasingam, Sankar; Longworth, James W; Simon, Peter; Szatmári, Sándor; Rhodes, Charles K

2016-04-01

The trajectory of discovery associated with the study of high-intensity nonlinear radiative interactions with matter and corresponding nonlinear modes of electromagnetic propagation through material that have been conducted over the last 50 years can be presented as a landscape in the intensity/quantum energy [I-ħω] plane. Based on an extensive series of experimental and theoretical findings, a universal zone of anomalous enhanced electromagnetic coupling, designated as the fundamental nonlinear domain, can be defined. Since the lower boundaries of this region for all atomic matter correspond to ħω ~ 10(3) eV and I  ≈  10(16) W cm(-2), it heralds a future dominated by x-ray and γ-ray studies of all phases of matter including nuclear states. The augmented strength of the interaction with materials can be generally expressed as an increase in the basic electromagnetic coupling constant in which the fine structure constant α  →  Z(2)α, where Z denotes the number of electrons participating in an ordered response to the driving field. Since radiative conditions strongly favoring the development of this enhanced electromagnetic coupling are readily produced in self-trapped plasma channels, the processes associated with the generation of nonlinear interactions with materials stand in natural alliance with the nonlinear mechanisms that induce confined propagation. An experimental example involving the Xe (4d(10)5s(2)5p(6)) supershell for which Z  ≅  18 that falls in the specified anomalous nonlinear domain is described. This yields an effective coupling constant of Z(2)α  ≅  2.4  >  1, a magnitude comparable to the strong interaction and a value rendering as useless conventional perturbative analyses founded on an expansion in powers of α. This enhancement can be quantitatively understood as a direct consequence of the dominant role played by coherently driven multiply-excited states in the dynamics of the coupling. It is also conclusively demonstrated by an abundance of data that the utterly peerless champion of the experimental campaign leading to the definition of the fundamental nonlinear domain was excimer laser technology. The basis of this unique role was the ability to satisfy simultaneously a triplet (ω, I, P) of conditions stating the minimal values of the frequency ω, intensity I, and the power P necessary to enable the key physical processes to be experimentally observed and controllably combined. The historical confluence of these developments creates a solid foundation for the prediction of future advances in the fundamental understanding of ultra-high power density states of matter. The atomic findings graciously generalize to the composition of a nuclear stanza expressing the accessibility of the nuclear domain. With this basis serving as the launch platform, a cadenza of three grand challenge problems representing both new materials and new interactions is presented for future solution; they are (1) the performance of an experimental probe of the properties of the vacuum state associated with the dark energy at an intensity approaching the Schwinger/Heisenberg limit, (2) the attainment of amplification in the γ-ray region (~1 MeV) and the discovery of a nuclear excimer, and (3) the determination of a path to the projected super-heavy nuclear island of stability.

Blind I/Q imbalance and nonlinear ISI mitigation in Nyquist-SCM direct detection system with cascaded widely linear and Volterra equalizer

NASA Astrophysics Data System (ADS)

Liu, Na; Ju, Cheng

2018-02-01

Nyquist-SCM signal after fiber transmission, direct detection (DD), and analog down-conversion suffers from linear ISI, nonlinear ISI, and I/Q imbalance, simultaneously. Theoretical analysis based on widely linear (WL) and Volterra series is given to explain the relationship and interaction of these three interferences. A blind equalization algorithm, cascaded WL and Volterra equalizer, is designed to mitigate these three interferences. Furthermore, the feasibility of the proposed cascaded algorithm is experimentally demonstrated based on a 40-Gbps data rate 16-quadrature amplitude modulation (QAM) virtual single sideband (VSSB) Nyquist-SCM DD system over 100-km standard single mode fiber (SSMF) transmission. In addition, the performances of conventional strictly linear equalizer, WL equalizer, Volterra equalizer, and cascaded WL and Volterra equalizer are experimentally evaluated, respectively.

Laser-Matter Interaction in Dielectrics: Insight from Picosecond-Pulsed Second-Harmonic Generation in Periodically Poled LiTaO3

NASA Astrophysics Data System (ADS)

Louchev, Oleg A.; Wada, Satoshi; Panchenko, Vladislav Ya.

2017-08-01

We develop a modified two-temperature (2T) model of laser-matter interaction in dielectrics based on experimental insight from picosecond-pulsed high-frequency temperature-controlled second-harmonic (515 nm) generation in periodically poled stoichiometric LiTaO3 crystal and required for computational treatment of short-pulsed nonlinear optics and materials processing applications. We show that the incorporation of an extended set of recombination-kinetics-related energy-release and heat-exchange processes following short-pulsed photoionization by two-photon absorption of the second harmonic allows accurate simulation of the electron-lattice relaxation dynamics and electron-lattice temperature evolution in LiTaO3 crystal in nonlinear laser-frequency conversion. Our experimentally confirmed model and detailed simulation study show that two-photon ionization with the recombination mechanism via ion-electron-lattice interaction followed by a direct transfer of the recombination energy to the lattice is the main laser-matter energy-transfer pathway responsible for the majority of the crystal lattice heating (approximately 90%) continuing for approximately 50 ps after laser-pulse termination and competing with effect of electron-phonon energy transfer from the free electrons. This time delay is due to a recombination bottleneck which hinders faster relaxation to thermal equilibrium in photoionized dielectric crystal. Generally, our study suggests that in dielectrics photoionized by short-pulsed radiation with intensity range used in nonlinear laser-frequency conversion, the electron-lattice relaxation period is defined by the recombination-stage bottleneck of a few tens of picoseconds and not by the time of the electron-phonon energy transfer. This modification of the 2T model can be applied to a broad range of processes involving laser-matter interactions in dielectrics and semiconductors for charge density reaching the range of 1021- 1022 cm-3 .

Fluctuating interaction network and time-varying stability of a natural fish community

NASA Astrophysics Data System (ADS)

Ushio, Masayuki; Hsieh, Chih-Hao; Masuda, Reiji; Deyle, Ethan R.; Ye, Hao; Chang, Chun-Wei; Sugihara, George; Kondoh, Michio

2018-02-01

Ecological theory suggests that large-scale patterns such as community stability can be influenced by changes in interspecific interactions that arise from the behavioural and/or physiological responses of individual species varying over time. Although this theory has experimental support, evidence from natural ecosystems is lacking owing to the challenges of tracking rapid changes in interspecific interactions (known to occur on timescales much shorter than a generation time) and then identifying the effect of such changes on large-scale community dynamics. Here, using tools for analysing nonlinear time series and a 12-year-long dataset of fortnightly collected observations on a natural marine fish community in Maizuru Bay, Japan, we show that short-term changes in interaction networks influence overall community dynamics. Among the 15 dominant species, we identify 14 interspecific interactions to construct a dynamic interaction network. We show that the strengths, and even types, of interactions change with time; we also develop a time-varying stability measure based on local Lyapunov stability for attractor dynamics in non-equilibrium nonlinear systems. We use this dynamic stability measure to examine the link between the time-varying interaction network and community stability. We find seasonal patterns in dynamic stability for this fish community that broadly support expectations of current ecological theory. Specifically, the dominance of weak interactions and higher species diversity during summer months are associated with higher dynamic stability and smaller population fluctuations. We suggest that interspecific interactions, community network structure and community stability are dynamic properties, and that linking fluctuating interaction networks to community-level dynamic properties is key to understanding the maintenance of ecological communities in nature.

Nonlinear Bubble Dynamics And The Effects On Propagation Through Near-Surface Bubble Layers

NASA Astrophysics Data System (ADS)

Leighton, Timothy G.

2004-11-01

Nonlinear bubble dynamics are often viewed as the unfortunate consequence of having to use high acoustic pressure amplitudes when the void fraction in the near-surface oceanic bubble layer is great enough to cause severe attenuation (e.g. >50 dB/m). This is seen as unfortunate since existing models for acoustic propagation in bubbly liquids are based on linear bubble dynamics. However, the development of nonlinear models does more than just allow quantification of the errors associated with the use of linear models. It also offers the possibility of propagation modeling and acoustic inversions which appropriately incorporate the bubble nonlinearity. Furthermore, it allows exploration and quantification of possible nonlinear effects which may be exploited. As a result, high acoustic pressure amplitudes may be desirable even in low void fractions, because they offer opportunities to gain information about the bubble cloud from the nonlinearities, and options to exploit the nonlinearities to enhance communication and sonar in bubbly waters. This paper presents a method for calculating the nonlinear acoustic cross-sections, scatter, attenuations and sound speeds from bubble clouds which may be inhomogeneous. The method allows prediction of the time dependency of these quantities, both because the cloud may vary and because the incident acoustic pulse may have finite and arbitrary time history. The method can be readily adapted for bubbles in other environments (e.g. clouds of interacting bubbles, sediments, structures, in vivo, reverberant conditions etc.). The possible exploitation of bubble acoustics by marine mammals, and for sonar enhancement, is explored.

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.

Some Boussinesq Equations with Saturation

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

Christou, M. A.

2010-11-25

We investigate numerically some Boussinesq type equations with square or cubic and saturated nonlinearity. We examine the propagation, interaction and overtake interaction of soliton solutions. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the square or cubic nonlinearity without saturation. We calculate numerically the phase shift experienced by the solitons upon collision and conclude the impact of saturation.

