Phase Equilibrium and Crystal Growth Studies on AgGaSe2 and Related Nonlinear Optical Materials

DTIC Science & Technology

1989-09-01

identify by block number) IELD GROUP SUB-GROUP - "°Silver selenogallate, AgGaSe2, nonlinear optical materials, infrared materials, optical defects 19...materials has unique nonlinear infrared optical properties( 1-4 ) including high nonlinear coefficients, and the ability to be phase matched through a...have a milky appearance in thin section or when viewed with a commercial infrared image converter. Microscopic examination of AgGaSe2 in both reflected

Recent advances in reduction methods for nonlinear problems. [in structural mechanics

NASA Technical Reports Server (NTRS)

Noor, A. K.

1981-01-01

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

Geographical variation of cerebrovascular disease in New York State: the correlation with income

PubMed Central

Han, Daikwon; Carrow, Shannon S; Rogerson, Peter A; Munschauer, Frederick E

2005-01-01

Background Income is known to be associated with cerebrovascular disease; however, little is known about the more detailed relationship between cerebrovascular disease and income. We examined the hypothesis that the geographical distribution of cerebrovascular disease in New York State may be predicted by a nonlinear model using income as a surrogate socioeconomic risk factor. Results We used spatial clustering methods to identify areas with high and low prevalence of cerebrovascular disease at the ZIP code level after smoothing rates and correcting for edge effects; geographic locations of high and low clusters of cerebrovascular disease in New York State were identified with and without income adjustment. To examine effects of income, we calculated the excess number of cases using a non-linear regression with cerebrovascular disease rates taken as the dependent variable and income and income squared taken as independent variables. The resulting regression equation was: excess rate = 32.075 - 1.22*10-4(income) + 8.068*10-10(income2), and both income and income squared variables were significant at the 0.01 level. When income was included as a covariate in the non-linear regression, the number and size of clusters of high cerebrovascular disease prevalence decreased. Some 87 ZIP codes exceeded the critical value of the local statistic yielding a relative risk of 1.2. The majority of low cerebrovascular disease prevalence geographic clusters disappeared when the non-linear income effect was included. For linear regression, the excess rate of cerebrovascular disease falls with income; each $10,000 increase in median income of each ZIP code resulted in an average reduction of 3.83 observed cases. The significant nonlinear effect indicates a lessening of this income effect with increasing income. Conclusion Income is a non-linear predictor of excess cerebrovascular disease rates, with both low and high observed cerebrovascular disease rate areas associated with higher income. Income alone explains a significant amount of the geographical variance in cerebrovascular disease across New York State since both high and low clusters of cerebrovascular disease dissipate or disappear with income adjustment. Geographical modeling, including non-linear effects of income, may allow for better identification of other non-traditional risk factors. PMID:16242043

A novel structure photonic crystal fiber based on bismuth-oxide for optical parametric amplification

NASA Astrophysics Data System (ADS)

Jin, Cang; Yuan, Jinhui; Yu, Chongxiu

2010-11-01

The heavy metal oxide glasses containing bismuth such as bismuth sesquioxide show unique high refractive index. In addition, the bismuth-oxide based glass does not include toxic elements such as Pb, As, Se, Te, and exhibits well chemical, mechanical and thermal stability. Hence, it is used to fabricate high nonlinear fiber for nonlinear optical application. Although the bismuth-oxide based high nonlinear fiber can be fusion-spliced to conventional silica fibers and have above advantages, yet it suffers from large group velocity dispersion because of material chromatic dispersion which restricts its utility. In regard to this, the micro-structure was introduced to adjust the dispersion of bismuth-oxide high nonlinear fiber in the 1550nm wave-band. In this paper, a hexagonal solid-core micro-structure is developed to balance its dispersion and nonlinearity. Our simulation and calculation results show that the bismuth-oxide based photonic crystal fiber has near zero dispersion around 1550nm where the optical parametric amplification suitable wavelength is. Its dispersion slop in the communication wavelength range is also relatively flat. Moreover, both nonlinear coefficient and model filed distribution were simulated, respectively.

Multi-application controls: Robust nonlinear multivariable aerospace controls applications

NASA Technical Reports Server (NTRS)

Enns, Dale F.; Bugajski, Daniel J.; Carter, John; Antoniewicz, Bob

1994-01-01

This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented as a method for analyzing robust performance and the mu-synthesis method will be presented as a method for synthesizing a robust control system. The paper concludes with the author's expectations regarding future applications of robust nonlinear multivariable controls.

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

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

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

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

2016-06-15

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

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

DOE PAGES

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

2016-04-04

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

Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber.

PubMed

Ta'eed, Vahid G; Fu, Libin; Pelusi, Mark; Rochette, Martin; Littler, Ian C; Moss, David J; Eggleton, Benjamin J

2006-10-30

We present the first demonstration of all optical wavelength conversion in chalcogenide glass fiber including system penalty measurements at 10 Gb/s. Our device is based on As2Se3 chalcogenide glass fiber which has the highest Kerr nonlinearity (n(2)) of any fiber to date for which either advanced all optical signal processing functions or system penalty measurements have been demonstrated. We achieve wavelength conversion via cross phase modulation over a 10 nm wavelength range near 1550 nm with 7 ps pulses at 2.1 W peak pump power in 1 meter of fiber, achieving only 1.4 dB excess system penalty. Analysis and comparison of the fundamental fiber parameters, including nonlinear coefficient, two-photon absorption coefficient and dispersion parameter with other nonlinear glasses shows that As(2)Se(3) based devices show considerable promise for radically integrated nonlinear signal processing devices.

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.

Study of Nonlinear Propagation of Ultrashort Laser Pulses and Its Application to Harmonic Generation

NASA Astrophysics Data System (ADS)

Weerawarne, Darshana L.

Laser filamentation, which is one of the exotic nonlinear optical phenomena, is self-guidance of high-power laser beams due to the dynamic balance between the optical Kerr effect (self-focusing) and other nonlinear effects such as plasma defocusing. It has many applications including supercontinuum generation (SCG), high-order harmonic generation (HHG), lightning guiding, stand-off sensing, and rain making. The main focus of this work is on studying odd-order harmonic generation (HG) (i.e., 3o, 5o, 7o, etc., where o is the angular frequency) in centrosymmetric media while a high-power, ultrashort harmonic-driving pulse undergoes nonlinear propagation such as laser filamentation. The investigation of highly-controversial nonlinear indices of refraction by measuring low-order HG in air is carried out. Furthermore, time-resolved (i.e., pump-probe) experiments and significant harmonic enhancements are presented and a novel HG mechanism based on higher-order nonlinearities is proposed to explain the experimental results. C/C++ numerical simulations are used to solve the nonlinear Schrodinger equation (NLSE) which supports the experimental findings. Another project which I have performed is selective sintering using lasers. Short-pulse lasers provide a fascinating tool for material processing, especially when the conventional oven-based techniques fail to process flexible materials for smart energy/electronics applications. I present experimental and theoretical studies on laser processing of nanoparticle-coated flexible materials, aiming to fabricate flexible electronic devices.

Transonic Flow Computations Using Nonlinear Potential Methods

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Kwak, Dochan (Technical Monitor)

2000-01-01

This presentation describes the state of transonic flow simulation using nonlinear potential methods for external aerodynamic applications. The presentation begins with a review of the various potential equation forms (with emphasis on the full potential equation) and includes a discussion of pertinent mathematical characteristics and all derivation assumptions. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, is discussed. Key characteristics of all numerical algorithm types used for solving nonlinear potential equations, including steady, unsteady, space marching, and design methods, are described. Both spatial discretization and iteration scheme characteristics are examined. Numerical results for various aerodynamic applications are included throughout the presentation to highlight key discussion points. The presentation ends with concluding remarks and recommendations for future work. Overall. nonlinear potential solvers are efficient, highly developed and routinely used in the aerodynamic design environment for cruise conditions. Published by Elsevier Science Ltd. All rights reserved.

Parametric Study on the Response of Compression-Loaded Composite Shells With Geometric and Material Imperfections

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Starnes, James H., Jr.

2004-01-01

The results of a parametric study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thinwalled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The imperfections considered include initial geometric shell-wall midsurface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these imperfections on the nonlinear responses and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable response characteristics.

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.

Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

NASA Astrophysics Data System (ADS)

Yao, Jianyong

2018-06-01

Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

The dissipation of electromagnetic waves in plasmas

NASA Astrophysics Data System (ADS)

Basov, N. G.

The present anthology includes articles concerning the experimental study of the interaction of high power electromagnetic waves with collisionless plasmas and with electrons. Among the topics covered are the nonlinear dissipation of electromagnetic waves in inhomogeneous collisionless plasmas, the collisionless absorption of electromagnetic waves in plasmas and 'slow' nonlinear phenomena, the nonlinear effects of electron plasma waves propagating in an inhomogeneous plasma layer, and secondary-emission microwave discharges having large electron transit angles.

Nonlinear aerodynamic effects on bodies in supersonic flow

NASA Technical Reports Server (NTRS)

Pittman, J. L.; Siclari, M. J.

1984-01-01

The supersonic flow about generic bodies was analyzed to identify the elments of the nonlinear flow and to determine the influence of geometry and flow conditions on the magnitude of these nonlinearities. The nonlinear effects were attributed to separated-flow nonlinearities and attached-flow nonlinearities. The nonlinear attached-flow contribution was further broken down into large-disturbance effects and entropy effects. Conical, attached-flow bundaries were developed to illustrate the flow regimes where the nonlinear effects are significant, and the use of these boundaries for angle of attack and three-dimensional geometries was indicated. Normal-force and pressure comparisons showed that the large-disturbance and separated-flow effects were the dominant nonlinear effects at low supersonic Mach numbers and that the entropy effects were dominant for high supersonic Mach number flow. The magnitude of all the nonlinear effects increased with increasing angle of attack. A full-potential method, NCOREL, which includes an approximate entropy correction, was shown to provide accurate attached-flow pressure estimates from Mach 1.6 through 4.6.

Characterizing acoustic shocks in high-performance jet aircraft flyover noise.

PubMed

Reichman, Brent O; Gee, Kent L; Neilsen, Tracianne B; Downing, J Micah; James, Michael M; Wall, Alan T; McInerny, Sally Anne

2018-03-01

Acoustic shocks have been previously documented in high-amplitude jet noise, including both the near and far fields of military jet aircraft. However, previous investigations into the nature and formation of shocks have historically concentrated on stationary, ground run-up measurements, and previous attempts to connect full-scale ground run-up and flyover measurements have omitted the effect of nonlinear propagation. This paper shows evidence for nonlinear propagation and the presence of acoustic shocks in acoustical measurements of F-35 flyover operations. Pressure waveforms, derivatives, and statistics indicate nonlinear propagation, and the resulting shock formation is significant at high engine powers. Variations due to microphone size, microphone height, and sampling rate are considered, and recommendations for future measurements are made. Metrics indicating nonlinear propagation are shown to be influenced by changes in sampling rate and microphone size, and exhibit less variation due to microphone height.

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.

Nonlinear Dot Plots.

PubMed

Rodrigues, Nils; Weiskopf, Daniel

2018-01-01

Conventional dot plots use a constant dot size and are typically applied to show the frequency distribution of small data sets. Unfortunately, they are not designed for a high dynamic range of frequencies. We address this problem by introducing nonlinear dot plots. Adopting the idea of nonlinear scaling from logarithmic bar charts, our plots allow for dots of varying size so that columns with a large number of samples are reduced in height. For the construction of these diagrams, we introduce an efficient two-way sweep algorithm that leads to a dense and symmetrical layout. We compensate aliasing artifacts at high dot densities by a specifically designed low-pass filtering method. Examples of nonlinear dot plots are compared to conventional dot plots as well as linear and logarithmic histograms. Finally, we include feedback from an expert review.

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

An Adaptive Moving Target Imaging Method for Bistatic Forward-Looking SAR Using Keystone Transform and Optimization NLCS.

PubMed

Li, Zhongyu; Wu, Junjie; Huang, Yulin; Yang, Haiguang; Yang, Jianyu

2017-01-23

Bistatic forward-looking SAR (BFSAR) is a kind of bistatic synthetic aperture radar (SAR) system that can image forward-looking terrain in the flight direction of an aircraft. Until now, BFSAR imaging theories and methods for a stationary scene have been researched thoroughly. However, for moving-target imaging with BFSAR, the non-cooperative movement of the moving target induces some new issues: (I) large and unknown range cell migration (RCM) (including range walk and high-order RCM); (II) the spatial-variances of the Doppler parameters (including the Doppler centroid and high-order Doppler) are not only unknown, but also nonlinear for different point-scatterers. In this paper, we put forward an adaptive moving-target imaging method for BFSAR. First, the large and unknown range walk is corrected by applying keystone transform over the whole received echo, and then, the relationships among the unknown high-order RCM, the nonlinear spatial-variances of the Doppler parameters, and the speed of the mover, are established. After that, using an optimization nonlinear chirp scaling (NLCS) technique, not only can the unknown high-order RCM be accurately corrected, but also the nonlinear spatial-variances of the Doppler parameters can be balanced. At last, a high-order polynomial filter is applied to compress the whole azimuth data of the moving target. Numerical simulations verify the effectiveness of the proposed method.

Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures

DTIC Science & Technology

2016-08-03

additional details including the experimental setup, the precise selection of the DEM pa- rameters and the quantitative nature of the agreement between theory ...by Dr. Farmer. [29] G. Iooss, G. James, Chaos 15, 015113 (2005). [30] J.P. Boyd, Nonlinearity 3, 177 (1990). [31] N. Lu, J. Diff. Eqs. 256, 745 (2014

Nonlinear optical microscopy for immunoimaging: a custom optimized system of high-speed, large-area, multicolor imaging

PubMed Central

Li, Hui; Cui, Quan; Zhang, Zhihong; Luo, Qingming

2015-01-01

Background The nonlinear optical microscopy has become the current state-of-the-art for intravital imaging. Due to its advantages of high resolution, superior tissue penetration, lower photodamage and photobleaching, as well as intrinsic z-sectioning ability, this technology has been widely applied in immunoimaging for a decade. However, in terms of monitoring immune events in native physiological environment, the conventional nonlinear optical microscope system has to be optimized for live animal imaging. Generally speaking, three crucial capabilities are desired, including high-speed, large-area and multicolor imaging. Among numerous high-speed scanning mechanisms used in nonlinear optical imaging, polygon scanning is not only linearly but also dispersion-freely with high stability and tunable rotation speed, which can overcome disadvantages of multifocal scanning, resonant scanner and acousto-optical deflector (AOD). However, low frame rate, lacking large-area or multicolor imaging ability make current polygonbased nonlinear optical microscopes unable to meet the requirements of immune event monitoring. Methods We built up a polygon-based nonlinear optical microscope system which was custom optimized for immunoimaging with high-speed, large-are and multicolor imaging abilities. Results Firstly, we validated the imaging performance of the system by standard methods. Then, to demonstrate the ability to monitor immune events, migration of immunocytes observed by the system based on typical immunological models such as lymph node, footpad and dorsal skinfold chamber are shown. Finally, we take an outlook for the possible advance of related technologies such as sample stabilization and optical clearing for more stable and deeper intravital immunoimaging. Conclusions This study will be helpful for optimizing nonlinear optical microscope to obtain more comprehensive and accurate information of immune events. PMID:25694951

Waveguide structures in anisotropic nonlinear crystals

NASA Astrophysics Data System (ADS)

Li, Da; Hong, Pengda; Meissner, Helmuth E.

2017-02-01

We report on the design and manufacturing parameters of waveguiding structures of anisotropic nonlinear crystals that are employed for harmonic conversions, using Adhesive-Free Bonding (AFB®). This technology enables a full range of predetermined refractive index differences that are essential for the design of single mode or low-mode propagation with high efficiency in anisotropic nonlinear crystals which in turn results in compact frequency conversion systems. Examples of nonlinear optical waveguides include periodically bonded walk-off corrected nonlinear optical waveguides and periodically poled waveguide components, such as lithium triborate (LBO), beta barium borate (β-BBO), lithium niobate (LN), potassium titanyl phosphate (KTP), zinc germanium phosphide (ZGP) and silver selenogallate (AGSE). Simulation of planar LN waveguide shows that when the electric field vector E lies in the k-c plane, the power flow is directed precisely along the propagation direction, demonstrating waveguiding effect in the planar waveguide. Employment of anisotropic nonlinear optical waveguides, for example in combination with AFB® crystalline fiber waveguides (CFW), provides access to the design of a number of novel high power and high efficiency light sources spanning the range of wavelengths from deep ultraviolet (as short as 200 nm) to mid-infrared (as long as about 18 μm). To our knowledge, the technique is the only generally applicable one because most often there are no compatible cladding crystals available to nonlinear optical cores, especially not with an engineer-able refractive index difference and large mode area.

Super-nonlinear fluorescence microscopy for high-contrast deep tissue imaging

NASA Astrophysics Data System (ADS)

Wei, Lu; Zhu, Xinxin; Chen, Zhixing; Min, Wei

2014-02-01

Two-photon excited fluorescence microscopy (TPFM) offers the highest penetration depth with subcellular resolution in light microscopy, due to its unique advantage of nonlinear excitation. However, a fundamental imaging-depth limit, accompanied by a vanishing signal-to-background contrast, still exists for TPFM when imaging deep into scattering samples. Formally, the focusing depth, at which the in-focus signal and the out-of-focus background are equal to each other, is defined as the fundamental imaging-depth limit. To go beyond this imaging-depth limit of TPFM, we report a new class of super-nonlinear fluorescence microscopy for high-contrast deep tissue imaging, including multiphoton activation and imaging (MPAI) harnessing novel photo-activatable fluorophores, stimulated emission reduced fluorescence (SERF) microscopy by adding a weak laser beam for stimulated emission, and two-photon induced focal saturation imaging with preferential depletion of ground-state fluorophores at focus. The resulting image contrasts all exhibit a higher-order (third- or fourth- order) nonlinear signal dependence on laser intensity than that in the standard TPFM. Both the physical principles and the imaging demonstrations will be provided for each super-nonlinear microscopy. In all these techniques, the created super-nonlinearity significantly enhances the imaging contrast and concurrently extends the imaging depth-limit of TPFM. Conceptually different from conventional multiphoton processes mediated by virtual states, our strategy constitutes a new class of fluorescence microscopy where high-order nonlinearity is mediated by real population transfer.

Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming

USGS Publications Warehouse

Yu, X.; Hsu, T.-J.; Hanes, D.M.

2010-01-01

Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

Quantitative theory of driven nonlinear brain dynamics.

PubMed

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Gyrofluid turbulence models with kinetic effects

NASA Astrophysics Data System (ADS)

Dorland, W.; Hammett, G. W.

1993-03-01

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

Dynamic analysis of nonlinear rotor-housing systems

NASA Technical Reports Server (NTRS)

Noah, Sherif T.

1988-01-01

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

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.

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

Nonlinear regional warming with increasing CO2 concentrations

NASA Astrophysics Data System (ADS)

Good, Peter; Lowe, Jason A.; Andrews, Timothy; Wiltshire, Andrew; Chadwick, Robin; Ridley, Jeff K.; Menary, Matthew B.; Bouttes, Nathaelle; Dufresne, Jean Louis; Gregory, Jonathan M.; Schaller, Nathalie; Shiogama, Hideo

2015-02-01

When considering adaptation measures and global climate mitigation goals, stakeholders need regional-scale climate projections, including the range of plausible warming rates. To assist these stakeholders, it is important to understand whether some locations may see disproportionately high or low warming from additional forcing above targets such as 2 K (ref. ). There is a need to narrow uncertainty in this nonlinear warming, which requires understanding how climate changes as forcings increase from medium to high levels. However, quantifying and understanding regional nonlinear processes is challenging. Here we show that regional-scale warming can be strongly superlinear to successive CO2 doublings, using five different climate models. Ensemble-mean warming is superlinear over most land locations. Further, the inter-model spread tends to be amplified at higher forcing levels, as nonlinearities grow--especially when considering changes per kelvin of global warming. Regional nonlinearities in surface warming arise from nonlinearities in global-mean radiative balance, the Atlantic meridional overturning circulation, surface snow/ice cover and evapotranspiration. For robust adaptation and mitigation advice, therefore, potentially avoidable climate change (the difference between business-as-usual and mitigation scenarios) and unavoidable climate change (change under strong mitigation scenarios) may need different analysis methods.

Highly Non-Linear Optical (NLO) organic crystals and films. Electrooptical organic materials

NASA Technical Reports Server (NTRS)

Mcmanus, Samuel P.; Rosenberger, Franz; Matthews, John

1987-01-01

Devices employing nonlinear optics (NLO) hold great promise for important applications in integrated optics, optical information processing and telecommunications. Properly designed organics possess outstanding optical and electrooptical properties which will substantially advance many technologies including electrooptical switching, optical amplification for communications, and parallel processing for hybrid optical computers. A brief comparison of organic and inorganic materials is given.

Linear and nonlinear winter atmospheric responses to extreme phases of low frequency Pacific sea surface temperature variability

NASA Astrophysics Data System (ADS)

Cao, Dandan; Wu, Qigang; Hu, Aixue; Yao, Yonghong; Liu, Shizuo; Schroeder, Steven R.; Yang, Fucheng

2018-02-01

This study examines Northern Hemisphere winter (DJFM) atmospheric responses to opposite strong phases of interdecadal (low frequency, LF) Pacific sea surface temperature (SST) forcing, which resembles El Niño-Southern Oscillation (ENSO) on a longer time scale, in observations and GFDL and CAM4 model simulations. Over the Pacific-North America (PNA) sector, linear observed responses of 500-hPa height (Z500) anomalies resemble the PNA teleconnection pattern, but show a PNA-like nonlinear response because of a westward Z500 shift in the negative (LF-) relative to the positive LF (LF+) phase. Significant extratropical linear responses include a North Atlantic Oscillation (NAO)-like Z500 anomaly, a dipole-like Z500 anomaly over northern Eurasia associated with warming over mid-high latitude Eurasia, and a Southern Annular anomaly pattern associated with warming in southern land areas. Significant nonlinear Z500 responses also include a NAO-like anomaly pattern. Models forced by LF+ and LF- SST anomalies reproduce many aspects of observed linear and nonlinear responses over the Pacific-North America sector, and linear responses over southern land, but not in the North Atlantic-European sector and Eurasia. Both models simulate PNA-like linear responses in the North Pacific-North America region similar to observed, but show larger PNA-like LF+ responses, resulting in a PNA nonlinear response. The nonlinear PNA responses result from both nonlinear western tropical Pacific rainfall changes and extratropical transient eddy feedbacks. With LF tropical Pacific forcing only (LFTP+ and LFTP-, climatological SST elsewhere), CAM4 simulates a significant NAO response to LFTP-, including a linear negative and nonlinear positive NAO response.

Thermal effects on nonlinear vibration of a carbon nanotube-based mass sensor using finite element analysis

NASA Astrophysics Data System (ADS)

Kang, Dong-Keun; Kim, Chang-Wan; Yang, Hyun-Ik

2017-01-01

In the present study we carried out a dynamic analysis of a CNT-based mass sensor by using a finite element method (FEM)-based nonlinear analysis model of the CNT resonator to elucidate the combined effects of thermal effects and nonlinear oscillation behavior upon the overall mass detection sensitivity. Mass sensors using carbon nanotube (CNT) resonators provide very high sensing performance. Because CNT-based resonators can have high aspect ratios, they can easily exhibit nonlinear oscillation behavior due to large displacements. Also, CNT-based devices may experience high temperatures during their manufacture and operation. These geometrical nonlinearities and temperature changes affect the sensing performance of CNT-based mass sensors. However, it is very hard to find previous literature addressing the detection sensitivity of CNT-based mass sensors including considerations of both these nonlinear behaviors and thermal effects. We modeled the nonlinear equation of motion by using the von Karman nonlinear strain-displacement relation, taking into account the additional axial force associated with the thermal effect. The FEM was employed to solve the nonlinear equation of motion because it can effortlessly handle the more complex geometries and boundary conditions. A doubly clamped CNT resonator actuated by distributed electrostatic force was the configuration subjected to the numerical experiments. Thermal effects upon the fundamental resonance behavior and the shift of resonance frequency due to attached mass, i.e., the mass detection sensitivity, were examined in environments of both high and low (or room) temperature. The fundamental resonance frequency increased with decreasing temperature in the high temperature environment, and increased with increasing temperature in the low temperature environment. The magnitude of the shift in resonance frequency caused by an attached mass represents the sensing performance of a mass sensor, i.e., its mass detection sensitivity, and it can be seen that this shift is affected by the temperature change and the amount of electrostatic force. The thermal effects on the mass detection sensitivity are intensified in the linear oscillation regime and increase with increasing CNT length; this intensification can either improve or worsen the detection sensitivity.

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.; Sandham, N. D.; Hadjadj, A.; Kwak, Dochan (Technical Monitor)

2000-01-01

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Super Nonlinear Electrodeposition-Diffusion-Controlled Thin-Film Selector.

PubMed

Ji, Xinglong; Song, Li; He, Wei; Huang, Kejie; Yan, Zhiyuan; Zhong, Shuai; Zhang, Yishu; Zhao, Rong

2018-03-28

Selector elements with high nonlinearity are an indispensable part in constructing high density, large-scale, 3D stackable emerging nonvolatile memory and neuromorphic network. Although significant efforts have been devoted to developing novel thin-film selectors, it remains a great challenge in achieving good switching performance in the selectors to satisfy the stringent electrical criteria of diverse memory elements. In this work, we utilized high-defect-density chalcogenide glass (Ge 2 Sb 2 Te 5 ) in conjunction with high mobility Ag element (Ag-GST) to achieve a super nonlinear selective switching. A novel electrodeposition-diffusion dynamic selector based on Ag-GST exhibits superior selecting performance including excellent nonlinearity (<5 mV/dev), ultra-low leakage (<10 fA), and bidirectional operation. With the solid microstructure evidence and dynamic analyses, we attributed the selective switching to the competition between the electrodeposition and diffusion of Ag atoms in the glassy GST matrix under electric field. A switching model is proposed, and the in-depth understanding of the selective switching mechanism offers an insight of switching dynamics for the electrodeposition-diffusion-controlled thin-film selector. This work opens a new direction of selector designs by combining high mobility elements and high-defect-density chalcogenide glasses, which can be extended to other materials with similar properties.

Fibre-optic nonlinear optical microscopy and endoscopy.

PubMed

Fu, L; Gu, M

2007-06-01

Nonlinear optical microscopy has been an indispensable laboratory tool of high-resolution imaging in thick tissue and live animals. Rapid developments of fibre-optic components in terms of growing functionality and decreasing size provide enormous opportunities for innovations in nonlinear optical microscopy. Fibre-based nonlinear optical endoscopy is the sole instrumentation to permit the cellular imaging within hollow tissue tracts or solid organs that are inaccessible to a conventional optical microscope. This article reviews the current development of fibre-optic nonlinear optical microscopy and endoscopy, which includes crucial technologies for miniaturized nonlinear optical microscopy and their embodiments of endoscopic systems. A particular attention is given to several classes of photonic crystal fibres that have been applied to nonlinear optical microscopy due to their unique properties for ultrashort pulse delivery and signal collection. Furthermore, fibre-optic nonlinear optical imaging systems can be classified into portable microscopes suitable for imaging behaving animals, rigid endoscopes that allow for deep tissue imaging with minimally invasive manners, and flexible endoscopes enabling imaging of internal organs. Fibre-optic nonlinear optical endoscopy is coming of age and a paradigm shift leading to optical microscope tools for early cancer detection and minimally invasive surgery.

Anatomy of Ag/Hafnia-Based Selectors with 10 10 Nonlinearity

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

Midya, Rivu; Wang, Zhongrui; Zhang, Jiaming

We developed a novel Ag/oxide-based threshold switching device with attractive features including ≈10 10 nonlinearity. Furthermore, in a high-resolution transmission electron microscopic analysis of the nanoscale crosspoint device it is suggested that elongation of an Ag nanoparticle under voltage bias followed by spontaneous reformation of a more spherical shape after power off, is responsible for the observed threshold switching.

On the pressure field of nonlinear standing water waves

NASA Technical Reports Server (NTRS)

Schwartz, L. W.

1980-01-01

The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.

Anatomy of Ag/Hafnia-Based Selectors with 10 10 Nonlinearity

DOE PAGES

Midya, Rivu; Wang, Zhongrui; Zhang, Jiaming; ...

2017-01-30

We developed a novel Ag/oxide-based threshold switching device with attractive features including ≈10 10 nonlinearity. Furthermore, in a high-resolution transmission electron microscopic analysis of the nanoscale crosspoint device it is suggested that elongation of an Ag nanoparticle under voltage bias followed by spontaneous reformation of a more spherical shape after power off, is responsible for the observed threshold switching.

Effective potentials in nonlinear polycrystals and quadrature formulae

NASA Astrophysics Data System (ADS)

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

Effective potentials in nonlinear polycrystals and quadrature formulae.

PubMed

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471 , 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

Benzothiazolium Single Crystals: A New Class of Nonlinear Optical Crystals with Efficient THz Wave Generation.

PubMed

Lee, Seung-Heon; Lu, Jian; Lee, Seung-Jun; Han, Jae-Hyun; Jeong, Chan-Uk; Lee, Seung-Chul; Li, Xian; Jazbinšek, Mojca; Yoon, Woojin; Yun, Hoseop; Kang, Bong Joo; Rotermund, Fabian; Nelson, Keith A; Kwon, O-Pil

2017-08-01

Highly efficient nonlinear optical organic crystals are very attractive for various photonic applications including terahertz (THz) wave generation. Up to now, only two classes of ionic crystals based on either pyridinium or quinolinium with extremely large macroscopic optical nonlinearity have been developed. This study reports on a new class of organic nonlinear optical crystals introducing electron-accepting benzothiazolium, which exhibit higher electron-withdrawing strength than pyridinium and quinolinium in benchmark crystals. The benzothiazolium crystals consisting of new acentric core HMB (2-(4-hydroxy-3-methoxystyryl)-3-methylbenzo[d]thiazol-3-ium) exhibit extremely large macroscopic optical nonlinearity with optimal molecular ordering for maximizing the diagonal second-order nonlinearity. HMB-based single crystals prepared by simple cleaving method satisfy all required crystal characteristics for intense THz wave generation such as large crystal size with parallel surfaces, moderate thickness and high optical quality with large optical transparency range (580-1620 nm). Optical rectification of 35 fs pulses at the technologically very important wavelength of 800 nm in 0.26 mm thick HMB crystal leads to one order of magnitude higher THz wave generation efficiency with remarkably broader bandwidth compared to standard inorganic 0.5 mm thick ZnTe crystal. Therefore, newly developed HMB crystals introducing benzothiazolium with extremely large macroscopic optical nonlinearity are very promising materials for intense broadband THz wave generation and other nonlinear optical applications. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Ultrafast optical pulse delivery with fibers for nonlinear microscopy

PubMed Central

Kim, Daekeun; Choi, Heejin; Yazdanfar, Siavash; So, Peter T. C.

2008-01-01

Nonlinear microscopies including multiphoton excitation fluorescence microscopy and multiple-harmonic generation microscopy have recently gained popularity for cellular and tissue imaging. The optimization of these imaging methods for minimally invasive use will require optical fibers to conduct light into tight space where free space delivery is difficult. The delivery of high peak power laser pulses with optical fibers is limited by dispersion resulting from nonlinear refractive index responses. In this paper, we characterize a variety of commonly used optical fibers in terms of how they affect pulse profile and imaging performance of nonlinear microscopy; the following parameters are quantified: spectral bandwidth and temporal pulse width, two-photon excitation efficiency, and optical resolution. A theoretical explanation for the measured performance of these is also provided. PMID:18816597

Application of dynamical systems theory to nonlinear aircraft dynamics

NASA Technical Reports Server (NTRS)

Culick, Fred E. C.; Jahnke, Craig C.

1988-01-01

Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

Numerical investigation of frequency spectrum in the Hasegawa-Wakatani model

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

Kim, Juhyung; Terry, P. W.

2013-10-15

The wavenumber-frequency spectrum of the two-dimensional Hasegawa-Wakatani model is investigated in the hydrodynamic, intermediate, and adiabatic regimes. A nonlinear frequency and a line width related to energy transfer properties provide a measure of the average frequency and spectral broadening, respectively. In the adiabatic regime, narrow spectra, typical of wave turbulence, are observed with a nonlinear frequency shift in the electron drift direction. In the hydrodynamic regime, broad spectra with almost zero nonlinear frequencies are observed. Nonlinear frequency shifts are shown to be related to nonlinear energy transfer by vorticity advection through the high frequency region of the spectrum. In themore » intermediate regime, the nonlinear frequency shift for density fluctuations is observed to be weaker than that of electrostatic potential fluctuations. The weaker frequency shift of the density fluctuations is due to nonlinear density advection, which favors energy transfer in the low frequency range. Both the nonlinear frequency and the spectral width increase with poloidal wavenumber k{sub y}. In addition, in the adiabatic regime where the nonlinear interactions manifest themselves in the nonlinear frequency shift, the cross-phase between the density and potential fluctuations is observed to match a linear relation, but only if the linear response of the linearly stable eigenmode branch is included. Implications of these numerical observations are discussed.« less

Multi-dimensional high order essentially non-oscillatory finite difference methods in generalized coordinates

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1992-01-01

The nonlinear stability of compact schemes for shock calculations is investigated. In recent years compact schemes were used in various numerical simulations including direct numerical simulation of turbulence. However to apply them to problems containing shocks, one has to resolve the problem of spurious numerical oscillation and nonlinear instability. A framework to apply nonlinear limiting to a local mean is introduced. The resulting scheme can be proven total variation (1D) or maximum norm (multi D) stable and produces nice numerical results in the test cases. The result is summarized in the preprint entitled 'Nonlinearly Stable Compact Schemes for Shock Calculations', which was submitted to SIAM Journal on Numerical Analysis. Research was continued on issues related to two and three dimensional essentially non-oscillatory (ENO) schemes. The main research topics include: parallel implementation of ENO schemes on Connection Machines; boundary conditions; shock interaction with hydrogen bubbles, a preparation for the full combustion simulation; and direct numerical simulation of compressible sheared turbulence.

Device and method for imaging of non-linear and linear properties of formations surrounding a borehole

DOEpatents

Johnson, Paul A; Tencate, James A; Le Bas, Pierre-Yves; Guyer, Robert; Vu, Cung Khac; Skelt, Christopher

2013-11-05

In some aspects of the disclosure, a method and an apparatus is disclosed for investigating material surrounding the borehole. The method includes generating a first low frequency acoustic wave within the borehole, wherein the first low frequency acoustic wave induces a linear and a nonlinear response in one or more features in the material that are substantially perpendicular to a radius of the borehole; directing a first sequence of high frequency pulses in a direction perpendicularly with respect to the longitudinal axis of the borehole into the material contemporaneously with the first acoustic wave; and receiving one or more second high frequency pulses at one or more receivers positionable in the borehole produced by an interaction between the first sequence of high frequency pulses and the one or more features undergoing linear and nonlinear elastic distortion due to the first low frequency acoustic wave to investigate the material surrounding the borehole.

Investigation of contact acoustic nonlinearities on metal and composite airframe structures via intensity based health monitoring.

PubMed

Romano, P Q; Conlon, S C; Smith, E C

2013-01-01

Nonlinear structural intensity (NSI) and nonlinear structural surface intensity (NSSI) based damage detection techniques were improved and extended to metal and composite airframe structures. In this study, the measurement of NSI maps at sub-harmonic frequencies was completed to provide enhanced understanding of the energy flow characteristics associated with the damage induced contact acoustic nonlinearity mechanism. Important results include NSI source localization visualization at ultra-subharmonic (nf/2) frequencies, and damage detection results utilizing structural surface intensity in the nonlinear domain. A detection metric relying on modulated wave spectroscopy was developed and implemented using the NSSI feature. The data fusion of the intensity formulation provided a distinct advantage, as both the single interrogation frequency NSSI and its modulated wave extension (NSSI-MW) exhibited considerably higher sensitivities to damage than using single-sensor (strain or acceleration) nonlinear detection metrics. The active intensity based techniques were also extended to composite materials, and results show both NSSI and NSSI-MW can be used to detect damage in the bond line of an integrally stiffened composite plate structure with high sensitivity. Initial damage detection measurements made on an OH-58 tailboom (Penn State Applied Research Laboratory, State College, PA) indicate the techniques can be transitioned to complex airframe structures achieving high detection sensitivities with minimal sensors and actuators.

Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses.

PubMed

Kim, Kihong; Phung, D K; Rotermund, F; Lim, H

2008-01-21

We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.

A Stewart isolator with high-static-low-dynamic stiffness struts based on negative stiffness magnetic springs

NASA Astrophysics Data System (ADS)

Zheng, Yisheng; Li, Qingpin; Yan, Bo; Luo, Yajun; Zhang, Xinong

2018-05-01

In order to improve the isolation performance of passive Stewart platforms, the negative stiffness magnetic spring (NSMS) is employed to construct high static low dynamic stiffness (HSLDS) struts. With the NSMS, the resonance frequencies of the platform can be reduced effectively without deteriorating its load bearing capacity. The model of the Stewart isolation platform with HSLDS struts is presented and the stiffness characteristic of its struts is studied firstly. Then the nonlinear dynamic model of the platform including both geometry nonlinearity and stiffness nonlinearity is established; and its simplified dynamic model is derived under the condition of small vibration. The effect of nonlinearity on the isolation performance is also evaluated. Finally, a prototype is built and the isolation performance is tested. Both simulated and experimental results demonstrate that, by using the NSMS, the resonance frequencies of the Stewart isolator are reduced and the isolation performance in all six directions is improved: the isolation frequency band is increased and extended to a lower-frequency level.

Probing the interatomic potential of solids with strong-field nonlinear phononics

NASA Astrophysics Data System (ADS)

von Hoegen, A.; Mankowsky, R.; Fechner, M.; Först, M.; Cavalleri, A.

2018-03-01

Nonlinear optical techniques at visible frequencies have long been applied to condensed matter spectroscopy. However, because many important excitations of solids are found at low energies, much can be gained from the extension of nonlinear optics to mid-infrared and terahertz frequencies. For example, the nonlinear excitation of lattice vibrations has enabled the dynamic control of material functions. So far it has only been possible to exploit second-order phonon nonlinearities at terahertz field strengths near one million volts per centimetre. Here we achieve an order-of-magnitude increase in field strength and explore higher-order phonon nonlinearities. We excite up to five harmonics of the A1 (transverse optical) phonon mode in the ferroelectric material lithium niobate. By using ultrashort mid-infrared laser pulses to drive the atoms far from their equilibrium positions, and measuring the large-amplitude atomic trajectories, we can sample the interatomic potential of lithium niobate, providing a benchmark for ab initio calculations for the material. Tomography of the energy surface by high-order nonlinear phononics could benefit many aspects of materials research, including the study of classical and quantum phase transitions.

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.

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.

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Reinforcement-learning-based dual-control methodology for complex nonlinear discrete-time systems with application to spark engine EGR operation.

PubMed

Shih, Peter; Kaul, Brian C; Jagannathan, S; Drallmeier, James A

2008-08-01

A novel reinforcement-learning-based dual-control methodology adaptive neural network (NN) controller is developed to deliver a desired tracking performance for a class of complex feedback nonlinear discrete-time systems, which consists of a second-order nonlinear discrete-time system in nonstrict feedback form and an affine nonlinear discrete-time system, in the presence of bounded and unknown disturbances. For example, the exhaust gas recirculation (EGR) operation of a spark ignition (SI) engine is modeled by using such a complex nonlinear discrete-time system. A dual-controller approach is undertaken where primary adaptive critic NN controller is designed for the nonstrict feedback nonlinear discrete-time system whereas the secondary one for the affine nonlinear discrete-time system but the controllers together offer the desired performance. The primary adaptive critic NN controller includes an NN observer for estimating the states and output, an NN critic, and two action NNs for generating virtual control and actual control inputs for the nonstrict feedback nonlinear discrete-time system, whereas an additional critic NN and an action NN are included for the affine nonlinear discrete-time system by assuming the state availability. All NN weights adapt online towards minimization of a certain performance index, utilizing gradient-descent-based rule. Using Lyapunov theory, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight estimates, and observer estimates are shown. The adaptive critic NN controller performance is evaluated on an SI engine operating with high EGR levels where the controller objective is to reduce cyclic dispersion in heat release while minimizing fuel intake. Simulation and experimental results indicate that engine out emissions drop significantly at 20% EGR due to reduction in dispersion in heat release thus verifying the dual-control approach.

Real-time optical image processing techniques

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang

1988-01-01

Nonlinear real-time optical processing on spatial pulse frequency modulation has been pursued through the analysis, design, and fabrication of pulse frequency modulated halftone screens and the modification of micro-channel spatial light modulators (MSLMs). Micro-channel spatial light modulators are modified via the Fabry-Perot method to achieve the high gamma operation required for non-linear operation. Real-time nonlinear processing was performed using the halftone screen and MSLM. The experiments showed the effectiveness of the thresholding and also showed the needs of higher SBP for image processing. The Hughes LCLV has been characterized and found to yield high gamma (about 1.7) when operated in low frequency and low bias mode. Cascading of two LCLVs should also provide enough gamma for nonlinear processing. In this case, the SBP of the LCLV is sufficient but the uniformity of the LCLV needs improvement. These include image correlation, computer generation of holograms, pseudo-color image encoding for image enhancement, and associative-retrieval in neural processing. The discovery of the only known optical method for dynamic range compression of an input image in real-time by using GaAs photorefractive crystals is reported. Finally, a new architecture for non-linear multiple sensory, neural processing has been suggested.

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.

User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

NASA Technical Reports Server (NTRS)

Whitcomb, J. D.; Dattaguru, B.

1984-01-01

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.

AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, 4th, Cleveland, OH, Sept. 21-23, 1992, Technical Papers. Pts. 1 & 2

NASA Technical Reports Server (NTRS)

1992-01-01

The papers presented at the symposium cover aerodynamics, design applications, propulsion systems, high-speed flight, structures, controls, sensitivity analysis, optimization algorithms, and space structures applications. Other topics include helicopter rotor design, artificial intelligence/neural nets, and computational aspects of optimization. Papers are included on flutter calculations for a system with interacting nonlinearities, optimization in solid rocket booster application, improving the efficiency of aerodynamic shape optimization procedures, nonlinear control theory, and probabilistic structural analysis of space truss structures for nonuniform thermal environmental effects.

Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications

NASA Astrophysics Data System (ADS)

Pesaresi, L.; Salles, L.; Jones, A.; Green, J. S.; Schwingshackl, C. W.

2017-02-01

Underplatform dampers (UPD) are commonly used in aircraft engines to mitigate the risk of high-cycle fatigue failure of turbine blades. The energy dissipated at the friction contact interface of the damper reduces the vibration amplitude significantly, and the couplings of the blades can also lead to significant shifts of the resonance frequencies of the bladed disk. The highly nonlinear behaviour of bladed discs constrained by UPDs requires an advanced modelling approach to ensure that the correct damper geometry is selected during the design of the turbine, and that no unexpected resonance frequencies and amplitudes will occur in operation. Approaches based on an explicit model of the damper in combination with multi-harmonic balance solvers have emerged as a promising way to predict the nonlinear behaviour of UPDs correctly, however rigorous experimental validations are required before approaches of this type can be used with confidence. In this study, a nonlinear analysis based on an updated explicit damper model having different levels of detail is performed, and the results are evaluated against a newly-developed UPD test rig. Detailed linear finite element models are used as input for the nonlinear analysis, allowing the inclusion of damper flexibility and inertia effects. The nonlinear friction interface between the blades and the damper is described with a dense grid of 3D friction contact elements which allow accurate capturing of the underlying nonlinear mechanism that drives the global nonlinear behaviour. The introduced explicit damper model showed a great dependence on the correct contact pressure distribution. The use of an accurate, measurement based, distribution, better matched the nonlinear dynamic behaviour of the test rig. Good agreement with the measured frequency response data could only be reached when the zero harmonic term (constant term) was included in the multi-harmonic expansion of the nonlinear problem, highlighting its importance when the contact interface experiences large normal load variation. The resulting numerical damper kinematics with strong translational and rotational motion, and the global blades frequency response were fully validated experimentally, showing the accuracy of the suggested high detailed explicit UPD modelling approach.

Effects of unbalance location on dynamic characteristics of high-speed gasoline engine turbocharger with floating ring bearings

NASA Astrophysics Data System (ADS)

Wang, Longkai; Bin, Guangfu; Li, Xuejun; Liu, Dingqu

2016-03-01

For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings(FRBs), the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.

Connective stability of nonlinear matrix systems

NASA Technical Reports Server (NTRS)

Siljak, D. D.

1974-01-01

Consideration of stability under structural perturbations of free dynamic systems described by the differential equation dx/dt = A(t,x)x, where the matrix A(t,x) has time-varying nonlinear elements. The concept of 'connective stability' is introduced to study the structural properties of competitive-cooperative nonlinear matrix systems. It is shown that stability reliability in such systems is high and that they remain stable despite time-varying (including 'on-off') interaction among individual agents present in the system. The results obtained can be used to study stability aspects of mathematical models arising in as diverse fields as economics, biology, arms races, and transistor circuits.

Development and validation of a general purpose linearization program for rigid aircraft models

NASA Technical Reports Server (NTRS)

Duke, E. L.; Antoniewicz, R. F.

1985-01-01

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. 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. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.

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

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Solid-state reversible quadratic nonlinear optical molecular switch with an exceptionally large contrast.

PubMed

Sun, Zhihua; Luo, Junhua; Zhang, Shuquan; Ji, Chengmin; Zhou, Lei; Li, Shenhui; Deng, Feng; Hong, Maochun

2013-08-14

Exceptional nonlinear optical (NLO) switching behavior, including an extremely large contrast (on/off) of ∼35 and high NLO coefficients, is displayed by a solid-state reversible quadratic NLO switch. The favorable results, induced by very fast molecular motion and anionic ordering, provides impetus for the design of a novel second-harmonic-generation switch involving molecular motion. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

High Temperature Composite Analyzer (HITCAN) demonstration manual, version 1.0

NASA Technical Reports Server (NTRS)

Singhal, S. N; Lackney, J. J.; Murthy, P. L. N.

1993-01-01

This manual comprises a variety of demonstration cases for the HITCAN (HIgh Temperature Composite ANalyzer) code. HITCAN is a general purpose computer program for predicting nonlinear global structural and local stress-strain response of arbitrarily oriented, multilayered high temperature metal matrix composite structures. HITCAN is written in FORTRAN 77 computer language and has been configured and executed on the NASA Lewis Research Center CRAY XMP and YMP computers. Detailed description of all program variables and terms used in this manual may be found in the User's Manual. The demonstration includes various cases to illustrate the features and analysis capabilities of the HITCAN computer code. These cases include: (1) static analysis, (2) nonlinear quasi-static (incremental) analysis, (3) modal analysis, (4) buckling analysis, (5) fiber degradation effects, (6) fabrication-induced stresses for a variety of structures; namely, beam, plate, ring, shell, and built-up structures. A brief discussion of each demonstration case with the associated input data file is provided. Sample results taken from the actual computer output are also included.

Hydrodynamic optical soliton tunneling

NASA Astrophysics Data System (ADS)

Sprenger, P.; Hoefer, M. A.; El, G. A.

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Generation of Raman lasers from nitrogen molecular ions driven by ultraintense laser fields

NASA Astrophysics Data System (ADS)

Yao, Jinping; Chu, Wei; Liu, Zhaoxiang; Xu, Bo; Chen, Jinming; Cheng, Ya

2018-03-01

Atmospheric lasing has aroused much interest in the past few years. The ‘air–laser’ opens promising potential for remote chemical sensing of trace gases with high sensitivity and specificity. At present, several approaches have been successfully implemented for generating highly coherent laser beams in atmospheric condition, including both amplified-spontaneous emission, and narrow-bandwidth stimulated emission in the forward direction in the presence of self-generated or externally injected seed pulses. Here, we report on generation of multiple-wavelength Raman lasers from nitrogen molecular ions ({{{N}}}2+), driven by intense mid-infrared laser fields. Intuitively, the approach appears problematic for the small nonlinear susceptibility of {{{N}}}2+ ions, whereas the efficiency of Raman laser can be significantly promoted in near-resonant condition. More surprisingly, a Raman laser consisting of a supercontinuum spanning from ∼310 to ∼392 nm has been observed resulting from a series near-resonant nonlinear processes including four-wave mixing, stimulated Raman scattering and cross phase modulation. To date, extreme nonlinear optics in molecular ions remains largely unexplored, which provides an alternative means for air–laser-based remote sensing applications.

Hydrodynamic optical soliton tunneling.

PubMed

Sprenger, P; Hoefer, M A; El, G A

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.

PubMed

Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A

2016-04-29

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Nonlinear electrodynamics of high-temperature superconductors

NASA Astrophysics Data System (ADS)

Zutic, Igor

We investigate the effects of nonlinear electrodynamics in unconventional superconductors. These effects can serve as fingerprints to identify the symmetry of the superconducting pairing state and to provide information about the unknown pairing mechanism in High Temperature Superconductors (HTSC). In the Meissner regime, at low temperatures, a nonlinear magnetic response arises from the presence of lines on the Fermi surface where the superconducting energy gap is very small or zero. This can be used to perform "node spectroscopy", that is, as a sensitive bulk probe to locate the angular position of those lines. We first compute the nonlinear magnetic moment as a function of applied field and geometry, assuming d-wave pairing and anisotropic penetration depth, for realistic finite sample. Our novel, numerically implemented, perturbative procedure exploits the small ratio of the penetration depths to the sample size and substantially reduces the computational work required. We next generalize these considerations to other candidates for the energy gap and to perform node spectroscopy. In calculating the nonlinear supercurrent response, we include the effects of orthorhombic distortion and a-b plane anisotropy. Analytic results presented demonstrate a systematic way to experimentally distinguish order parameters of different symmetries, including cases with mixed symmetry (for example, d+s and s+id). We finally extend our findings to the case of low frequency harmonic magnetic field. The nonlinear magnetic response for various physical quantities generates higher harmonics of the frequency of the applied field. We discuss how examination of the field and angular dependences of these harmonics allows determination of the structure of the energy gap. We show how to distinguish nodes from small minima ("quasinodes"). Gaps with nodal lines give rise to universal power law field dependences for the nonlinear magnetic moment and torque. They both have separable temporal and angular dependences. In contrast, with gap functions which only have quasinodes, these quantities do not display power laws in the applied field, and their temporal and angular dependences are not separable. We discuss how to perform measurements so as to maximize the nonlinear signal, and how to determine the gap function symmetry.

High-Alpha Research Vehicle (HARV) longitudinal controller: Design, analyses, and simulation resultss

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Hoffler, Keith D.; Proffitt, Melissa S.; Brown, Philip W.; Phillips, Michael R.; Rivers, Robert A.; Messina, Michael D.; Carzoo, Susan W.; Bacon, Barton J.; Foster, John F.

1994-01-01

This paper describes the design, analysis, and nonlinear simulation results (batch and piloted) for a longitudinal controller which is scheduled to be flight-tested on the High-Alpha Research Vehicle (HARV). The HARV is an F-18 airplane modified for and equipped with multi-axis thrust vectoring. The paper includes a description of the facilities, a detailed review of the feedback controller design, linear analysis results of the feedback controller, a description of the feed-forward controller design, nonlinear batch simulation results, and piloted simulation results. Batch simulation results include maximum pitch stick agility responses, angle of attack alpha captures, and alpha regulation for full lateral stick rolls at several alpha's. Piloted simulation results include task descriptions for several types of maneuvers, task guidelines, the corresponding Cooper-Harper ratings from three test pilots, and some pilot comments. The ratings show that desirable criteria are achieved for almost all of the piloted simulation tasks.

High energy efficient solid state laser sources

NASA Technical Reports Server (NTRS)

Byer, Robert L.

1988-01-01

Recent progress in the development of highly efficient coherent optical sources is reviewed. This work focusses on nonlinear frequency conversion of the highly coherent output of the Non-Planar Ring Laser Oscillators developed earlier in the program, and includes high efficiency second harmonic generation and the operation of optical parametric oscillators for wavelength diversity and tunability.

Generation of High Frequency Response in a Dynamically Loaded, Nonlinear Soil Column

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

Spears, Robert Edward; Coleman, Justin Leigh

2015-08-01

Detailed guidance on linear seismic analysis of soil columns is provided in “Seismic Analysis of Safety-Related Nuclear Structures and Commentary (ASCE 4, 1998),” which is currently under revision. A new Appendix in ASCE 4-2014 (draft) is being added to provide guidance for nonlinear time domain analysis which includes evaluation of soil columns. When performing linear analysis, a given soil column is typically evaluated with a linear, viscous damped constitutive model. When submitted to a sine wave motion, this constitutive model produces a smooth hysteresis loop. For nonlinear analysis, the soil column can be modelled with an appropriate nonlinear hysteretic soilmore » model. For the model in this paper, the stiffness and energy absorption result from a defined post yielding shear stress versus shear strain curve. This curve is input with tabular data points. When submitted to a sine wave motion, this constitutive model produces a hysteresis loop that looks similar in shape to the input tabular data points on the sides with discontinuous, pointed ends. This paper compares linear and nonlinear soil column results. The results show that the nonlinear analysis produces additional high frequency response. The paper provides additional study to establish what portion of the high frequency response is due to numerical noise associated with the tabular input curve and what portion is accurately caused by the pointed ends of the hysteresis loop. Finally, the paper shows how the results are changed when a significant structural mass is added to the top of the soil column.« less

Nonlinear propagation of light in Dirac matter.

PubMed

Eliasson, Bengt; Shukla, P K

2011-09-01

The nonlinear interaction between intense laser light and a quantum plasma is modeled by a collective Dirac equation coupled with the Maxwell equations. The model is used to study the nonlinear propagation of relativistically intense laser light in a quantum plasma including the electron spin-1/2 effect. The relativistic effects due to the high-intensity laser light lead, in general, to a downshift of the laser frequency, similar to a classical plasma where the relativistic mass increase leads to self-induced transparency of laser light and other associated effects. The electron spin-1/2 effects lead to a frequency upshift or downshift of the electromagnetic (EM) wave, depending on the spin state of the plasma and the polarization of the EM wave. For laboratory solid density plasmas, the spin-1/2 effects on the propagation of light are small, but they may be significant in superdense plasma in the core of white dwarf stars. We also discuss extensions of the model to include kinetic effects of a distribution of the electrons on the nonlinear propagation of EM waves in a quantum plasma.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

NASA Astrophysics Data System (ADS)

Lu, S. F.; Zhang, W.; Song, X. J.

2017-09-01

Using Reddy's high-order shear theory for laminated plates and Hamilton's principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

Probabilistic micromechanics for metal matrix composites

NASA Astrophysics Data System (ADS)

Engelstad, S. P.; Reddy, J. N.; Hopkins, Dale A.

A probabilistic micromechanics-based nonlinear analysis procedure is developed to predict and quantify the variability in the properties of high temperature metal matrix composites. Monte Carlo simulation is used to model the probabilistic distributions of the constituent level properties including fiber, matrix, and interphase properties, volume and void ratios, strengths, fiber misalignment, and nonlinear empirical parameters. The procedure predicts the resultant ply properties and quantifies their statistical scatter. Graphite copper and Silicon Carbide Titanlum Aluminide (SCS-6 TI15) unidirectional plies are considered to demonstrate the predictive capabilities. The procedure is believed to have a high potential for use in material characterization and selection to precede and assist in experimental studies of new high temperature metal matrix composites.