Design optimization of single mixed refrigerant LNG process using a hybrid modified coordinate descent algorithm

NASA Astrophysics Data System (ADS)

Qyyum, Muhammad Abdul; Long, Nguyen Van Duc; Minh, Le Quang; Lee, Moonyong

2018-01-01

Design optimization of the single mixed refrigerant (SMR) natural gas liquefaction (LNG) process involves highly non-linear interactions between decision variables, constraints, and the objective function. These non-linear interactions lead to an irreversibility, which deteriorates the energy efficiency of the LNG process. In this study, a simple and highly efficient hybrid modified coordinate descent (HMCD) algorithm was proposed to cope with the optimization of the natural gas liquefaction process. The single mixed refrigerant process was modeled in Aspen Hysys® and then connected to a Microsoft Visual Studio environment. The proposed optimization algorithm provided an improved result compared to the other existing methodologies to find the optimal condition of the complex mixed refrigerant natural gas liquefaction process. By applying the proposed optimization algorithm, the SMR process can be designed with the 0.2555 kW specific compression power which is equivalent to 44.3% energy saving as compared to the base case. Furthermore, in terms of coefficient of performance (COP), it can be enhanced up to 34.7% as compared to the base case. The proposed optimization algorithm provides a deep understanding of the optimization of the liquefaction process in both technical and numerical perspectives. In addition, the HMCD algorithm can be employed to any mixed refrigerant based liquefaction process in the natural gas industry.

An interactive program for pharmacokinetic modeling.

PubMed

Lu, D R; Mao, F

1993-05-01

A computer program, PharmK, was developed for pharmacokinetic modeling of experimental data. The program was written in C computer language based on the high-level user-interface Macintosh operating system. The intention was to provide a user-friendly tool for users of Macintosh computers. An interactive algorithm based on the exponential stripping method is used for the initial parameter estimation. Nonlinear pharmacokinetic model fitting is based on the maximum likelihood estimation method and is performed by the Levenberg-Marquardt method based on chi 2 criterion. Several methods are available to aid the evaluation of the fitting results. Pharmacokinetic data sets have been examined with the PharmK program, and the results are comparable with those obtained with other programs that are currently available for IBM PC-compatible and other types of computers.

Nonlinear optical interactions in silicon waveguides

NASA Astrophysics Data System (ADS)

Kuyken, B.; Leo, F.; Clemmen, S.; Dave, U.; Van Laer, R.; Ideguchi, T.; Zhao, H.; Liu, X.; Safioui, J.; Coen, S.; Gorza, S. P.; Selvaraja, S. K.; Massar, S.; Osgood, R. M.; Verheyen, P.; Van Campenhout, J.; Baets, R.; Green, W. M. J.; Roelkens, G.

2017-03-01

The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.

Study of solar wind spectra by nonlinear waves interaction

NASA Astrophysics Data System (ADS)

Dwivedi, Navin; Sharma, Rampal; Narita, Yasuhito

2014-05-01

The nature of small-scale turbulent fluctuations in the solar wind (SW) turbulence is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations predict the evidence of the dominance of kinetic Alfvén waves (KAW) at sub-ion scales with frequency below than ion cyclotron frequency, while other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode is more relevant. In the present work, nonlinear interaction of kinetic Alfvén wave with whistler wave is considered as one of the possible cause responsible for the solar wind turbulence. A set of coupled dimensionless equations are derived for the intermediate beta plasmas and the nonlinear interaction between these two wave modes has been studied. As a consequence of ponderomotive nonlinearity, the pump KAW becomes filamented when its power exceeds the threshold for the filamentation instability. Whistler is considered to be weak and thus doesn't have enough intensity to initiate its own localization. It gets localized while propagating through the density channel created by KAW localization. In addition, spectral scales of power spectra of KAW and whistler are also calculated. The steeper spectra are found with scaling greater than -5/3. This type of nonlinear interaction between different wave modes and steeper spectra is one of the reasons for the solar wind turbulence and particles acceleration. This work is partially supported by DST (India) and FP7/STORM (313038)

On the interaction of small-scale linear waves with nonlinear solitary waves

NASA Astrophysics Data System (ADS)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow interaction in a fully nonlinear framework.

Wave-vortex interactions in the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Guo, Yuan; Bühler, Oliver

2014-02-01

This is a theoretical study of wave-vortex interaction effects in the two-dimensional nonlinear Schrödinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave-vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave-vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.

Nonlinearly stacked low noise turbofan stator

NASA Technical Reports Server (NTRS)

Schuster, William B. (Inventor); Nolcheff, Nick A. (Inventor); Gunaraj, John A. (Inventor); Kontos, Karen B. (Inventor); Weir, Donald S. (Inventor)

2009-01-01

A nonlinearly stacked low noise turbofan stator vane having a characteristic curve that is characterized by a nonlinear sweep and a nonlinear lean is provided. The stator is in an axial fan or compressor turbomachinery stage that is comprised of a collection of vanes whose highly three-dimensional shape is selected to reduce rotor-stator and rotor-strut interaction noise while maintaining the aerodynamic and mechanical performance of the vane. The nonlinearly stacked low noise turbofan stator vane reduces noise associated with the fan stage of turbomachinery to improve environmental compatibility.

Dynamic electrical impedance imaging with the interacting multiple model scheme.

PubMed

Kim, Kyung Youn; Kim, Bong Seok; Kim, Min Chan; Kim, Sin; Isaacson, David; Newell, Jonathan C

2005-04-01

In this paper, an effective dynamical EIT imaging scheme is presented for on-line monitoring of the abruptly changing resistivity distribution inside the object, based on the interacting multiple model (IMM) algorithm. The inverse problem is treated as a stochastic nonlinear state estimation problem with the time-varying resistivity (state) being estimated on-line with the aid of the IMM algorithm. In the design of the IMM algorithm multiple models with different process noise covariance are incorporated to reduce the modeling uncertainty. Simulations and phantom experiments are provided to illustrate the proposed algorithm.

Nonlinear analysis of a shock-loaded membrane.

NASA Technical Reports Server (NTRS)

Madden, R.; Remington, P. J.

1973-01-01

Results from a computer method for analyzing the unsteady interaction of a fluid stream and a flat circular elastic membrane are presented. The loading on the membrane is assumed to be caused by the firing of a shock tube. The fluid pressures and velocities are determined from a scheme based on the numerical method of characteristics, and the membrane is analyzed using exact relations for membrane strain. The interactive solution is found to give peak stresses 40% lower than a solution which assumes a pressure invariant in space and time.

SPIP: A computer program implementing the Interaction Picture method for simulation of light-wave propagation in optical fibre

NASA Astrophysics Data System (ADS)

Balac, Stéphane; Fernandez, Arnaud

2016-02-01

The computer program SPIP is aimed at solving the Generalized Non-Linear Schrödinger equation (GNLSE), involved in optics e.g. in the modelling of light-wave propagation in an optical fibre, by the Interaction Picture method, a new efficient alternative method to the Symmetric Split-Step method. In the SPIP program a dedicated costless adaptive step-size control based on the use of a 4th order embedded Runge-Kutta method is implemented in order to speed up the resolution.

Several localized waves induced by linear interference between a nonlinear plane wave and bright solitons

NASA Astrophysics Data System (ADS)

Qin, Yan-Hong; Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicates that the soliton-soliton interaction induced phase shift brings the collision between these localized waves which can be inelastic for solitons involving collision and can be elastic for breathers. These characters come from the fact that the profile of solitons depends on the relative phase between bright solitons and a plane wave, and the profile of breathers does not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Specifically, the solitons or breathers obtained here are not related to modulational instability. The underlying reasons are discussed in detail. In addition, possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.

Stabilization of business cycles of finance agents using nonlinear optimal control

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

Crystal growth and DFT insight on sodium para-nitrophenolate para-nitrophenol dihydrate single crystal for NLO applications

NASA Astrophysics Data System (ADS)

Selvakumar, S.; Boobalan, Maria Susai; Anthuvan Babu, S.; Ramalingam, S.; Leo Rajesh, A.

2016-12-01

Single crystals of sodium para-nitrophenolate para-nitrophenol dihydrate (SPPD) were grown by slow evaporation technique and its structure has been studied by FT-IR, FT-Raman and single crystal X-ray diffraction techniques. The optical and electrical properties were characterized by UV-Vis spectrum, and dielectric studies respectively. SPPD was thermally stable up to 128 °C as determined by TG-DTA curves. Using the Kurtz-Perry powder method, the second-harmonic generation efficiency was found to be five times to that of KDP. Third-order nonlinear response was studied using Z-scan technique with a He-Ne laser (632.8 nm) and NLO parameters such as intensity dependent refractive index, nonlinear absorption coefficient and third-order susceptibility were also estimated. The molecular geometry from X-ray experiment in the ground state has been compared using density functional theory (DFT) with appropriate basis set. The first-order hyperpolarizability also calculated using DFT approaches. Stability of the molecule arising from hyperconjugative interactions leading to its nonlinear optical activity and charge delocalization were analyzed using natural bond orbital technique. HOMO-LUMO energy gap value suggests the possibility of charge transfer within the molecule. Based on optimized ground state geometries, Natural bond orbital (NBO) analysis was performed to study donor-acceptor interactions.

Conditionally prepared photon and quantum imaging

NASA Astrophysics Data System (ADS)

Lvovsky, Alexander I.; Aichele, Thomas

2004-10-01

We discuss a classical model allowing one to visualize and characterize the optical mode of the single photon generated by means of a conditional measurement on a biphoton produced in parametric down-conversion. The model is based on Klyshko's advanced wave interpretation, but extends beyond it, providing a precise mathematical description of the advanced wave. The optical mode of the conditional photon is shown to be identical to the mode of the classical difference-frequency field generated due to nonlinear interaction of the partially coherent advanced wave with the pump pulse. With this "nonlinear advanced wave model" most coherence properties of the conditional photon become manifest, which permits one to intuitively understand many recent results, in particular, in quantum imaging.

Masking effects of low-frequency sinusoidal gratings on the detection of contrast modulation in high-frequency carriers

NASA Astrophysics Data System (ADS)

Henning, G. Bruce

2004-04-01

A modification and extension of Kortum and Geisler's model [Vision Res. 35, 1595 (1995)] of early visual nonlinearities that incorporates an expansive nonlinearity (consistent with neurophysiological findings [Vision Res. 35, 2725 (1995)], a normalization based on a local average retinal illumination, similar to Mach's proposal [F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, Calif., 1965)], and a subsequent compression suggested by Henning et al. [J. Opt. Soc. Am A 17, 1147 (2000)] captures a range of hitherto unexplained interactions between a sinusoidal grating of low spatial frequency and a contrast-modulated grating 2 octaves higher in spatial frequency.

An endochronic theory for transversely isotropic fibrous composites

NASA Technical Reports Server (NTRS)

Pindera, M. J.; Herakovich, C. T.

1981-01-01

A rational methodology of modelling both nonlinear and elastic dissipative response of transversely isotropic fibrous composites is developed and illustrated with the aid of the observed response of graphite-polyimide off-axis coupons. The methodology is based on the internal variable formalism employed within the text of classical irreversible thermodynamics and entails extension of Valanis' endochronic theory to transversely isotropic media. Applicability of the theory to prediction of various response characteristics of fibrous composites is illustrated by accurately modelling such often observed phenomena as: stiffening reversible behavior along fiber direction; dissipative response in shear and transverse tension characterized by power-laws with different hardening exponents; permanent strain accumulation; nonlinear unloading and reloading; and stress-interaction effects.

Three-dimensional instability of standing waves

NASA Astrophysics Data System (ADS)

Zhu, Qiang; Liu, Yuming; Yue, Dick K. P.

2003-12-01

We investigate the three-dimensional instability of finite-amplitude standing surface waves under the influence of gravity. The analysis employs the transition matrix (TM) approach and uses a new high-order spectral element (HOSE) method for computation of the nonlinear wave dynamics. HOSE is an extension of the original high-order spectral method (HOS) wherein nonlinear wave wave and wave body interactions are retained up to high order in wave steepness. Instead of global basis functions in HOS, however, HOSE employs spectral elements to allow for complex free-surface geometries and surface-piercing bodies. Exponential convergence of HOS with respect to the total number of spectral modes (for a fixed number of elements) and interaction order is retained in HOSE. In this study, we use TM-HOSE to obtain the stability of general three-dimensional perturbations (on a two-dimensional surface) on two classes of standing waves: plane standing waves in a rectangular tank; and radial/azimuthal standing waves in a circular basin. For plane standing waves, we confirm the known result of two-dimensional side-bandlike instability. In addition, we find a novel three-dimensional instability for base flow of any amplitude. The dominant component of the unstable disturbance is an oblique (standing) wave oriented at an arbitrary angle whose frequency is close to the (nonlinear) frequency of the original standing wave. This finding is confirmed by direct long-time simulations using HOSE which show that the nonlinear evolution leads to classical Fermi Pasta Ulam recurrence. For the circular basin, we find that, beyond a threshold wave steepness, a standing wave (of nonlinear frequency Omega) is unstable to three-dimensional perturbations. The unstable perturbation contains two dominant (standing-wave) components, the sum of whose frequencies is close to 2Omega. From the cases we consider, the critical wave steepness is found to generally decrease/increase with increasing radial/azimuthal mode number of the base standing wave. Finally, we show that the instability we find for both two- and three-dimensional standing waves is a result of third-order (quartet) resonance.

Advanced composites structural concepts and materials technologies for primary aircraft structures: Structural response and failure analysis

NASA Technical Reports Server (NTRS)

Dorris, William J.; Hairr, John W.; Huang, Jui-Tien; Ingram, J. Edward; Shah, Bharat M.

1992-01-01

Non-linear analysis methods were adapted and incorporated in a finite element based DIAL code. These methods are necessary to evaluate the global response of a stiffened structure under combined in-plane and out-of-plane loading. These methods include the Arc Length method and target point analysis procedure. A new interface material model was implemented that can model elastic-plastic behavior of the bond adhesive. Direct application of this method is in skin/stiffener interface failure assessment. Addition of the AML (angle minus longitudinal or load) failure procedure and Hasin's failure criteria provides added capability in the failure predictions. Interactive Stiffened Panel Analysis modules were developed as interactive pre-and post-processors. Each module provides the means of performing self-initiated finite elements based analysis of primary structures such as a flat or curved stiffened panel; a corrugated flat sandwich panel; and a curved geodesic fuselage panel. This module brings finite element analysis into the design of composite structures without the requirement for the user to know much about the techniques and procedures needed to actually perform a finite element analysis from scratch. An interactive finite element code was developed to predict bolted joint strength considering material and geometrical non-linearity. The developed method conducts an ultimate strength failure analysis using a set of material degradation models.

Interaction between two stopped light pulses

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

Chen, Yi-Hsin, E-mail: yhchen920@gmail.com; Lee, Meng-Jung, E-mail: yhchen920@gmail.com; Hung, Weilun, E-mail: yhchen920@gmail.com

The efficiency of a nonlinear optical process is proportional to the interaction time. We report a scheme of all-optical switching based on two motionless light pulses via the effect of electromagnetically induced transparency. One pulse was stopped as the stationary light pulse (SLP) and the other was stopped as stored light. The time of their interaction via the medium can be prolonged and, hence, the optical nonlinearity is greatly enhanced. Using a large optical density (OD) of 190, we achieved a very long interaction time of 6.9 μs. This can be analogous to the scheme of trapping light pulses bymore » an optical cavity with a Q factor of 8×10{sup 9}. With the approach of using moving light pulses in the best situation, a switch can only be activated at 2 photons per atomic absorption cross section. With the approach of employing a SLP and a stored light pulse, a switch at only 0.56 photons was achieved and the efficiency is significantly improved. Moreover, the simulation results are in good agreement with the experimental data and show that the efficiency can be further improved by increasing the OD of the medium. Our work advances the technology in quantum information manipulation utilizing photons.« less

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).

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Spatially Nonlinear Interdependence of Alpha-Oscillatory Neural Networks under Chan Meditation

PubMed Central

Chang, Chih-Hao

2013-01-01

This paper reports the results of our investigation of the effects of Chan meditation on brain electrophysiological behaviors from the viewpoint of spatially nonlinear interdependence among regional neural networks. Particular emphasis is laid on the alpha-dominated EEG (electroencephalograph). Continuous-time wavelet transform was adopted to detect the epochs containing substantial alpha activities. Nonlinear interdependence quantified by similarity index S(X∣Y), the influence of source signal Y on sink signal X, was applied to the nonlinear dynamical model in phase space reconstructed from multichannel EEG. Experimental group involved ten experienced Chan-Meditation practitioners, while control group included ten healthy subjects within the same age range, yet, without any meditation experience. Nonlinear interdependence among various cortical regions was explored for five local neural-network regions, frontal, posterior, right-temporal, left-temporal, and central regions. In the experimental group, the inter-regional interaction was evaluated for the brain dynamics under three different stages, at rest (stage R, pre-meditation background recording), in Chan meditation (stage M), and the unique Chakra-focusing practice (stage C). Experimental group exhibits stronger interactions among various local neural networks at stages M and C compared with those at stage R. The intergroup comparison demonstrates that Chan-meditation brain possesses better cortical inter-regional interactions than the resting brain of control group. PMID:24489583

Wavepacket dynamics in a family of nonlinear Fibonacci lattices

NASA Astrophysics Data System (ADS)

Pandey, Mohit; Campbell, David

We examine the dynamics of a quantum particle in a variety of one-dimensional Fibonacci lattices (which are shifted from each other) in the presence of interaction. To describe the nonlinear interactions we employ the discrete nonlinear Schrödinger (DNLS) equation. Using a single-site localized state in the lattice as our initial condition, we evolve the wavepacket numerically using DNLS equation. We compute the root-mean-square width of the wavepacket as it evolves in time and show how the ``global location'' of initial wavepacket affects the dynamics. We compare and contrast our results with earlier studies of related but distinct models.

Nonlinear electromagnetic interactions in energetic materials

DOE PAGES

Wood, Mitchell Anthony; Dalvit, Diego Alejandro; Moore, David Steven

2016-01-12

We study the scattering of electromagnetic waves in anisotropic energetic materials. Nonlinear light-matter interactions in molecular crystals result in frequency-conversion and polarization changes. Applied electromagnetic fields of moderate intensity can induce these nonlinear effects without triggering chemical decomposition, offering a mechanism for the nonionizing identification of explosives. We use molecular-dynamics simulations to compute such two-dimensional THz spectra for planar slabs made of pentaerythritol tetranitrate and ammonium nitrate. Finally, we discuss third-harmonic generation and polarization-conversion processes in such materials. These observed far-field spectral features of the reflected or transmitted light may serve as an alternative tool for standoff explosive detection.

Third order nonlinear phenomena in silica solid and hollow whispering gallery mode resonators

NASA Astrophysics Data System (ADS)

Farnesi, D.; Barucci, A.; Berneschi, S.; Cosi, F.; Righini, G. C.; Nunzi Conti, G.; Soria, Silvia

2016-03-01

We report efficient generation of nonlinear phenomena related to third order optical non-linear susceptibility χ(3) interactions in resonant silica microspheres and microbubbles in the regime of normal dispersion. The interactions here reported are: Stimulated Raman Scattering (SRS), and four wave mixing processes comprising Stimulated Anti-stokes Raman Scattering (SARS) and comb generation. Unusually strong anti-Stokes components and extraordinarily symmetric spectra have been observed. Resonant SARS and SRS corresponding to different Raman bands were also observed. The lack of correlation between stimulated anti-stokes and stokes scattering spectra indicates that the signal has to be resonant with the cavity.

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.