Nonlinear analysis and dynamic structure in the energy market

NASA Astrophysics Data System (ADS)

Aghababa, Hajar

This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non-OPEC production time series data does not reveal signs of nonlinearity. The third essay explores nonlinear structure in the case of high dimensionality of the observations, different frequencies of sample sizes, and division of the samples into sub-samples. It systematically examines the robustness of the inference methods at various levels of time aggregation by employing daily spot prices on crude oil for 26 years as well as monthly spot price index on crude oil for 41 years. The daily and monthly samples are divided into sub-samples as well. All the tests detect strong evidence of nonlinear structure in the daily spot price of crude oil; whereas in monthly observations the evidence of nonlinear dependence is less dramatic, indicating that the nonlinear serial dependence will not be as intense when the time aggregation increase in time series observations.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

Free-vibration acoustic resonance of a nonlinear elastic bar

NASA Astrophysics Data System (ADS)

Tarumi, Ryuichi; Oshita, Yoshihito

2011-02-01

Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.

Catch-Disperse-Release Readout for Superconducting Qubits

DTIC Science & Technology

2013-03-01

adiabatic, a fast high-fidelity qubit readout is possible even in the strongly nonlinear dispersive regime. Interestingly, the Jaynes - Cummings nonlinearity...will be included later) and describe the system by the Jaynes - Cummings (JC) Hamiltonian [7] with a microwave drive (we use ~ = 1) H = ωq(t)σ+σ− + ωra...λeff,0 rotates on the phase plane faster than in the two-level approximation , while λeff,1 rotates slower (some- times even in the opposite

Toroidal gyrofluid equations for simulations of tokamak turbulence

NASA Astrophysics Data System (ADS)

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

1996-11-01

A set of nonlinear gyrofluid equations for simulations of tokamak turbulence are derived by taking moments of the nonlinear toroidal gyrokinetic equation. The moment hierarchy is closed with approximations that model the kinetic effects of parallel Landau damping, toroidal drift resonances, and finite Larmor radius effects. These equations generalize the work of Dorland and Hammett [Phys. Fluids B 5, 812 (1993)] to toroidal geometry by including essential toroidal effects. The closures for phase mixing from toroidal ∇B and curvature drifts take the basic form presented in Waltz et al. [Phys. Fluids B 4, 3138 (1992)], but here a more rigorous procedure is used, including an extension to higher moments, which provides significantly improved accuracy. In addition, trapped ion effects and collisions are incorporated. This reduced set of nonlinear equations accurately models most of the physics considered important for ion dynamics in core tokamak turbulence, and is simple enough to be used in high resolution direct numerical simulations.

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

PubMed

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

Nonlinear acoustics in the pant-hoot vocalization of common chimpanzees (Pan troglodytes)

NASA Astrophysics Data System (ADS)

Riede, Tobias; Arcadi, Adam Clark; Owren, Michael J.

2003-04-01

Pant-hoots produced by chimpanzees are multi-call vocalizations. While predominantly harmonically structured, pant-hoots can exhibit acoustic complexity that has recently been found to result from inherent nonlinearity in the vocal-fold dynamics. This complexity reflects abrupt shifts between qualitatively distinct vibration patterns (known as modes), which include but are not limited to simple, synchronous movements by the two vocal folds. Studies with humans in particular have shown that as the amplitude and vibration rate increase, vocal-fold action becomes increasingly susceptible to higher-order synchronizations, desynchronized movements, and irregular behavior. We examined the occurrence of these sorts of nonlinear phenomena in pant-hoots, contrasting quieter and lower-pitched introduction components with loud and high-pitched climax calls in the same sounds. Spectrographic evidence revealed four classic kinds of nonlinear phenomena, including discrete frequency jumps, subharmonics, biphonation, and deterministic chaos. While these events were virtually never found in the introduction, they occurred in more than half of the climax calls. Biphonation was by far the most common. Individual callers varied in the degree to which their climax calls exhibited nonlinear phenomena, but we are consistent in showing more biphonation than any of the other forms. These outcomes demonstrate that understanding these calls requisitely requires an understanding of such events.

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 Fano-Resonant Dielectric Metasurfaces

DOE PAGES

Yang, Yuanmu; Wang, Wenyi; Boulesbaa, Abdelaziz; ...

2015-10-26

Strong nonlinear light matter interaction is highly sought-after for a variety of applications including lasing and all-optical light modulation. Recently, resonant plasmonic structures have been considered promising candidates for enhancing nonlinear optical processes due to their ability to greatly enhance the optical near-field; however, their small mode volumes prevent the inherently large nonlinear susceptibility of the metal from being efficiently exploited. We present an alternative approach that utilizes a Fano-resonant silicon metasurface. The metasurface results in strong near-field enhancement within the volume of the silicon resonator while minimizing two photon absorption. Here, we measure a third harmonic generation enhancement factormore » of 1.5 105 with respect to an unpatterned silicon film and an absolute conversion efficiency of 1.2 10 6 with a peak pump intensity of 3.2 GW cm 2. The enhanced nonlinearity, combined with a sharp linear transmittance spectrum, results in transmission modulation with a modulation depth of 36%. Finally, the modulation mechanism is studied by pump probe experiments« less

The analysis of non-linear dynamic behavior (including snap-through) of postbuckled plates by simple analytical solution

NASA Technical Reports Server (NTRS)

Ng, C. F.

1988-01-01

Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.

Mid-infrared high birefringence As2Se3-based PCF with large nonlinearity and distinctive dispersion by using asymmetric elliptical air hole cladding

NASA Astrophysics Data System (ADS)

Hui, Zhanqiang; Yang, Min; Zhang, Youkun; Zhang, Meizhi

2018-01-01

A novel high birefringence As2Se3-based hexagonal lattice photonic crystal fiber (PCF) is proposed. In the structure, a central defect core and three kinds of elliptical air holes with different major axes length and ellipticity are introduced in the cladding. The finite difference time domain (FDTD) method with perfectly matched layer (PML) absorption boundary conditions are used to simulate the guided modes of the designed PCF. The properties of this PCF are investigated in detail including the birefringence, beat length, dispersion, nonlinearity and polarization mode dispersion in the 2-5 μm mid-infrared range. The results show that for the optimized structure parameters of Λ = 1.6μm, a = 0.4μm, b = 0.1μm, a1 = 0.6μm, b1 = 0.04μm, a2 = 0.8μm, b2 = 0.06μm, the high birefringence of 0.1192 and beat length of 41.93 μm are obtained. The maximum nonlinearity coefficient of 10,050 w-1km-1 and 15,200 w-1km-1 for x- and y-polarization modes are achieved. The distinctive dispersion is analyzed, which is all-normal in x-polarization direction while it has two zero dispersion points at 3.18 μm and 3.65 μm in y-polarization direction. The designed PCF with high birefringence, large nonlinearity and distinctive dispersion will be beneficial for mid-infrared fiber sensing, mid-infrared spectroscopy and nonlinear optics applications.

Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint

NASA Technical Reports Server (NTRS)

Bullock, S. J.; Peterson, L. D.

1994-01-01

The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.

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.

A non-linear model of economic production processes

NASA Astrophysics Data System (ADS)

Ponzi, A.; Yasutomi, A.; Kaneko, K.

2003-06-01

We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.

Modeling of fatigue crack induced nonlinear ultrasonics using a highly parallelized explicit local interaction simulation approach

NASA Astrophysics Data System (ADS)

Shen, Yanfeng; Cesnik, Carlos E. S.

2016-04-01

This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.

High energy efficient solid state laser sources

NASA Technical Reports Server (NTRS)

Byer, Robert L.

1989-01-01

Recent progress in the development of highly efficient coherent optical sources was reviewed. This work has focused on nonlinear frequency conversion of the highly coherent output of the non-planar ring laser oscillators developed earlier in the program, and includes high efficiency second harmonic generation and the operation of optical parametric oscillators for wavelength diversity and tunability.

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.

Mechanics of the acoustic radiation force in tissue-like solids

NASA Astrophysics Data System (ADS)

Dontsov, Egor V.

The acoustic radiation force (ARF) is a phenomenon affiliated with the nonlinear effects of high-intensity wave propagation. It represents the mean momentum transfer from the sound wave to the medium, and allows for an effective computation of the mean motion (e.g. acoustic streaming in fluids) induced by a high-intensity sound wave. Nowadays, the high-intensity focused ultrasound is frequently used in medical diagnosis applications due to its ability to "push" inside the tissue with the radiation body force and facilitate the local quantification of tissue's viscoelastic properties. The main objectives of this study include: i) the theoretical investigation of the ARF in fluids and tissue-like solids generated respectively by the amplitude modulated plane wave and focused ultrasound; ii) computation of the nonlinear acoustic wave propagation when the amplitude of the focused ultrasound field is modulated by a low-frequency signal, and iii) modeling of the ARF-induced motion in tissue-like solids for the purpose of quantifying their nonlinear elasticity via the magnitude of the ARF. Regarding the first part, a comparison with the existing theory of the ARF reveals a number of key features that are brought to light by the new formulation, including the contributions to the ARF of ultrasound modulation and thermal expansion, as well as the precise role of constitutive nonlinearities in generating the sustained body force in tissue-like solids by a focused ultrasound beam. In the second part, the hybrid time-frequency domain algorithm for the numerical analysis of the nonlinear wave equation is proposed. The approach is validated by comparing the results to the finite-difference modeling in time domain. Regarding the third objective, the Fourier transform approach is used to compute the ARF-induced shear wave motion in tissue-mimicking phantoms. A comparison between the experiment (tests performed at the Mayo Clinic) and model permitted the estimation of a particular coefficient of nonlinear tissue elasticity from the amplitude of the ARF-generated shear waves. For completeness, the ARF estimates of this coefficient are verified via an established technique known as acoustoelasticity.

Elastoviscoplastic snap-through behavior of shallow arches subjected to thermomechanical loads

NASA Technical Reports Server (NTRS)

Simitses, George J.; Song, Yuzhao; Sheinman, Izhak

1991-01-01

The problem of snap-through buckling of clamped shallow arches under thermomechanical loads is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations. A finite element approach is employed to predict the, in general, inelastic buckling behavior. The construction material is alloy B1900 + Hf, which is commonly utilized in high-temperature environments. The effect of several parameters is assessed. These parameters include the rise parameter and temperature. Comparison between elastic and elastoviscoplastic responses is also presented.

Device and method for imaging of non-linear and linear properties of formations surrounding a borehole

DOEpatents

Johnson, Paul A; Tencate, James A; Le Bas, Pierre-Yves; Guyer, Robert; Vu, Cung Khac; Skelt, Christopher

2013-10-08

In some aspects of the disclosure, a method and an apparatus is disclosed for investigating material surrounding the borehole. The method includes generating within a borehole an intermittent low frequency vibration that propagates as a tube wave longitudinally to the borehole and induces a nonlinear response in one or more features in the material that are substantially perpendicular to a longitudinal axis of the borehole; generating within the borehole a sequence of high frequency pulses directed such that they travel longitudinally to the borehole within the surrounding material; and receiving, at one or more receivers positionable in the borehole, a signal that includes components from the low frequency vibration and the sequence of high frequency pulses during intermittent generation of the low frequency vibration, to investigate the material surrounding the borehole.

Dielectric Yagi-Uda nanoantennas driven by electron-hole plasma photoexcitation

NASA Astrophysics Data System (ADS)

Li, S.; Lepeshov, S.; Savelev, R.; Baranov, D.; Belov, P.; Krasnok, A.

2017-11-01

All-dielectric nanophotonics based on high-index dielectric nanoparticles became a powerful platform for modern light science, providing many fascinating applications, including high-efficient nanoantennas and metamaterials. High-index dielectric nanostructures are of a special interest for nonlinear nanophotonics, where they demonstrate special types of optical nonlinearity, such as electron-hole plasma photoexcitation, which are not inherent to plasmonic nanostructures. Here, we propose a novel type of highly tunable all-dielectric Yagi-Uda nanoantennas, consisting of a chain of Si nanoparticles exciting by an electric dipole source, which allow tuning of their radiating properties via electron-hole plasma photoexcitation. We theoretically and numerically demonstrate the tuning of radiation power patterns and the Purcell effect by additional pumping of several boundary nanoparticles with relatively low peak intensities of fs-laser.

Nonlinear and Anisotropic Tensile Properties of Graft Materials used in Soft Tissue Applications

PubMed Central

Yoder, Jonathon H; Elliott, Dawn M

2010-01-01

Background The mechanical properties of extracellular matrix grafts that are intended to augment or replace soft tissues should be comparable to the native tissue. Such grafts are often used in fiber-reinforced tissue applications that undergo multi-axial loading and therefore knowledge of the anisotropic and nonlinear properties are needed, including the moduli and Poisson's ratio in two orthogonal directions within the plane of the graft. The objective of this study was to measure the tensile mechanical properties of several marketed grafts: Alloderm, Restore, CuffPatch, and OrthADAPT. Methods The degree of anisotropy and nonlinearity within each graft was evaluated from uniaxial tensile tests and compared to their native tissue. Results The Alloderm graft was anisotropic in both the toe and linear-region of the stress-strain response, was highly nonlinear, and generally had low properties. The Restore and CuffPatch grafts had similar stress-strain responses, were largely isotropic, had a linear-region modulus of 18 MPa, and were nonlinear. OrthADAPT was anisotropic in the linear region (131 vs 47 MPa) and was highly nonlinear. The Poisson ratio for all grafts was between 0.4 and 0.7, except for the parallel orientation of Restore which was greater than 1.0. Interpretation Having an informed understanding of how the available grafts perform mechanically will allow for better assessment by the physician for which graft to apply depending upon its application. PMID:20129728

Nonlinear and anisotropic tensile properties of graft materials used in soft tissue applications.