All-optical 40Gbit/s format conversion from NRZ to RZ based on SFG in a PPLN waveguide

NASA Astrophysics Data System (ADS)

Wang, Jian; Sun, Junqiang

2006-01-01

A novel all-optical 40Gbit/s NRZ-to-RZ data format conversion scheme based on sum-frequency generation (SFG) interaction in a periodically poled LiNbO 3 (PPLN) waveguide is presented for the first time, using a Mach-Zehnder interferometer (MZI). The conversion mechanism relies on the combination of attenuation and nonlinear phase shift Φ NL induced on the signal field. The performance of the conversion is numerically evaluated, with the result showing that it is more effective to yield Φ NL when appropriately phase mismatched for SFG process but Φ NL~0 when quasi-phase-matching (QPM). Compared with the cascaded second-order nonlinear interactions (SHG+DFG) with the influence of walk-off effect, a high conversion efficiency and good performance are achieved with peak power 500mw and width 2ps of the pump, which can be used in super high-speed situation (40Gbit/s and above). Finally, the inverse process of SFG and corresponding walk-off effect are analyzed and the optimum arrangement of power is proposed, showing that proper power, pump width, and waveguide length are necessary for achieving a satisfied conversion effect.

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.

2018-05-01

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

Investigation about relationships between the symmetries of ferroelectric crystal Ca0.28Ba0.72Nb2O6 and second-harmonic patterns

NASA Astrophysics Data System (ADS)

Xu, Tianxiang; Yu, Haohai; Zhang, Huaijin; Wang, Jiyang

2015-08-01

The broadband quasi-phase matching (QPM) process in a uniaxial ferroelectric crystal Ca0.28Ba0.72Nb2O6 (CBN-28) was demonstrated with the second-harmonic wavelength range from 450 nm to 650 nm, and the relationship between the symmetries of CBN-28 and the second-harmonic patterns was experimentally and theoretically investigated based on the random anti-parallel domains in the crystal and QPM conditions. The dependences of frequency-doubled patterns on the wavelength and anisotropy of the nonlinear crystal were also studied, and the frequency-doubled photons were found to be trapped on circles. By analyzing the light-matter interacting Hamiltonians, the trapping force for second-harmonic photons was found to be centripetal and tunable by the fundamental lasers, and the variation tendencies of the rotational velocity of second-harmonic generation photons could also be predicated. The results indicate that the CBN-28 ferroelectric crystal is a promising nonlinear optical material for the generation of broadband frequency-doubled waves, and the analysis on centripetal force based on the interaction Hamiltonians may provide a novel recognition for the investigation of QPM process to be further studied.

Analytical modeling of soliton interactions in a nonlocal nonlinear medium analogous to gravitational force

NASA Astrophysics Data System (ADS)

Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan

2018-01-01

We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.

Quantum corrections to the generalized Proca theory via a matter field

NASA Astrophysics Data System (ADS)

Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab

2017-09-01

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.

Nonlinear interaction of infrared waves on a VO2 surface at a semiconductor-metal phase transition

NASA Astrophysics Data System (ADS)

Berger, N. K.; Zhukov, E. A.; Novokhatskii, V. V.

1984-04-01

Nonlinear interactions (including wavefront reversal) of light from CW or pulsed 10.6-micron CO2 lasers at the semiconductor-metal phase transition in a VO2 film are investigated experimentally. The results are presented in graphs and characterized in detail. The intensity reflection coefficients of the three-wave interactions are found to be 0.5 percent for a CW reference wave of intensity 900 mW/sq cm and 42 percent for a pulsed reference wave of threshold density 600-800 microjoule/sq cm.

Light-induced valley polarization in interacting and nonlinear Weyl semimetals

NASA Astrophysics Data System (ADS)

Bertrand, Simon; Garate, Ion; Côté, René

2017-08-01

It has been recently predicted that the interplay between Coulomb interactions and Berry curvature can produce interesting optical phenomena in topologically nontrivial two-dimensional insulators. Here, we present a theory of the interband optical absorption for three-dimensional, doped Weyl semimetals. We find that the Berry curvature, Coulomb interactions, and the nonlinearity in the single-particle energy spectrum can together enable a light-induced valley polarization. We support and supplement our numerical results with an analytical toy model calculation, which unveils topologically nontrivial Mahan excitons with nonzero vorticity.

Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1983-01-01

A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.

NASA LeRC/Akron University Graduate Cooperative Fellowship Program and Graduate Student Researchers Program

NASA Technical Reports Server (NTRS)

Fertis, D. G.; Simon, A. L.

1981-01-01

The requisite methodology to solve linear and nonlinear problems associated with the static and dynamic analysis of rotating machinery, their static and dynamic behavior, and the interaction between the rotating and nonrotating parts of an engine is developed. Linear and nonlinear structural engine problems are investigated by developing solution strategies and interactive computational methods whereby the man and computer can communicate directly in making analysis decisions. Representative examples include modifying structural models, changing material, parameters, selecting analysis options and coupling with interactive graphical display for pre- and postprocessing capability.

Second order nonlinear QED processes in ultra-strong laser fields

NASA Astrophysics Data System (ADS)

Mackenroth, Felix

2017-10-01

In the interaction of ultra-intense laser fields with matter the ever increasing peak laser intensities render nonlinear QED effects ever more important. For long, ultra-intense laser pulses scattering large systems, like a macroscopic plasma, the interaction time can be longer than the scattering time, leading to multiple scatterings. These are usually approximated as incoherent cascades of single-vertex processes. Under certain conditions, however, this common cascade approximation may be insufficient, as it disregards several effects such as coherent processes, quantum interferences or pulse shape effects. Quantifying deviations of the full amplitude of multiple scatterings from the commonly employed cascade approximations is a formidable, yet unaccomplished task. In this talk we are going to discuss how to compute second order nonlinear QED amplitudes and relate them to the conventional cascade approximation. We present examples for typical second order processes and benchmark the full result against common approximations. We demonstrate that the approximation of multiple nonlinear QED scatterings as a cascade of single interactions has certain limitations and discuss these limits in light of upcoming experimental tests.

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

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

Engineering high-order nonlinear dissipation for quantum superconducting circuits

NASA Astrophysics Data System (ADS)

Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

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

PubMed

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

2000-04-15

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

Self-Consistent and Time-Dependent Solar Wind Models

NASA Technical Reports Server (NTRS)

Ong, K. K.; Musielak, Z. E.; Rosner, R.; Suess, S. T.; Sulkanen, M. E.

1997-01-01

We describe the first results from a self-consistent study of Alfven waves for the time-dependent, single-fluid magnetohydrodynamic (MHD) solar wind equations, using a modified version of the ZEUS MHD code. The wind models we examine are radially symmetrical and magnetized; the initial outflow is described by the standard Parker wind solution. Our study focuses on the effects of Alfven waves on the outflow and is based on solving the full set of the ideal nonlinear MHD equations. In contrast to previous studies, no assumptions regarding wave linearity, wave damping, and wave-flow interaction are made; thus, the models naturally account for the back-reaction of the wind on the waves, as well as for the nonlinear interaction between different types of MHD waves. Our results clearly demonstrate when momentum deposition by Alfven waves in the solar wind can be sufficient to explain the origin of fast streams in solar coronal holes; we discuss the range of wave amplitudes required to obtained such fast stream solutions.

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.

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.

Note: Nonpolar solute partial molar volume response to attractive interactions with water.

PubMed

Williams, Steven M; Ashbaugh, Henry S

2014-01-07

The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.

Note: Nonpolar solute partial molar volume response to attractive interactions with water

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

Williams, Steven M.; Ashbaugh, Henry S., E-mail: hanka@tulane.edu

2014-01-07

The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.

Principles of Nonlinear Optics

DTIC Science & Technology

1989-11-01

modelled by a ring cavity. The nonlinear meterial is between mirrors I and 2. E., E and I r E denote the incident, reflected and transmitted electric...Pasta and S. Ulam, "Studies of Nonlinear Problems I," Los Alamos Rep. LA 1940, 1955. 10. L. F. McGoldrick, "Resonant Interactions among Capillary- gravity ...34 Proc. IEEE, vol. 67, pp. 1442-1443, 1979. 23. P. P. Banerjee, A. Korpel and K. E. Lonngren," Self-refraction of Nonlinear Capillary- gravity Waves

Veering and nonlinear interactions of a clamped beam in bending and torsion

NASA Astrophysics Data System (ADS)

Ehrhardt, David A.; Hill, Thomas L.; Neild, Simon A.; Cooper, Jonathan E.

2018-03-01

Understanding the linear and nonlinear dynamic behaviour of beams is critical for the design of many engineering structures such as spacecraft antennae, aircraft wings, and turbine blades. When the eigenvalues of such structures are closely-spaced, nonlinearity may lead to interactions between the underlying linear normal modes (LNMs). This work considers a clamped-clamped beam which exhibits nonlinear behaviour due to axial tension from large amplitudes of deformation. An additional cross-beam, mounted transversely and with a movable mass at each tip, allows tuning of the primary torsion LNM such that it is close to the primary bending LNM. Perturbing the location of one mass relative to that of the other leads to veering between the eigenvalues of the bending and torsion LNMs. For a number of selected geometries in the region of veering, a nonlinear reduced order model (NLROM) is created and the nonlinear normal modes (NNMs) are used to describe the underlying nonlinear behaviour of the structure. The relationship between the 'closeness' of the eigenvalues and the nonlinear dynamic behaviour is demonstrated in the NNM backbone curves, and veering-like behaviour is observed. Finally, the forced and damped dynamics of the structure are predicted using several analytical and numerical tools and are compared to experimental measurements. As well as showing a good agreement between the predicted and measured responses, phenomena such as a 1:1 internal resonance and quasi-periodic behaviour are identified.

Semiconductor Nonlinear Dynamics Study by Broadband Terahertz Spectroscopy

NASA Astrophysics Data System (ADS)

Ho, I.-Chen

Semiconductor nonlinearity in the terahertz (THz) frequency range has been attracting considerable attention due to the recent development of high-power semiconductor-based nanodevices. However, the underlying physics concerning carrier dynamics in the presence of high-field THz transients is still obscure. This thesis introduces an ultrafast, time-resolved THz pump/THz probe approach to the study of semiconductor properties in the nonlinear regime. The carrier dynamics regarding two mechanisms, intervalley scattering and impact ionization, is observed for doped InAs on a sub-picosecond time scale. In addition, polaron modulation driven by intense THz pulses is experimentally and theoretically investigated. The observed polaron dynamics verifies the interaction between energetic electrons and a phonon field. In contrast to previous work which reports optical phonon responses, acoustic phonon modulations are addressed in this study. A further understanding of the intense field interacting with solid materials will accelerate the development of semiconductor devices. This thesis starts with the design and performance of a table-top THz spectrometer which has the advantages of ultra-broad bandwidth (one order higher bandwidth compared to a conventional ZnTe sensor) and high electric field strength (>100 kV/cm). Unlike the conventional THz time-domain spectroscopy, the spectrometer integrates a novel THz air-biased-coherent-detection (THz-ABCD) technique and utilizes selected gases as THz emitters and sensors. In comparison with commonly used electro-optic (EO) crystals or photoconductive (PC) dipole antennas, the gases have the benefits of no phonon absorption as existing in EO crystals and no carrier life time limitation as observed in PC dipole antennas. The newly development THz-ABCD spectrometer with a strong THz field strength capability provides a platform for various research topics especially on the nonlinear carrier dynamics of semiconductors. Two mechanisms, electron intervalley scattering and impact ionization of InAs crystals, are observed under the excitation of intense THz field on a sub-picosecond time scale. These two competing mechanisms are demonstrated by changing the impurity doping type of the semiconductors and varying the strength of the THz field. Another investigation of nonlinear carrier dynamics is the observation of coherent polaron oscillation in n-doped semiconductors excited by intense THz pulses. Through modulations of surface reflection with a THz pump/THz probe technique, this work experimentally verifies the interaction between energetic electrons and a phonon field, which has been theoretically predicted by previous publications, and shows that this interaction applies for the acoustic phonon modes. Usually, two transverse acoustic (2TA) phonon responses are inactive in infrared measurement, while they are detectable in second-order Raman spectroscopy. The study of polaron dynamics, with nonlinear THz spectroscopy (in the far-infrared range), provides a unique method to diagnose the overtones of 2TA phonon responses of semiconductors, and therefore incorporates the abilities of both infrared and Raman spectroscopy. This work presents a new milestone in wave-matter interaction and seeks to benefit the industrial applications in high power, small scale devices.

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

NASA Astrophysics Data System (ADS)

Gupta, Shamik

2017-10-01

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

A nonlinear analysis of the terahertz serpentine waveguide traveling-wave amplifier

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

Li, Ke, E-mail: like.3714@163.com; Cao, Miaomiao, E-mail: mona486@yeah.net; Institute of Electronics, University of Chinese Academy of Sciences, Beijing 100190

A nonlinear model for the numerical simulation of terahertz serpentine waveguide traveling-wave tube (SW-TWT) is described. In this model, the electromagnetic wave transmission in the SW is represented as an infinite set of space harmonics to interact with an electron beam. Analytical expressions for axial electric fields in axisymmetric interaction gaps of SW-TWTs are derived and compared with the results from CST simulation. The continuous beam is treated as discrete macro-particles with different initial phases. The beam-tunnel field equations, space-charge field equations, and motion equations are combined to solve the beam-wave interaction. The influence of backward wave and relativistic effectmore » is also considered in the series of equations. The nonlinear model is used to design a 340 GHz SW-TWT. Several favorable comparisons of model predictions with results from a 3-D Particle-in-cell simulation code CHIPIC are presented, in which the output power versus beam voltage and interaction periods are illustrated. The relative error of the predicted output power is less than 15% in the 3 dB bandwidth and the relative error of the saturated length is less than 8%.The results show that the 1-D nonlinear analysis model is appropriate to solve the terahertz SW-TWT operation characteristics.« less

Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.

NASA Astrophysics Data System (ADS)

Risser, Steven Michael

This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb interactions in the Huckel Hamiltonian results in calculated hyperpolarizabilities that are much larger than the experimentally determined values. Comparison of hyperpolarizabilities calculated for small benzene derivatives using both the Huckel and PPP Hamiltonians shows that inclusion of explicit Coulomb interactions is not as significant for aromatic molecules. This assertion is supported by comparison of the calculated results to the experimentally determined values. This allows for predictions of the hyperpolarizability of various liquid crystal molecules to be made.

Optimization of composite box-beam structures including effects of subcomponent interactions

NASA Technical Reports Server (NTRS)

Ragon, Scott A.; Guerdal, Zafer; Starnes, James H., Jr.

1995-01-01

Minimum mass designs are obtained for a simple box beam structure subject to bending, torque and combined bending/torque load cases. These designs are obtained subject to point strain and linear buckling constraints. The present work differs from previous efforts in that special attention is payed to including the effects of subcomponent panel interaction in the optimal design process. Two different approaches are used to impose the buckling constraints. When the global approach is used, buckling constraints are imposed on the global structure via a linear eigenvalue analysis. This approach allows the subcomponent panels to interact in a realistic manner. The results obtained using this approach are compared to results obtained using a traditional, less expensive approach, called the local approach. When the local approach is used, in-plane loads are extracted from the global model and used to impose buckling constraints on each subcomponent panel individually. In the global cases, it is found that there can be significant interaction between skin, spar, and rib design variables. This coupling is weak or nonexistent in the local designs. It is determined that weight savings of up to 7% may be obtained by using the global approach instead of the local approach to design these structures. Several of the designs obtained using the linear buckling analysis are subjected to a geometrically nonlinear analysis. For the designs which were subjected to bending loads, the innermost rib panel begins to collapse at less than half the intended design load and in a mode different from that predicted by linear analysis. The discrepancy between the predicted linear and nonlinear responses is attributed to the effects of the nonlinear rib crushing load, and the parameter which controls this rib collapse failure mode is shown to be the rib thickness. The rib collapse failure mode may be avoided by increasing the rib thickness above the value obtained from the (linear analysis based) optimizer. It is concluded that it would be necessary to include geometric nonlinearities in the design optimization process if the true optimum in this case were to be found.

ISS method for coordination control of nonlinear dynamical agents under directed topology.

PubMed

Wang, Xiangke; Qin, Jiahu; Yu, Changbin

2014-10-01

The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.

Study of Piezoelectric Vibration Energy Harvester with non-linear conditioning circuit using an integrated model

NASA Astrophysics Data System (ADS)

Manzoor, Ali; Rafique, Sajid; Usman Iftikhar, Muhammad; Mahmood Ul Hassan, Khalid; Nasir, Ali

2017-08-01

Piezoelectric vibration energy harvester (PVEH) consists of a cantilever bimorph with piezoelectric layers pasted on its top and bottom, which can harvest power from vibrations and feed to low power wireless sensor nodes through some power conditioning circuit. In this paper, a non-linear conditioning circuit, consisting of a full-bridge rectifier followed by a buck-boost converter, is employed to investigate the issues of electrical side of the energy harvesting system. An integrated mathematical model of complete electromechanical system has been developed. Previously, researchers have studied PVEH with sophisticated piezo-beam models but employed simplistic linear circuits, such as resistor, as electrical load. In contrast, other researchers have worked on more complex non-linear circuits but with over-simplified piezo-beam models. Such models neglect different aspects of the system which result from complex interactions of its electrical and mechanical subsystems. In this work, authors have integrated the distributed parameter-based model of piezo-beam presented in literature with a real world non-linear electrical load. Then, the developed integrated model is employed to analyse the stability of complete energy harvesting system. This work provides a more realistic and useful electromechanical model having realistic non-linear electrical load unlike the simplistic linear circuit elements employed by many researchers.

Local numerical modelling of ultrasonic guided waves in linear and nonlinear media

NASA Astrophysics Data System (ADS)

Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.

Modeling of Nonlinear Hydrodynamics of the Coastal Areas of the Black Sea by the Chain of the Proprietary and Open Source Models

NASA Astrophysics Data System (ADS)

Kantardgi, Igor; Zheleznyak, Mark; Demchenko, Raisa; Dykyi, Pavlo; Kivva, Sergei; Kolomiets, Pavlo; Sorokin, Maxim

2014-05-01

The nearshore hydrodynamic fields are produced by the nonlinear interactions of the shoaling waves of different time scales and currents. To simulate the wind wave and swells propagated to the coasts, wave generated near shore currents, nonlinear-dispersive wave transformation and wave diffraction in interaction with coastal and port structure, sediment transport and coastal erosion the chains of the models should be used. The objective of this presentation is to provide an overview of the results of the application of the model chains for the assessment of the wave impacts on new construction designed at the Black Sea coasts and the impacts of these constructions on the coastal erosion/ accretion processes to demonstrate needs for further development of the nonlinear models for the coastal engineering applications. The open source models Wave Watch III and SWAN has been used to simulate wave statistics of the dedicated areas of the Black Sea in high resolution to calculated the statistical parameters of the extreme wave approaching coastal zone construction in accordance with coastal engineering standards. As the main tool for the costal hydrodynamic simulations the modeling system COASTOX-MORPHO has been used, that includes the following models. HWAVE -code based on hyperbolic version of mild slope equations., HWAVE-S - spectral version of HWAVE., BOUSS-FNL - fully nonlinear system of Boussinesq equations for simulation wave nonlinear -dispersive wave transformation in coastal areas. COASTOX-CUR - the code provided the numerical solution of the Nonlinear Shallow Water Equations (NLSWE) by finite-volume methods on the unstructured grid describing the long wave transformation in the coastal zone with the efficient drying -wetting algorithms to simulate the inundation of the coastal areas including tsunami wave runup. Coastox -Cur equations with the radiation stress term calculated via near shore wave fields simulate the wave generated nearhore currents. COASTOX-SED - the module of the simulation of the sediment transport in which the suspended sediments are simulated on the basis of the solution of 2-D advection -diffusion equation and the bottom sediment transport calculations are provided the basis of a library of the most popular semi-empirical formulas. MORPH - the module of the simulation of the morphological transformation of coastal zone based on the mass balance equation, on the basis of the sediment fluxes, calculated in the SED module. MORPH management submodel is responsible for the execution of the model chain "waves- current- sediments - morphodynamics- waves". The open source model SWASH has been used to simulate nonlinear resonance phenomena in coastal waters. The model chain was applied to simulate the potential impact of the designed shore protection structures at the Sochi Olympic Park on coastal morphodynamics, the wave parameters and nonlinear oscillations in the new ports designed in Gelenddjik and Taman at North-East coast of the Black Sea. The modeling results are compared with the results of the physical modeling in the hydraulic flumes of Moscow University of Civil Engineering.