PubMed

Yoder, Jonathon H; Elliott, Dawn M

2010-05-01

The mechanical properties of extracellular matrix grafts that are intended to augment or replace soft tissues should be comparable to the native tissue. Such grafts are often used in fiber-reinforced tissue applications that undergo multi-axial loading and therefore knowledge of the anisotropic and nonlinear properties are needed, including the moduli and Poisson's ratio in two orthogonal directions within the plane of the graft. The objective of this study was to measure the tensile mechanical properties of several marketed grafts: Alloderm, Restore, CuffPatch, and OrthADAPT. The degree of anisotropy and non-linearity within each graft was evaluated from uniaxial tensile tests and compared to their native tissue. The Alloderm graft was anisotropic in both the toe- and linear-region of the stress-strain response, was highly nonlinear, and generally had low properties. The Restore and CuffPatch grafts had similar stress-strain responses, were largely isotropic, had a linear-region modulus of 18MPa, and were nonlinear. OrthADAPT was anisotropic in the linear-region (131 MPA vs 47MPa in the toe-region) and was highly nonlinear. The Poisson ratio for all grafts was between 0.4 and 0.7, except for the parallel orientation of Restore which was greater than 1.0. Having an informed understanding of how the available grafts perform mechanically will allow for better assessment by the physician for which graft to apply depending upon its application. Copyright 2010 Elsevier Ltd. All rights reserved.

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

Third order nonlinear optical properties of Mn doped CeO2 nanostructures

NASA Astrophysics Data System (ADS)

Mani Rahulan, K.; Angeline Little Flower, N.; Annie Sujatha, R.; Mohana Priya, P.; Gopalakrishnan, C.

2018-05-01

Mn doped CeO2 nanoparticles with different ratios of Mn were synthesized by hydrothermal method and their structural properties were characterized using X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and Scanning electron microscopy (SEM). XRD patterns revealed that the peaks are highly crystalline structure with no segregation of Mn. The surface morphology from SEM reveals that particle size decreases with increase in Mn concentration. Nonlinear optical studies of the samples were measured by single-beam open aperture Z-scan technique using 5 ns laser pulses at 532 nm. The measured optical nonlinearity of all the samples exhibit typical third order nonlinear optical behavior including two-photon absorption (2 PA) and reverse saturable absorption (RSA). The experimental results show that the presence of RSA in these nanoparticles makes them a promising material for the fabrication of optical limiting devices. .

Frequency-domain full-waveform inversion with non-linear descent directions

NASA Astrophysics Data System (ADS)

Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

2018-05-01

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a benchmark FWI approach involving the standard gradient.

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.

Nonlinear Whirl Response of a High-Speed Seal Test Rotor With Marginal and Extended Squeeze-Film Dampers

NASA Technical Reports Server (NTRS)

Proctor, Margaret P.; Gunter, Edgar J.

2005-01-01

Synchronous and nonsynchronous whirl response analysis of a double overhung, high-speed seal test rotor with ball bearings supported in 5.84- and 12.7-mm-long, un-centered squeeze-film oil dampers is presented. Test performance with the original damper of length 5.84 mm was marginal, with nonsynchronous whirling at the overhung seal test disk and high amplitude synchronous response above 32,000 rpm near the drive spline section occurring. A system critical speed analysis of the drive system and the high-speed seal test rotor indicated that the first two critical speeds are associated with the seal test rotor. Nonlinear synchronous unbalance and time transient whirl studies were conducted on the seal test rotor with the original and extended damper lengths. With the original damper design, the nonlinear synchronous response showed that unbalance could cause damper lockup at 33,000 rpm. Alford cross-coupling forces were also included at the overhung seal test disk for the whirl analysis. Sub-synchronous whirling at the seal test disk was observed in the nonlinear time transient analysis. With the extended damper length of 12.7 mm, the sub-synchronous motion was eliminated and the rotor unbalance response was acceptable to 45,000 rpm with moderate rotor unbalance. However, with high rotor unbalance, damper lockup could still occur at 33,000 rpm, even with the extended squeeze-film dampers. Therefore, the test rotor must be reasonably balanced in order for the un-centered dampers to be effective.

High Speed Civil Transport Aircraft Simulation: Reference-H Cycle 1, MATLAB Implementation

NASA Technical Reports Server (NTRS)

Sotack, Robert A.; Chowdhry, Rajiv S.; Buttrill, Carey S.

1999-01-01

The mathematical model and associated code to simulate a high speed civil transport aircraft - the Boeing Reference H configuration - are described. The simulation was constructed in support of advanced control law research. In addition to providing time histories of the dynamic response, the code includes the capabilities for calculating trim solutions and for generating linear models. The simulation relies on the nonlinear, six-degree-of-freedom equations which govern the motion of a rigid aircraft in atmospheric flight. The 1962 Standard Atmosphere Tables are used along with a turbulence model to simulate the Earth atmosphere. The aircraft model has three parts - an aerodynamic model, an engine model, and a mass model. These models use the data from the Boeing Reference H cycle 1 simulation data base. Models for the actuator dynamics, landing gear, and flight control system are not included in this aircraft model. Dynamic responses generated by the nonlinear simulation are presented and compared with results generated from alternate simulations at Boeing Commercial Aircraft Company and NASA Langley Research Center. Also, dynamic responses generated using linear models are presented and compared with dynamic responses generated using the nonlinear simulation.

High-Alpha Research Vehicle Lateral-Directional Control Law Description, Analyses, and Simulation Results

NASA Technical Reports Server (NTRS)

Davidson, John B.; Murphy, Patrick C.; Lallman, Frederick J.; Hoffler, Keith D.; Bacon, Barton J.

1998-01-01

This report contains a description of a lateral-directional control law designed for the NASA High-Alpha Research Vehicle (HARV). The HARV is a F/A-18 aircraft modified to include a research flight computer, spin chute, and thrust-vectoring in the pitch and yaw axes. Two separate design tools, CRAFT and Pseudo Controls, were integrated to synthesize the lateral-directional control law. This report contains a description of the lateral-directional control law, analyses, and nonlinear simulation (batch and piloted) results. Linear analysis results include closed-loop eigenvalues, stability margins, robustness to changes in various plant parameters, and servo-elastic frequency responses. Step time responses from nonlinear batch simulation are presented and compared to design guidelines. Piloted simulation task scenarios, task guidelines, and pilot subjective ratings for the various maneuvers are discussed. Linear analysis shows that the control law meets the stability margin guidelines and is robust to stability and control parameter changes. Nonlinear batch simulation analysis shows the control law exhibits good performance and meets most of the design guidelines over the entire range of angle-of-attack. This control law (designated NASA-1A) was flight tested during the Summer of 1994 at NASA Dryden Flight Research Center.

Flexible twist for pitch control in a high altitude long endurance aircraft with nonlinear response

NASA Astrophysics Data System (ADS)

Bond, Vanessa L.

Information dominance is the key motivator for employing high-altitude long-endurance (HALE) aircraft to provide continuous coverage in the theaters of operation. A joined-wing configuration of such a craft gives the advantage of a platform for higher resolution sensors. Design challenges emerge with structural flexibility that arise from a long-endurance aircraft design. The goal of this research was to demonstrate that scaling the nonlinear response of a full-scale finite element model was possible if the model was aeroelastically and "nonlinearly" scaled. The research within this dissertation showed that using the first three modes and the first bucking modes was not sufficient for proper scaling. In addition to analytical scaling several experiments were accomplished to understand and overcome design challenges of HALE aircraft. One such challenge is combated by eliminating pitch control surfaces and replacing them with an aft-wing twist concept. This design option was physically realized through wind tunnel measurement of forces, moments and pressures on a subscale experimental model. This design and experiment demonstrated that pitch control with aft-wing twist is feasible. Another challenge is predicting the nonlinear response of long-endurance aircraft. This was addressed by experimental validation of modeling nonlinear response on a subscale experimental model. It is important to be able to scale nonlinear behavior in this type of craft due to its highly flexible nature. The validation accomplished during this experiment on a subscale model will reduce technical risk for full-scale development of such pioneering craft. It is also important to experimentally reproduce the air loads following the wing as it deforms. Nonlinearities can be attributed to these follower forces that might otherwise be overlooked. This was found to be a significant influence in HALE aircraft to include the case study of the FEM and experimental models herein.

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.

Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration.

PubMed

Chen, Yunjin; Pock, Thomas

2017-06-01

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (i.e., linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD-Trainable Nonlinear Reaction Diffusion. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.

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

PubMed

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

2015-05-01

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

Optical nonlinearities in plasmonic metamaterials (Conference Presentation)

NASA Astrophysics Data System (ADS)

Zayats, Anatoly V.

2016-04-01

Metals exhibit strong and fast nonlinearities making metallic, plasmonic, structures very promising for ultrafast all-optical applications at low light intensities. Combining metallic nanostructures in metamaterials provides additional functionalities via prospect of precise engineering of spectral response and dispersion. From this point of view, hyperbolic metamaterials, in particular those based on plasmonic nanorod arrays, provide wealth of exciting possibilities in nonlinear optics offering designed linear and nonlinear properties, polarization control, spontaneous emission control and many others. Experiments and modeling have already demonstrated very strong Kerr-nonlinear response and its ultrafast recovery due to the nonlocal nature of the plasmonic mode of the metamaterial, so that small changes in the permittivity of the metallic component under the excitation modify the nonlocal response that in turn leads to strong changes of the metamaterial transmission. In this talk, we will discuss experimental studies and numerical modeling of second- and third-order nonlinear optical processes in hyperbolic metamaterials based on metallic nanorods and other plasmonic systems where coupling between the resonances plays important role in defining nonlinear response. Second-harmonic generation and ultrafast Kerr-type nonlinearity originating from metallic component of the metamaterial will be considered, including nonlinear magneto-optical effects. Nonlinear optical response of stand-alone as well as integrated metamaterial components will be presented. Some of the examples to be discussed include nonlinear polarization control, nonlinear metamaterial integrated in silicon photonic circuitry and second-harmonic generation, including magneto-optical effects.

Controlling the stability of nonlinear optical modes via electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Zhang, Kun; Liang, Yi-zeng; Lin, Ji; Li, Hui-jun

2018-02-01

We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having Λ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schrödinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.

Second order nonlinear equations of motion for spinning highly flexible line-elements. [for spacecraft solar sail

NASA Technical Reports Server (NTRS)

Salama, M.; Trubert, M.

1979-01-01

A formulation is given for the second order nonlinear equations of motion for spinning line-elements having little or no intrinsic structural stiffness. Such elements have been employed in recent studies of structural concepts for future large space structures such as the Heliogyro solar sailer. The derivation is based on Hamilton's variational principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line-element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison has revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.

The equivalent angle-of-attack method for estimating the nonlinear aerodynamic characteristics of missile wings and control surfaces

NASA Technical Reports Server (NTRS)

Hemsch, M. J.; Nielsen, J. N.

1982-01-01

A method has been developed for estimating the nonlinear aerodynamic characteristics of missile wing and control surfaces. The method is based on the following assumption: if a fin on a body has the same normal-force coefficient as a wing alone composed of two of the same fins joined together at their root chords, then the other force and moment coefficients of the fin and the wing alone are the same including the nonlinearities. The method can be used for deflected fins at arbitrary bank angles and at high angles of attack. In the paper, a full derivation of the method is given, its accuracy demonstrated and its use in extending missile data bases is shown.

Bayesian dynamical systems modelling in the social sciences.

PubMed

Ranganathan, Shyam; Spaiser, Viktoria; Mann, Richard P; Sumpter, David J T

2014-01-01

Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.

Quantitative evaluation method for nonlinear characteristics of piezoelectric transducers under high stress with complex nonlinear elastic constant

NASA Astrophysics Data System (ADS)

Miyake, Susumu; Kasashima, Takashi; Yamazaki, Masato; Okimura, Yasuyuki; Nagata, Hajime; Hosaka, Hiroshi; Morita, Takeshi

2018-07-01

The high power properties of piezoelectric transducers were evaluated considering a complex nonlinear elastic constant. The piezoelectric LCR equivalent circuit with nonlinear circuit parameters was utilized to measure them. The deformed admittance curve of piezoelectric transducers was measured under a high stress and the complex nonlinear elastic constant was calculated by curve fitting. Transducers with various piezoelectric materials, Pb(Zr,Ti)O3, (K,Na)NbO3, and Ba(Zr,Ti)O3–(Ba,Ca)TiO3, were investigated by the proposed method. The measured complex nonlinear elastic constant strongly depends on the linear elastic and piezoelectric constants. This relationship indicates that piezoelectric high power properties can be controlled by modifying the linear elastic and piezoelectric constants.

A reduced-order model from high-dimensional frictional hysteresis

PubMed Central

Biswas, Saurabh; Chatterjee, Anindya

2014-01-01

Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a low-order model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation through signum nonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof. PMID:24910522

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

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

DOE PAGES

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

2015-03-11

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

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

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

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

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

A Large-Particle Monte Carlo Code for Simulating Non-Linear High-Energy Processes Near Compact Objects

NASA Technical Reports Server (NTRS)

Stern, Boris E.; Svensson, Roland; Begelman, Mitchell C.; Sikora, Marek

1995-01-01

High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.

Incorporating a Spatial Prior into Nonlinear D-Bar EIT Imaging for Complex Admittivities.

PubMed

Hamilton, Sarah J; Mueller, J L; Alsaker, M

2017-02-01

Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filter to include higher frequency components in the reconstruction, in particular, features that are known with high confidence. This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.

Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1985-01-01

The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.

Numerical simulation of incoherent optical wave propagation in nonlinear fibers

NASA Astrophysics Data System (ADS)

Fernandez, Arnaud; Balac, Stéphane; Mugnier, Alain; Mahé, Fabrice; Texier-Picard, Rozenn; Chartier, Thierry; Pureur, David

2013-11-01

The present work concerns the study of pulsed laser systems containing a fiber amplifier for boosting optical output power. In this paper, this fiber amplification device is included into a MOPFA laser, a master oscillator coupled with fiber amplifier, usually a cladding-pumped high-power amplifier often based on an ytterbium-doped fiber. An experimental study has established that the observed nonlinear effects (such as Kerr effect, four waves mixing, Raman effect) could behave very differently depending on the characteristics of the optical source emitted by the master laser. However, it has not yet been possible to determine from the experimental data if the statistics of the photons is alone responsible for the various nonlinear scenarios observed. Therefore, we have developed a numerical simulation software for solving the generalized nonlinear Schrödinger equation with a stochastic source term in order to validate the hypothesis that the coherence properties of the master laser are mainly liable for the behavior of the observed nonlinear effects. Contribution to the Topical Issue "Numelec 2012", Edited by Adel Razek.