Bayesian inference of interaction properties of noisy dynamical systems with time-varying coupling: capabilities and limitations

NASA Astrophysics Data System (ADS)

Wilting, Jens; Lehnertz, Klaus

2015-08-01

We investigate a recently published analysis framework based on Bayesian inference for the time-resolved characterization of interaction properties of noisy, coupled dynamical systems. It promises wide applicability and a better time resolution than well-established methods. At the example of representative model systems, we show that the analysis framework has the same weaknesses as previous methods, particularly when investigating interacting, structurally different non-linear oscillators. We also inspect the tracking of time-varying interaction properties and propose a further modification of the algorithm, which improves the reliability of obtained results. We exemplarily investigate the suitability of this algorithm to infer strength and direction of interactions between various regions of the human brain during an epileptic seizure. Within the limitations of the applicability of this analysis tool, we show that the modified algorithm indeed allows a better time resolution through Bayesian inference when compared to previous methods based on least square fits.

Selected Problems in Nonlinear Dynamics and Sociophysics

NASA Astrophysics Data System (ADS)

Westley, Alexandra Renee

This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

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

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

Bierwage, Andreas; Shinohara, Kouji

2016-04-15

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

Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.

PubMed

Balzani, Daniel; Deparis, Simone; Fausten, Simon; Forti, Davide; Heinlein, Alexander; Klawonn, Axel; Quarteroni, Alfio; Rheinbach, Oliver; Schröder, Joerg

2016-10-01

The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

New class of turbulence in active fluids.

PubMed

Bratanov, Vasil; Jenko, Frank; Frey, Erwin

2015-12-08

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier-Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such "living fluids" that is based on the Navier-Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308-14313]. This introduces a cubic nonlinearity, related to the Toner-Tu theory of flocking, which can interact with the quadratic Navier-Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.

New class of turbulence in active fluids

PubMed Central

Bratanov, Vasil; Frey, Erwin

2015-01-01

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier–Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such “living fluids” that is based on the Navier–Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308–14313]. This introduces a cubic nonlinearity, related to the Toner–Tu theory of flocking, which can interact with the quadratic Navier–Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows. PMID:26598708

Development of non-linear models predicting daily fine particle concentrations using aerosol optical depth retrievals and ground-based measurements at a municipality in the Brazilian Amazon region

NASA Astrophysics Data System (ADS)

Gonçalves, Karen dos Santos; Winkler, Mirko S.; Benchimol-Barbosa, Paulo Roberto; de Hoogh, Kees; Artaxo, Paulo Eduardo; de Souza Hacon, Sandra; Schindler, Christian; Künzli, Nino

2018-07-01

Epidemiological studies generally use particulate matter measurements with diameter less 2.5 μm (PM2.5) from monitoring networks. Satellite aerosol optical depth (AOD) data has considerable potential in predicting PM2.5 concentrations, and thus provides an alternative method for producing knowledge regarding the level of pollution and its health impact in areas where no ground PM2.5 measurements are available. This is the case in the Brazilian Amazon rainforest region where forest fires are frequent sources of high pollution. In this study, we applied a non-linear model for predicting PM2.5 concentration from AOD retrievals using interaction terms between average temperature, relative humidity, sine, cosine of date in a period of 365,25 days and the square of the lagged relative residual. Regression performance statistics were tested comparing the goodness of fit and R2 based on results from linear regression and non-linear regression for six different models. The regression results for non-linear prediction showed the best performance, explaining on average 82% of the daily PM2.5 concentrations when considering the whole period studied. In the context of Amazonia, it was the first study predicting PM2.5 concentrations using the latest high-resolution AOD products also in combination with the testing of a non-linear model performance. Our results permitted a reliable prediction considering the AOD-PM2.5 relationship and set the basis for further investigations on air pollution impacts in the complex context of Brazilian Amazon Region.

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.

Modeling of Tool-Tissue Interactions for Computer-Based Surgical Simulation: A Literature Review

PubMed Central

Misra, Sarthak; Ramesh, K. T.; Okamura, Allison M.

2009-01-01

Surgical simulators present a safe and potentially effective method for surgical training, and can also be used in robot-assisted surgery for pre- and intra-operative planning. Accurate modeling of the interaction between surgical instruments and organs has been recognized as a key requirement in the development of high-fidelity surgical simulators. Researchers have attempted to model tool-tissue interactions in a wide variety of ways, which can be broadly classified as (1) linear elasticity-based, (2) nonlinear (hyperelastic) elasticity-based finite element (FE) methods, and (3) other techniques that not based on FE methods or continuum mechanics. Realistic modeling of organ deformation requires populating the model with real tissue data (which are difficult to acquire in vivo) and simulating organ response in real time (which is computationally expensive). Further, it is challenging to account for connective tissue supporting the organ, friction, and topological changes resulting from tool-tissue interactions during invasive surgical procedures. Overcoming such obstacles will not only help us to model tool-tissue interactions in real time, but also enable realistic force feedback to the user during surgical simulation. This review paper classifies the existing research on tool-tissue interactions for surgical simulators specifically based on the modeling techniques employed and the kind of surgical operation being simulated, in order to inform and motivate future research on improved tool-tissue interaction models. PMID:20119508

Perturbative and Ab-Initio Calculations of Electrical Susceptibilities of Atoms

NASA Astrophysics Data System (ADS)

Spott, Andrew

Perturbative nonlinear optics consists of many powerful predictive theoretical methods, including the perturbative series of observables related to the interaction of light with matter. The light intensity limits of such series have been studied in the past for highly nonlinear processes such as above threshold ionization and high harmonic generation. A more recent debate focuses on the limits of applicability of perturbation theory for the nonlinear electrical susceptibility and the nonlinear index of refraction of atoms, which are important parameters to study, for example, for filamentation of laser pulses in nonlinear media. In this thesis we analyze theoretical predictions for the electrical susceptibility of atoms for the transition from the perturbative to the nonperturbative intensity regime. To this end, we apply a numerical basis state method that allows us to perform respective calculations in the framework of perturbation theory as well as using ab-initio methods. The results let us identify the intensity at which the application of perturbation theory breaks down. Furthermore, we provide an analysis of the nonlinear susceptibility as a function of time during the interaction with the laser pulse and find that theoretical predictions are in good agreement with recent experimental data.

Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids.

PubMed

Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A

2003-06-01

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

PubMed

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

NASA Astrophysics Data System (ADS)

Whelan, G. G.; Pueschel, M. J.; Terry, P. W.

2018-04-01

The physical causes for the strong stabilizing effect of finite plasma β on ion-temperature-gradient-driven turbulence, which far exceeds quasilinear estimates, are identified from nonlinear gyrokinetic simulations. The primary contribution stems from a resonance of frequencies in the dominant nonlinear interaction between the unstable mode, the stable mode, and zonal flows, which maximizes the triplet correlation time and therefore the energy transfer efficiency. A modification to mixing-length transport estimates is constructed, which reproduces nonlinear heat fluxes throughout the examined β range.

Breathers in systems with intrinsic and extrinsic nonlinearities

NASA Astrophysics Data System (ADS)

Cruzeiro-Hansson, L.; Eilbeck, J. C.; Marín, J. L.; Russell, F. M.

2000-08-01

We study the interplay between nonlinearity and localization in a model consisting of a quantum quasiparticle interacting with a nonlinear extended lattice. The isolated lattice can support discrete breathers, and the coupling of the quasiparticle to the lattice leads to localized quasiparticle states. Minimum energy states of the full system can have both a breather and a solitonic character. Excited states lead to interesting new phenomena, such as full breather states, which arise from the combination of intrinsic and extrinsic nonlinearity.

Nonlinear interaction and wave breaking with a submerged porous structure

NASA Astrophysics Data System (ADS)

Hsieh, Chih-Min; Sau, Amalendu; Hwang, Robert R.; Yang, W. C.

2016-12-01

Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ɛ turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold "clockwise" and "anticlockwise" rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.

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

NASA Astrophysics Data System (ADS)

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

2006-02-01

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

All-optical simultaneous multichannel quadrature phase shift keying signal regeneration based on phase-sensitive amplification

NASA Astrophysics Data System (ADS)

Wang, Hongxiang; Wang, Qi; Bai, Lin; Ji, Yuefeng

2018-01-01

A scheme is proposed to realize the all-optical phase regeneration of four-channel quadrature phase shift keying (QPSK) signal based on phase-sensitive amplification. By utilizing conjugate pump and common pump in a highly nonlinear optical fiber, degenerate four-wave mixing process is observed, and QPSK signals are regenerated. The number of waves is reduced to decrease the cross talk caused by undesired nonlinear interaction during the coherent superposition process. In addition, to avoid the effect of overlapping frequency, frequency spans between pumps and signals are set to be nonintegral multiples. Optical signal-to-noise ratio improvement is validated by bit error rate measurements. Compared with single-channel regeneration, multichannel regeneration brings 0.4-dB OSNR penalty when the value of BER is 10-3, which shows the cross talk in regeneration process is negligible.

Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System

NASA Technical Reports Server (NTRS)

Rizvi, Farheen; Weitl, Raquel M.

2011-01-01

The Cassini spacecraft dynamics-related telemetry during long Main Engine (ME) burns has indicated the presence of stable limit cycles between 0.03-0.04 Hz frequencies. These stable limit cycles cause the spacecraft to possess non-zero oscillating rates for extended periods of time. This indicates that the linear ME guidance control system does not model the complete dynamics of the spacecraft. In this study, we propose that the observed limit cycles in the spacecraft dynamics telemetry appear from a stable interaction between the unmodeled nonlinear elements in the ME guidance control system. Many nonlinearities in the control system emerge from translating the linear engine gimbal actuator (EGA) motion into a spacecraft rotation. One such nonlinearity comes from the gear backlash in the EGA system, which is the focus of this paper. The limit cycle characteristics and behavior can be predicted by modeling this gear backlash nonlinear element via a describing function and studying the interaction of this describing function with the overall dynamics of the spacecraft. The linear ME guidance controller and gear backlash nonlinearity are modeled analytically. The frequency, magnitude, and nature of the limit cycle are obtained from the frequency response of the ME guidance controller and nonlinear element. In addition, the ME guidance controller along with the nonlinearity is simulated. The simulation response contains a limit cycle with similar characterstics as predicted analytically: 0.03-0.04 Hz frequency and stable, sustained oscillations. The analytical and simulated limit cycle responses are compared to the flight telemetry for long burns such as the Saturn Orbit Insertion and Main Engine Orbit Trim Maneuvers. The analytical and simulated limit cycle characteristics compare well with the actual observed limit cycles in the flight telemetry. Both have frequencies between 0.03-0.04 Hz and stable oscillations. This work shows that the stable limit cycles occur due to the interaction between the unmodeled nonlinear elements and linear ME guidance controller.

Nonlinear light-matter interactions in engineered optical media

NASA Astrophysics Data System (ADS)

Litchinitser, Natalia

In this talk, we consider fundamental optical phenomena at the interface of nonlinear and singular optics in artificial media, including theoretical and experimental studies of linear and nonlinear light-matter interactions of vector and singular optical beams in metamaterials. We show that unique optical properties of metamaterials open unlimited prospects to ``engineer'' light itself. Thanks to their ability to manipulate both electric and magnetic field components, metamaterials open new degrees of freedom for tailoring complex polarization states and orbital angular momentum (OAM) of light. We will discuss several approaches to structured light manipulation on the nanoscale using metal-dielectric, all-dielectric and hyperbolic metamaterials. These new functionalities, including polarization and OAM conversion, beam magnification and de-magnification, and sub-wavelength imaging using novel non-resonant hyperlens are likely to enable a new generation of on-chip or all-fiber structured light applications. The emergence of metamaterials also has a strong potential to enable a plethora of novel nonlinear light-matter interactions and even new nonlinear materials. In particular, nonlinear focusing and defocusing effects are of paramount importance for manipulation of the minimum focusing spot size of structured light beams necessary for nanoscale trapping, manipulation, and fundamental spectroscopic studies. Colloidal suspensions offer as a promising platform for engineering polarizibilities and realization of large and tunable nonlinearities. We will present our recent studies of the phenomenon of spatial modulational instability leading to laser beam filamentation in an engineered soft-matter nonlinear medium. Finally, we introduce so-called virtual hyperbolic metamaterials formed by an array of plasma channels in air as a result of self-focusing of an intense laser pulse, and show that such structure can be used to manipulate microwave beams in a free space. This work was supported by the Army Research Office Awards (W911NF-15-1-0146, W911NF-11-1-0297).

Sorption of selected organic compounds from water to a peat soil and its humic-acid and humin fractions: Potential sources of the sorption nonlinearity

USGS Publications Warehouse

Chiou, C.T.; Kile, D.E.; Rutherford, D.W.; Sheng, G.; Boyd, S.A.

2000-01-01

The sorption isotherms of ethylene dibromide (EDB), diuron (DUN), and 3,5-dichlorophenol (DCP) from water on the humic acid and humin fractions of a peat soil and on the humic-acid of a muck soil have been measured. The data were compared with those of the solutes with the whole peat from which the humic-acid (HA) and humin (HM) fractions were derived and on which the sorption of the solutes exhibited varying extents of nonlinear capacities at low relative concentrations (C(e)/S(w)). The HA fraction as prepared by the density-fractionated method is relatively pure and presumably free of high- surface-area carbonaceous material (HSACM) that is considered to be responsible for the observed nonlinear sorption for nonpolar solutes (e.g., EDB) on the peat; conversely, the base-insoluble HM fraction as prepared is presumed to be enriched with HSACM, as manifested by the greatly higher BET- (N2) surface area than that of the whole peat. The sorption of EDB on HA exhibits no visible nonlinear effect, whereas the sorption on HM shows an enhanced nonlinearity over that on the whole peat. The sorption of polar DUN and DCP on HA and HM display nonlinear effects comparable with those on the whole peat; the effects are much more significant than those with nonpolar EDB. These results conform to the hypothesis that adsorption onto a small amount of strongly adsorbing HSACM is largely responsible for the nonlinear sorption of nonpolar solutes on soils and that additional specific interactions with the active groups of soil organic matter are responsible for the generally higher nonlinear sorption of the polar solutes.

Nonlinear Relaxation in Population Dynamics

NASA Astrophysics Data System (ADS)

Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Interactions of localized wave structures and dynamics in the defocusing coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong

2017-04-01

We investigate the defocusing coupled nonlinear Schrödinger equations from a 3×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.

Nonlinear cavity optomechanics with nanomechanical thermal fluctuations

PubMed Central

Leijssen, Rick; La Gala, Giada R.; Freisem, Lars; Muhonen, Juha T.; Verhagen, Ewold

2017-01-01

Although the interaction between light and motion in cavity optomechanical systems is inherently nonlinear, experimental demonstrations to date have allowed a linearized description in all except highly driven cases. Here, we demonstrate a nanoscale optomechanical system in which the interaction between light and motion is so large (single-photon cooperativity C0≈103) that thermal motion induces optical frequency fluctuations larger than the intrinsic optical linewidth. The system thereby operates in a fully nonlinear regime, which pronouncedly impacts the optical response, displacement measurement and radiation pressure backaction. Specifically, we measure an apparent optical linewidth that is dominated by thermo-mechanically induced frequency fluctuations over a wide temperature range, and show that in this regime thermal displacement measurements cannot be described by conventional analytical models. We perform a proof-of-concept demonstration of exploiting the nonlinearity to conduct sensitive quadratic readout of nanomechanical displacement. Finally, we explore how backaction in this regime affects the mechanical fluctuation spectra. PMID:28685755

Nonlinear two-dimensional terahertz photon echo and rotational spectroscopy in the gas phase.

PubMed

Lu, Jian; Zhang, Yaqing; Hwang, Harold Y; Ofori-Okai, Benjamin K; Fleischer, Sharly; Nelson, Keith A

2016-10-18

Ultrafast 2D spectroscopy uses correlated multiple light-matter interactions for retrieving dynamic features that may otherwise be hidden under the linear spectrum; its extension to the terahertz regime of the electromagnetic spectrum, where a rich variety of material degrees of freedom reside, remains an experimental challenge. We report a demonstration of ultrafast 2D terahertz spectroscopy of gas-phase molecular rotors at room temperature. Using time-delayed terahertz pulse pairs, we observe photon echoes and other nonlinear signals resulting from molecular dipole orientation induced by multiple terahertz field-dipole interactions. The nonlinear time domain orientation signals are mapped into the frequency domain in 2D rotational spectra that reveal J-state-resolved nonlinear rotational dynamics. The approach enables direct observation of correlated rotational transitions and may reveal rotational coupling and relaxation pathways in the ground electronic and vibrational state.

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.

Substrate clamping effects on irreversible domain wall dynamics in lead zirconate titanate thin films.

PubMed

Griggio, F; Jesse, S; Kumar, A; Ovchinnikov, O; Kim, H; Jackson, T N; Damjanovic, D; Kalinin, S V; Trolier-McKinstry, S

2012-04-13

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.

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.

Localized states and their stability in an anharmonic medium with a nonlinear defect

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

Gerasimchuk, I. V., E-mail: igor.gera@gmail.com

2015-10-15

A comprehensive analysis of soliton states localized near a plane defect (a defect layer) possessing nonlinear properties is carried out within a quasiclassical approach for different signs of nonlinearity of the medium and different characters of interaction of elementary excitations of the medium with the defect. A quantum interpretation is given to these nonlinear localized modes as a bound state of a large number of elementary excitations. The domains of existence of such states are determined, and their properties are analyzed as a function of the character of interaction of elementary excitations between each other and with the defect. Amore » full analysis of the stability of all the localized states with respect to small perturbations of amplitude and phase is carried out analytically, and the frequency of small oscillations of the state localized on the defect is determined.« less

Giant Kerr response of ultrathin gold films from quantum size effect.

PubMed

Qian, Haoliang; Xiao, Yuzhe; Liu, Zhaowei

2016-10-10

With the size of plasmonic devices entering into the nanoscale region, the impact of quantum physics needs to be considered. In the past, the quantum size effect on linear material properties has been studied extensively. However, the nonlinear aspects have not been explored much so far. On the other hand, much effort has been put into the field of integrated nonlinear optics and a medium with large nonlinearity is desirable. Here we study the optical nonlinear properties of a nanometre scale gold quantum well by using the z-scan method and nonlinear spectrum broadening technique. The quantum size effect results in a giant optical Kerr susceptibility, which is four orders of magnitude higher than the intrinsic value of bulk gold and several orders larger than traditional nonlinear media. Such high nonlinearity enables efficient nonlinear interaction within a microscopic footprint, making quantum metallic films a promising candidate for integrated nonlinear optical applications.

Interaction between Liénard and Ikeda dynamics in a nonlinear electro-optical oscillator with delayed bandpass feedback.

PubMed

Marquez, Bicky A; Larger, Laurent; Brunner, Daniel; Chembo, Yanne K; Jacquot, Maxime

2016-12-01

We report on experimental and theoretical analysis of the complex dynamics generated by a nonlinear time-delayed electro-optic bandpass oscillator. We investigate the interaction between the slow- and fast-scale dynamics of autonomous oscillations in the breather regime. We analyze in detail the coupling between the fast-scale behavior associated to a characteristic low-pass Ikeda behavior and the slow-scale dynamics associated to a Liénard limit-cycle. Finally, we show that when projected onto a two-dimensional phase space, the attractors corresponding to periodic and chaotic breathers display a spiral-like pattern, which strongly depends on the shape of the nonlinear function.

Hopfield-Kerr model and analogue black hole radiation in dielectrics

NASA Astrophysics Data System (ADS)

Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M.

2017-11-01

In the context of the interaction between the electromagnetic field and a dielectric dispersive lossless medium, we present a nonlinear version of the relativistically covariant Hopfield model, which is suitable for the description of a dielectric Kerr perturbation propagating in a dielectric medium. The nonlinearity is introduced in the Lagrangian through a self-interacting term proportional to the fourth power of the polarization field. We find an exact solution for the nonlinear equations describing a propagating perturbation in the dielectric medium. Furthermore, the presence of an analogue Hawking effect, as well as the thermal properties of the model, are discussed, confirming and improving the results achieved in the scalar case.

Verification of nonlinear dynamic structural test results by combined image processing and acoustic analysis

NASA Astrophysics Data System (ADS)

Tene, Yair; Tene, Noam; Tene, G.

1993-08-01

An interactive data fusion methodology of video, audio, and nonlinear structural dynamic analysis for potential application in forensic engineering is presented. The methodology was developed and successfully demonstrated in the analysis of heavy transportable bridge collapse during preparation for testing. Multiple bridge elements failures were identified after the collapse, including fracture, cracks and rupture of high performance structural materials. Videotape recording by hand held camcorder was the only source of information about the collapse sequence. The interactive data fusion methodology resulted in extracting relevant information form the videotape and from dynamic nonlinear structural analysis, leading to full account of the sequence of events during the bridge collapse.

Vibron Solitons and Soliton-Induced Infrared Spectra of Crystalline Acetanilide

NASA Astrophysics Data System (ADS)

Takeno, S.

1986-01-01

Red-shifted infrared spectra at low temperatures of amide I (C=O stretching) vibrations of crystalline acetanilide measured by Careri et al. are shown to be due to vibron solitons, which are nonlinearity-induced localized modes of vibrons arising from their nonlinear interactions with optic-type phonons. A nonlinear eigenvalue equation giving the eigenfrequency of stationary solitons is solved approximately by introducing lattice Green's functions, and the obtained result is in good agreement with the experimental result. Inclusion of interactions with acoustic phonons yields the Debye-Waller factor in the zero-phonon line spectrum of vibron solitons, in a manner analogous to the case of impurity-induced localized harmonic phonon modes in alkali halides.

User's manual for interactive LINEAR: A FORTRAN program to derive linear aircraft models

NASA Technical Reports Server (NTRS)

Antoniewicz, Robert F.; Duke, Eugene L.; Patterson, Brian P.

1988-01-01

An interactive FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models is documented in this report. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.

Nonlinear dynamics of toroidal Alfvén eigenmodes in presence of tearing modes

NASA Astrophysics Data System (ADS)

Zhu, Jia; Ma, Zhiwei; Wang, Sheng; Zhang, Wei

2016-10-01

A new hybrid kinetic-MHD code CLT-K is developed to study nonlinear dynamics of n =1 toroidal Alfvén eigenmodes (TAEs) with the m/n =2/1 tearing mode. It is found that the n =1 TAE is first excited by isotropic energetic particles in the earlier stage and reaches the steady state due to wave-particle interaction. After the saturation of the n =1 TAE, the tearing mode intervenes and triggers the second growth of the mode. The modes goes into the second steady state due to multiple tearing mode-mode nonlinear coupling. Both wave-particle and wave-wave interactions are observed in our hybrid simulation.

Nonlinear quantum Rabi model in trapped ions

NASA Astrophysics Data System (ADS)

Cheng, Xiao-Hang; Arrazola, Iñigo; Pedernales, Julen S.; Lamata, Lucas; Chen, Xi; Solano, Enrique

2018-02-01

We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a blockade on the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We propose to use this blockade as a resource for the dissipative generation of high-number Fock states. Also, we compare the linear and nonlinear cases of the quantum Rabi model in the ultrastrong and deep strong-coupling regimes. Moreover, we propose a scheme to simulate the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red- and blue-sideband interactions in a single trapped ion, yielding applications as a dynamical quantum filter.

Simulations of heart valves by thin shells with non-linear material properties

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez; Hedayat, Mohammadali

2016-11-01

The primary function of a heart valve is to allow blood to flow in only one direction through the heart. Triangular thin-shell finite element formulation is implemented, which considers only translational degrees of freedom, in three-dimensional domain to simulate heart valves undergoing large deformations. The formulation is based on the nonlinear Kirchhoff thin-shell theory. The developed method is intensively validated against numerical and analytical benchmarks. This method is added to previously developed membrane method to obtain more realistic results since ignoring bending forces can results in unrealistic wrinkling of heart valves. A nonlinear Fung-type constitutive relation, based on experimentally measured biaxial loading tests, is used to model the material properties for response of the in-plane motion in heart valves. Furthermore, the experimentally measured liner constitutive relation is used to model the material properties to capture the flexural motion of heart valves. The Fluid structure interaction solver adopts a strongly coupled partitioned approach that is stabilized with under-relaxation and the Aitken acceleration technique. This work was supported by American Heart Association (AHA) Grant 13SDG17220022 and the Center of Computational Research (CCR) of University at Buffalo.

Nonlinear optical response in a zincblende GaN cylindrical quantum dot with donor impurity center

NASA Astrophysics Data System (ADS)

Hoyos, Jaime H.; Correa, J. D.; Mora-Ramos, M. E.; Duque, C. A.

2016-03-01

We calculate the nonlinear optical absorption coefficient of a cylindrical zincblende GaN-based quantum dot. For this purpose, we consider Coulomb interactions between electrons and an impurity ionized donor atom. The electron-donor-impurity spectrum and the associated quantum states are calculated using the effective mass approximation with a parabolic potential energy model describing both the radial and axial electron confinement. We also include the effects of the hydrostatic pressure and external electrostatic fields. The energy spectrum is obtained through an expansion of the eigenstates as a linear combination of Gaussian-type functions which reduces the computational effort since all the matrix elements are obtained analytically. Therefore, the numerical problem is reduced to the direct diagonalization of the Hamiltonian. The obtained energies are used in the evaluation of the dielectric susceptibility and the nonlinear optical absorption coefficient within a modified two-level approach in a rotating wave approximation. This quantity is investigated as a function of the quantum dot dimensions, the impurity position, the external electric field intensity and the hydrostatic pressure. The results of this research could be important in the design and fabrication of zincblende GaN-quantum-dot-based electro-optical devices.

Linear Mechanisms and Pressure Fluctuations in Wall Turbulence

NASA Astrophysics Data System (ADS)

Septham, Kamthon; Morrison, Jonathan

2014-11-01

Full-domain, linear feedback control of turbulent channel flow at Reτ <= 400 via vU' at low wavenumbers is an effective method to attenuate turbulent channel flow such that it is relaminarised. The passivity-based control approach is adopted and explained by the conservative characteristics of the nonlinear terms contributing to the Reynolds-Orr equation (Sharma et al .Phys .Fluids 2011). The linear forcing acts on the wall-normal velocity field and thus the pressure field via the linear (rapid) source term of the Poisson equation for pressure fluctuations, 2U'∂v/∂x . The minimum required spanwise wavelength resolution without losing control is constant at λz+ = 125, based on the wall friction velocity at t = 0 . The result shows that the maximum forcing is located at y+ ~ 20 , corresponding to the location of the maximum in the mean-square pressure gradient. The effectiveness of linear control is qualitatively explained by Landahl's theory for timescales, in that the control proceeds via the shear interaction timescale which is much shorter than both the nonlinear and viscous timescales. The response of the rapid (linear) and slow (nonlinear) pressure fluctuations to the linear control is examined and discussed.

Strong terahertz radiation from relativistic laser interaction with solid density plasmas

NASA Astrophysics Data System (ADS)

Li, Y. T.; Li, C.; Zhou, M. L.; Wang, W. M.; Du, F.; Ding, W. J.; Lin, X. X.; Liu, F.; Sheng, Z. M.; Peng, X. Y.; Chen, L. M.; Ma, J. L.; Lu, X.; Wang, Z. H.; Wei, Z. Y.; Zhang, J.

2012-06-01

We report a plasma-based strong THz source generated in intense laser-solid interactions at relativistic intensities >1018 W/cm2. Energies up to 50 μJ/sr per THz pulse is observed when the laser pulses are incident onto a copper foil at 67.5°. The temporal properties of the THz radiation are measured by a single shot, electro-optic sampling method with a chirped laser pulse. The THz radiation is attributed to the self-organized transient fast electron currents formed along the target surface. Such a source allows potential applications in THz nonlinear physics and provides a diagnostic of transient currents generated in intense laser-solid interactions.