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.

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.

PubMed

Shang, Xituan; Yen, Michael R T; Gaber, M Waleed

2010-06-01

The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.

Dynamics identification of a piezoelectric vibrational energy harvester by image analysis with a high speed camera

NASA Astrophysics Data System (ADS)

Wolszczak, Piotr; Łygas, Krystian; Litak, Grzegorz

2018-07-01

This study investigates dynamic responses of a nonlinear vibration energy harvester. The nonlinear mechanical resonator consists of a flexible beam moving like an inverted pendulum between amplitude limiters. It is coupled with a piezoelectric converter, and excited kinematically. Consequently, the mechanical energy input is converted into the electrical power output on the loading resistor included in an electric circuit attached to the piezoelectric electrodes. The curvature of beam mode shapes as well as deflection of the whole beam are examined using a high speed camera. The visual identification results are compared with the voltage output generated by the piezoelectric element for corresponding frequency sweeps and analyzed by the Hilbert transform.

Highly coherent octave-spanning supercontinuum generation in CS2-filled photonic crystal fiber with strong slow nonlinearity

NASA Astrophysics Data System (ADS)

Wang, Liyun; Yuan, Jinhui; Wang, Kuiru; Kang, Zhe; Sang, Xinzhu; Yu, Chongxiu; Yan, Binbin

2016-11-01

In this paper, the supercontinuum (SC) generation in a carbon disulfide (CS2)-filled photonic crystal fiber (PCF) with strong slow nonlinearity is investigated. When the PCF is pumped at 1.55 μm in the anomalous dispersion region, we obtain highly coherent SC spanning from 0.99 to 2.32 μm, at -40 dB level. Moreover, the influences of the slow nonlinearity, the input pulse width, the pulse peak power, the fiber length, and the temperature on the supercontinuum generation (SCG) are studied. The role of the slow nonlinearity in enhancing the coherence of SC is proved. To our best knowledge, this is the first demonstration on generating the octave-spanning SC with high coherence using the slow nonlinearity of CS2. CS2 is a material that has high nonlinearity coefficient and well transparency in infrared. What's more, the slow nonlinearity is very strong in this material.

Experimental observation of multi-scale interactions among kink /tearing modes and high-frequency fluctuations in the HL-2A core NBI plasmas

NASA Astrophysics Data System (ADS)

Chen, W.; Jiang, M.; Xu, Y.; Shi, P. W.; Yu, L. M.; Ding, X. T.; Shi, Z. B.; Ji, X. Q.; Yu, D. L.; Li, Y. G.; Yang, Z. C.; Zhong, W. L.; Qiu, Z. Y.; Li, J. Q.; Dong, J. Q.; Yang, Q. W.; Liu, Yi.; Yan, L. W.; Xu, M.; Duan, X. R.

2017-11-01

Multi-scale interactions have been observed recently in the HL-2A core NBI plasmas, including the synchronous coupling between m/n=1/1 kink mode and m/n=2/1 tearing mode, nonlinear couplings of TAE/BAE and m/n=2/1 TM near q=2 surface, AITG/KBM/BAE and m/n=1/1 kink mode near q=1 surface, and between m/n=1/1 kink mode and high-frequency turbulence. Experimental results suggest that several couplings can exist simultaneously, Alfvenic fluctuations have an important contribution to the high-frequency turbulence spectra, and the couplings reveal the electromagnetic character. Multi-scale interactions via the nonlinear modulation process maybe enhance plasma transport and trigger sawtooth-crash onset.

Highly Stable Nanolattice Structures using Nonlinear Laser Lithography

NASA Astrophysics Data System (ADS)

Yavuz, Ozgun; Tokel, Onur; Ergecen, Emre; Pavlov, Ihor; Makey, Ghaith; Ilday, Fatih Omer

Periodic nanopatterning is crucial for multiple technologies, including photovoltaics and display technologies. Conventional optical lithography techniques require complex masks, while e-beam and ion-beam lithography require expensive equipment. With the Nonlinear Laser Lithography (NLL) technique, we had recently shown that various surfaces can be covered with extremely periodic nanopatterns with ultrafast lasers through a single-step, maskless and inexpensive method. Here, we expand NLL nanopatterns to flexible materials, and also present a fully predictive model for the formation of NLL nanostructures as confirmed with experiments. In NLL, a nonlocal positive feedback mechanism (dipole scattering) competes with a rate limiting negative feedback mechanism. Here, we show that judicious use of the laser polarisation can constrain the lattice symmetry, while the nonlinearities regulate periodicity. We experimentally demonstrate that in addition to one dimensional periodic stripes, two dimensional lattices can be produced on surfaces. In particular, hexagonal and square lattices were produced, which are highly desired for display technologies. Notably, with this approach, we can tile flexible substrates, which can find applications in next generation display technologies.

Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers

NASA Astrophysics Data System (ADS)

Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan

2018-03-01

Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.

Editorial development

NASA Astrophysics Data System (ADS)

Wileman, Chris

2013-01-01

We are delighted to announce that from January 2013, Professor Edgar Knobloch of the University of California, Berkeley, USA, will be the new co-Editor-in-Chief of Nonlinearity, joining current co-Editor-in-Chief Professor Anatoly Neishtadt. Edgar comes to the position with a wealth of experience, including a spell as a valued member of the Editorial Board of Nonlinearity, and wide respect from across the nonlinear science community. We very much look forward to working with Edgar to continue to develop the journal's high standards of quality and interest to the readership. Whilst welcoming Edgar to the position, we would also like to extend our gratitude to Professor Jon Keating for his tremendous contribution to Nonlinearity during his time as co-Editor-in-Chief. Jon joined the journal in 1997 as a member of the Editorial Board, taking over as co-Editor-in-Chief in 2004. Throughout his time as both a member of the Editorial Board and as a co-Editor-in-Chief, Jon worked tirelessly to uphold the highest quality standards and to ensure that Nonlinearity is a place where researchers can both read and publish the most stimulating work in nonlinear science. His joint leadership with Professor Anatoly Neishtadt has seen Nonlinearity continue from strength to strength. Jon will be sorely missed. On behalf of the London Mathematical Society, Institute of Physics and the entire Editorial Board we wish him all the best in the future.

Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.

2006-01-01

Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.

Response phase mapping of nonlinear joint dynamics using continuous scanning LDV measurement method

NASA Astrophysics Data System (ADS)

Di Maio, D.; Bozzo, A.; Peyret, Nicolas

2016-06-01

This study aims to present a novel work aimed at locating discrete nonlinearities in mechanical assemblies. The long term objective is to develop a new metric for detecting and locating nonlinearities using Scanning LDV systems (SLDV). This new metric will help to improve the modal updating, or validation, of mechanical assemblies presenting discrete and sparse nonlinearities. It is well established that SLDV systems can scan vibrating structures with high density of measurement points and produc e highly defined Operational Deflection Shapes (ODSs). This paper will present some insights on how to use response phase mapping for locating nonlinearities of a bolted flange. This type of structure presents two types of nonlinearities, which are geometr ical and frictional joints. The interest is focussed on the frictional joints and, therefore, the ability to locate which joint s are responsible for nonlinearity is seen highly valuable for the model validation activities.

Nonlinear Analysis and Preliminary Testing Results of a Hybrid Wing Body Center Section Test Article

NASA Technical Reports Server (NTRS)

Przekop, Adam; Jegley, Dawn C.; Rouse, Marshall; Lovejoy, Andrew E.; Wu, Hsi-Yung T.

2015-01-01

A large test article was recently designed, analyzed, fabricated, and successfully tested up to the representative design ultimate loads to demonstrate that stiffened composite panels with through-the-thickness reinforcement are a viable option for the next generation large transport category aircraft, including non-conventional configurations such as the hybrid wing body. This paper focuses on finite element analysis and test data correlation of the hybrid wing body center section test article under mechanical, pressure and combined load conditions. Good agreement between predictive nonlinear finite element analysis and test data is found. Results indicate that a geometrically nonlinear analysis is needed to accurately capture the behavior of the non-circular pressurized and highly-stressed structure when the design approach permits local buckling.

Nonlinear optical whispering gallery mode resonators

NASA Technical Reports Server (NTRS)

Ilchenko, Vladimir (Inventor); Matsko, Andrey B. (Inventor); Savchenkov, Anatoliy (Inventor); Maleki, Lutfollah (Inventor)

2005-01-01

Whispering gallery mode (WGM) optical resonators comprising nonlinear optical materials, where the nonlinear optical material of a WGM resonator includes a plurality of sectors within the optical resonator and nonlinear coefficients of two adjacent sectors are oppositely poled.

Mathematical nonlinear optics

NASA Astrophysics Data System (ADS)

McLaughlin, David W.

1995-08-01

The principal investigator, together with a post-doctoral fellows Tetsuji Ueda and Xiao Wang, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics and to equations directly relevant to nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals and chaotic, homoclinic, small dispersive, and random behavior of solutions of the nonlinear Schroedinger equation. In project 1, the extremely strong nonlinear response of a continuous wave laser beam in a nematic liquid crystal medium has produced striking undulation and filamentation of the laser beam which has been observed experimentally and explained theoretically. In project 2, qualitative properties of the nonlinear Schroedinger equation (which is the fundamental equation for nonlinear optics) have been identified and studied. These properties include optical shocking behavior in the limit of very small dispersion, chaotic and homoclinic behavior in discretizations of the partial differential equation, and random behavior.

FOREWORD: Workshop on Large Amplitude Waves and Fields in Plasmas, sponsored by the Commission of the European Communities

NASA Astrophysics Data System (ADS)

Bingham, R.; De Angelis, U.; Shukla, P. K.; Stenflo, L.

1990-01-01

During the last decade considerable progress has been made in the area of nonlinear plasma wave phenomena and their applications. In order to exhibit the present state-of-art in this field, a one-week (22-26 May) workshop on Large Amplitude Waves and Fields was organized at the International Centre for Theoretical Physics (ICTP), Trieste, Italy, during the bi-yearly activity of the Spring College on Plasma Physics (15 May-9 June, 1989). Most of the invited lectures are published in this Topical Issue of Physica Scripta so that scientists working, or who want to enter the field of nonlinear plasma wave theory, can find out what has been achieved and what are the current research trends in this area. The material included here consists of general plasma wave theory, results of computer simulations, and experimental verifications. Without going into any detail, we shall just highlight the topics and the general features of the lectures contained in these proceedings. Various aspects of the excitation, propagation and interaction of nonlinear waves in plasmas are reviewed. Their relevance to plasma-based beat wave accelerators, short pulse laser and particle beam wake-field accelerators, plasma lenses, laser fusion and ionospheric modification experiments is discussed. Some introductory lectures present the general physics of nonlinear plasma waves including the saturation mechanisms and wave breaking conditions for both non-relativistic and relativistic nonlinearities. Three wave and four wave processes which include stimulated Raman, Brillouin and Compton scattering, modulational instabilities, self-focusing and collapse of the waves are discussed, emphasizing the important effects due to the relativistic electron mass variation and ponderomotive force. Detailed numerical studies of the interaction of high frequency plasma waves with low frequency density fluctuations described by the Zakharov equations show the localization of the high frequency field in density cavities and their burn-out resulting in very strong turbulence. Remarkable agreement between the simulations and ionospheric modification experiments have been demonstrated. The articles presented also attempted to correlate the theories of parametric instabilities with experimental observations. The properties of plasma lenses used for focusing of high energy particle beams is also presented as part of the uses of the nonlinear plasmas. Self-organisation of plasmas resulting in coherent nonlinear structures and particle diffusion processes are reported. On the experimental side the nonlinear optics of plasmas as a new area of research has been reviewed. This is becoming an important area for research since it treats the plasma from the outset as a nonlinear medium. Experimental observations of phase conjugation of electromagnetic signals demonstrate once again the importance of the nonlinearities inherent in the interaction of large amplitude waves with plasmas. Finally the importance of turbulence in space plasmas is emphasized in a discussion of the auroral phenomenon, presenting the plasma physicists point of view on this topic. The workshop, attended by scientists from all over the world, stimulated a great deal of lively discussions about the theoretical foundations, experimental observations and interpretations together with computer simulation results on the physics of nonlinear plasma wave phenomena. The workshop was made possible by the kind support of Professors A Salam, L Bertocchi and M Hassan. We are grateful to them for giving us the opportunity to organize the workshop within the activities of the Spring College on Plasma Physics. Thanks are also due to the ICTP and the European Economic Community (EEC) for providing partial financial support. Finally, our most cordial thanks are extended to the invited speakers for coming to Trieste delivering excellent talks and enhancing the activity of the Spring College.

Properties of Nonlinear Dynamo Waves

NASA Technical Reports Server (NTRS)

Tobias, S. M.

1997-01-01

Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.

Nonlinear time-series-based adaptive control applications

NASA Technical Reports Server (NTRS)

Mohler, R. R.; Rajkumar, V.; Zakrzewski, R. R.

1991-01-01

A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.

Nonlinear elasticity in rocks: A comprehensive three-dimensional description

DOE PAGES

Lott, Martin; Remillieux, Marcel; Garnier, Vincent; ...

2017-07-17

Here we study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency “pump” wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe” wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists ofmore » the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $P$ and (shear) $S$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.« less

How Artificial Should the Treatment of a Plasma's Viscosity Be?

NASA Astrophysics Data System (ADS)

Whitney, K. G.; Velikovich, A. L.; Thornhill, J. W.; Davis, J.

1999-11-01

Electron viscosity dominates over ion viscosity and is important in describing the generation of shock fronts in highly ionizable plasmas. The sizes of shock front jumps in electron and ion temperature are determined from the magnitudes of the heat flow vector and pressure tensor, which, in turn, acquire non-negligible nonlinear contributions from the temperature and density gradients when these gradients are large. Thus, a consistent treatment of steep gradient formation in plasmas must come from investigations that include the effects of these nonlinear contributions to heat and momentum transport. Coefficients for each of five nonlinear contributions to the pressure tensor for an (r,z) Z-pinch geometry are presented and discussed in this talk. Hydrodynamic code calculations generally are not designed to provide a testbed for directly evaluating the kinetic energy dissipation that occurs at shock fronts; therefore, the strength of these nonlinear pressure tensor terms will be estimated by post-processing a Z-pinch hydrodynamics calculation and a steady-state planar shock wave calculation.

Generation of High Purity Photon-Pair in a Short Highly Non-Linear Fiber

DTIC Science & Technology

2013-01-01

Avalanche photodiode. A 10 m long HNLF fabricated by Sumitomo with a core diameter of 4 microns is fusion spliced to a single mode fiber for a...parametric down conversion (SPDC) was first observed in χ(2) nonlinear crystal [3]. However, the compatibility of a nonlinear crystal source with fiber and...PAIR IN A SHORT HIGHLY NON-LINEAR FIBER 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA8750-12-1-0136 5c. PROGRAM ELEMENT NUMBER N/A 6. AUTHOR(S

Fast prediction of pulsed nonlinear acoustic fields from clinically relevant sources using Time-Averaged Wave Envelope approach: comparison of numerical simulations and experimental results

PubMed Central

Wójcik, J.; Kujawska, T.; Nowicki, A.; Lewin, P.A.

2008-01-01

The primary goal of this work was to verify experimentally the applicability of the recently introduced Time-Averaged Wave Envelope (TAWE) method [1] as a tool for fast prediction of four dimensional (4D) pulsed nonlinear pressure fields from arbitrarily shaped acoustic sources in attenuating media. The experiments were performed in water at the fundamental frequency of 2.8 MHz for spherically focused (focal length F = 80 mm) square (20 × 20 mm) and rectangular (10 × 25 mm) sources similar to those used in the design of 1D linear arrays operating with ultrasonic imaging systems. The experimental results obtained with 10-cycle tone bursts at three different excitation levels corresponding to linear, moderately nonlinear and highly nonlinear propagation conditions (0.045, 0.225 and 0.45 MPa on-source pressure amplitude, respectively) were compared with those yielded using the TAWE approach [1]. The comparison of the experimental results and numerical simulations has shown that the TAWE approach is well suited to predict (to within ± 1 dB) both the spatial-temporal and spatial-spectral pressure variations in the pulsed nonlinear acoustic beams. The obtained results indicated that implementation of the TAWE approach enabled shortening of computation time in comparison with the time needed for prediction of the full 4D pulsed nonlinear acoustic fields using a conventional (Fourier-series) approach [2]. The reduction in computation time depends on several parameters, including the source geometry, dimensions, fundamental resonance frequency, excitation level as well as the strength of the medium nonlinearity. For the non-axisymmetric focused transducers mentioned above and excited by a tone burst corresponding to moderately nonlinear and highly nonlinear conditions the execution time of computations was 3 and 12 hours, respectively, when using a 1.5 GHz clock frequency, 32-bit processor PC laptop with 2 GB RAM memory, only. Such prediction of the full 4D pulsed field is not possible when using conventional, Fourier-series scheme as it would require increasing the RAM memory by at least 2 orders of magnitude. PMID:18474387

FIBER LASER CONSTRUCTION AND THEORY INCLUDING FIBER BRAGG GRATINGS Photonic Crystal Fibers (PCFs) and applications of gas filled PCFs

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

Sutton, Jacob O.

The principles used in fiber lasers have been around for a while but it is only within the past few years that fiber lasers have become commercially available and used in high power laser applications. This paper will focus on the basic design principles of fiber lasers, including fiber Bragg gratings, principles of operation, and forms of non-linear effects. It will describe the type and associated doping of the fiber used and difficult designs used to guide energy from the pump to the active medium. Topics covered include fiber laser design, fiber Bragg gratings, materials used, differences in quantum energymore » loss, thermo-optical effects, stimulated Raman scattering, Brillouin scattering, photonic crystal fibers and applications of gas filled Photonic Crystal Fibers (PCFs). Thanks to fiber lasers, the energy required to produce high power lasers has greatly dropped and as such we can now produce kW power using a standard 120V 15A circuit. High power laser applications are always requiring more power. The fiber laser can now deliver the greater power that these applications demand. Future applications requiring more power than can be combined using standard materials or configurations will need to be developed to overcome the high energy density and high non-linear optical scattering effects present during high power operations.« less

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

PubMed

Kanagawa, Tetsuya

2015-05-01

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

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

Nonlinear friction dynamics on polymer surface under accelerated movement

NASA Astrophysics Data System (ADS)

Aita, Yuuki; Asanuma, Natsumi; Takahashi, Akira; Mayama, Hiroyuki; Nonomura, Yoshimune

2017-04-01

Nonlinear phenomena on the soft material surface are one of the most exciting topics of chemical physics. However, only a few reports exist on the friction phenomena under accelerated movement, because friction between two solid surfaces is considered a linear phenomenon in many cases. We aim to investigate how nonlinear accelerated motion affects friction on solid surfaces. In the present study, we evaluate the frictional forces between two polytetrafluoroethylene (PTFE) resins using an advanced friction evaluation system. On PTFE surfaces, the normalized delay time δ, which is the time lag in the response of the friction force to the accelerated movement, is observed in the pre-sliding friction process. Under high-velocity conditions, kinetic friction increases with velocity. Based on these experimental results, we propose a two-phase nonlinear model including a pre-sliding process (from the beginning of sliding of a contact probe to the establishment of static friction) and a kinetic friction process. The present model consists of several factors including velocity, acceleration, stiffness, viscosity, and vertical force. The findings reflecting the viscoelastic properties of soft material is useful for various fields such as in the fabrication of clothes, cosmetics, automotive materials, and virtual reality systems as well as for understanding friction phenomena on soft material surfaces.

Nonlinear Site Response Validation Studies Using KIK-net Strong Motion Data

NASA Astrophysics Data System (ADS)

Asimaki, D.; Shi, J.

2014-12-01

Earthquake simulations are nowadays producing realistic ground motion time-series in the range of engineering design applications. Of particular significance to engineers are simulations of near-field motions and large magnitude events, for which observations are scarce. With the engineering community slowly adopting the use of simulated ground motions, site response models need to be re-evaluated in terms of their capabilities and limitations to 'translate' the simulated time-series from rock surface output to structural analyses input. In this talk, we evaluate three one-dimensional site response models: linear viscoelastic, equivalent linear and nonlinear. We evaluate the performance of the models by comparing predictions to observations at 30 downhole stations of the Japanese network KIK-Net that have recorded several strong events, including the 2011 Tohoku earthquake. Velocity profiles are used as the only input to all models, while additional parameters such as quality factor, density and nonlinear dynamic soil properties are estimated from empirical correlations. We quantify the differences of ground surface predictions and observations in terms of both seismological and engineering intensity measures, including bias ratios of peak ground response and visual comparisons of elastic spectra, and inelastic to elastic deformation ratio for multiple ductility ratios. We observe that PGV/Vs,30 — as measure of strain— is a better predictor of site nonlinearity than PGA, and that incremental nonlinear analyses are necessary to produce reliable estimates of high-frequency ground motion components at soft sites. We finally discuss the implications of our findings on the parameterization of nonlinear amplification factors in GMPEs, and on the extensive use of equivalent linear analyses in probabilistic seismic hazard procedures.

Nonlinear acoustic spectroscopy of cracked flaws and disbonds: Fundamentals, techniques, and applications

NASA Astrophysics Data System (ADS)

Maev, R. Gr.; Solodov, I. Yu.

2000-05-01

Classical nonlinear acoustics of solids operates with distributed material nonlinearity related to unharmonicity of molecular interaction forces. Weakening of molecular bonds in a defect area or intermittent lack of elastic coupling between the faces of a vibrating crack or unbond ("clapping") results in anomalously high local contact acoustic nonlinearity (CAN). CAN properties and spectral features are different from those of the classical analog and important to develop new acoustic NDE techniques. Three approaches to nonlinear NDE methodology have been experimentally verified: low-frequency (hundreds of Hz) vibration technique, intermediate-frequency (hundreds of kHz) standing wave and high-frequency (tens of MHz) propagation modes. Low-frequency nonlinear contact vibrations revealed multiple sub- and super-harmonics generation featuring non-monotonous (sinx/x type) spectra. Parametric instability observed in resonator with a nonlinear contact leads to the output spectrum splitting up into successive sub-harmonics as the wave amplitude increases. High-frequency experiments demonstrated abnormal increases in the third harmonic amplitude: 3 or 4 order enhancement of the 3-ω nonlinear parameter was measured for the nonlinear contact. The CAN spectral features in both acoustic and vibration modes were used for nonlinear NDE of simulated and realistic flaws in glass, metal welds, etc. The sensitivities of the techniques are compared and their practical applicability assessed.

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

NASA Technical Reports Server (NTRS)

McKinley, David P.

2006-01-01

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

Real-time monitoring of acoustic linear and nonlinear behavior of titanium alloys during low-cycle fatigue and high-cycle fatigue

NASA Astrophysics Data System (ADS)

Frouin, Jerome; Sathish, Shamachary; Na, Jeong K.

2000-05-01

An in-situ technique to measure sound velocity, ultrasonic attenuation and acoustic nonlinear property has been developed for characterization and early detection of fatigue damage in aerospace materials. For this purpose we have developed a computer software and measurement technique including hardware for the automation of the measurement. New transducer holder and special grips are designed. The automation has allowed us to test the long-term stability of the electronics over a period of time and so proof of the linearity of the system. Real-time monitoring of the material nonlinearity has been performed on dog-bone specimens from zero fatigue all the way to the final fracture under low-cycle fatigue test condition (LCF) and high-cycle test condition (HCF). Real-time health monitoring of the material can greatly contribute to the understanding of material behavior under cyclic loading. Interpretation of the results show that correlation exist between the slope of the curve described by the material nonlinearity and the life of the component. This new methodology was developed with an objective to predict the initiation of fatigue microcracks, and to detect, in-situ fatigue crack initiation as well as to quantify early stages of fatigue damage.

Ultrasensitive detection enabled by nonlinear magnetization of nanomagnetic labels.

PubMed

Nikitin, M P; Orlov, A V; Sokolov, I L; Minakov, A A; Nikitin, P I; Ding, J; Bader, S D; Rozhkova, E A; Novosad, V

2018-06-21

Geometrically confined magnetic particles due to their unique response to external magnetic fields find a variety of applications, including magnetic guidance, heat and drug delivery, magneto-mechanical actuation, and contrast enhancement. Highly sensitive detection and imaging techniques based on the nonlinear properties of nanomagnets were recently proposed as innovative strong-translational potential methods applicable in complex, often opaque, biological systems. Here we report on the significant enhancement of the detection capability using optical-lithography-defined, ferromagnetic iron-nickel alloy disk-shaped particles. We show that an irreversible transition between strongly non-collinear (vortex) and single domain states, driven by an alternating magnetic field, translates into a nonlinear magnetic response that enables ultrasensitive detection of these particles. The record sensitivity of ∼3.5 × 10-9 emu, which is equivalent to ∼39 pg of magnetic material is demonstrated at room temperature for arrays of patterned disks. We also show that unbound disks suspended in the aqueous buffer can be successfully detected and quantified in real-time when administered into a live animal allowing for tracing of their biodistribution. The use of nanoscale ferromagnetic particles with engineered nonlinear properties opens prospects for further enhancing the sensitivity, scalability, and tunability of noise-free magnetic tag detection in high-background environments for various applications spanning from biosensing and medical imaging to anti-counterfeiting technologies.

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

PubMed

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

2013-11-01

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

Experimental Results and Issues on Equalization for Nonlinear Memory Channel: Pre-Cursor Enhanced Ram-DFE Canceler

NASA Technical Reports Server (NTRS)

Yuan, Lu; LeBlanc, James

1998-01-01

This thesis investigates the effects of the High Power Amplifier (HPA) and the filters over a satellite or telemetry channel. The Volterra series expression is presented for the nonlinear channel with memory, and the algorithm is based on the finite-state machine model. A RAM-based algorithm operating on the receiver side, Pre-cursor Enhanced RAM-FSE Canceler (PERC) is developed. A high order modulation scheme , 16-QAM is used for simulation, the results show that PERC provides an efficient and reliable method to transmit data on the bandlimited nonlinear channel. The contribution of PERC algorithm is that it includes both pre-cursors and post-cursors as the RAM address lines, and suggests a new way to make decision on the pre-addresses. Compared with the RAM-DFE structure that only includes post- addresses, the BER versus Eb/NO performance of PERC is substantially enhanced. Experiments are performed for PERC algorithms with different parameters on AWGN channels, and the results are compared and analyzed. The investigation of this thesis includes software simulation and hardware verification. Hardware is setup to collect actual TWT data. Simulation on both the software-generated data and the real-world data are performed. Practical limitations are considered for the hardware collected data. Simulation results verified the reliability of the PERC algorithm. This work was conducted at NMSU in the Center for Space Telemetering and Telecommunications Systems in the Klipsch School of Electrical and Computer Engineering Department.

Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

NASA Astrophysics Data System (ADS)

Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.

2017-03-01

Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.

Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations

NASA Astrophysics Data System (ADS)

Sotoudeh, Zahra

2011-07-01

Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.

Uncertainty quantification for PZT bimorph actuators

NASA Astrophysics Data System (ADS)

Bravo, Nikolas; Smith, Ralph C.; Crews, John

2018-03-01

In this paper, we discuss the development of a high fidelity model for a PZT bimorph actuator used for micro-air vehicles, which includes the Robobee. We developed a high-fidelity model for the actuator using the homogenized energy model (HEM) framework, which quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. We then discussed an inverse problem on the model. We included local and global sensitivity analysis of the parameters in the high-fidelity model. Finally, we will discuss the results of Bayesian inference and uncertainty quantification on the HEM.

Supersonic Aerodynamic Design Improvements of an Arrow-Wing HSCT Configuration Using Nonlinear Point Design Methods

NASA Technical Reports Server (NTRS)

Unger, Eric R.; Hager, James O.; Agrawal, Shreekant

1999-01-01

This paper is a discussion of the supersonic nonlinear point design optimization efforts at McDonnell Douglas Aerospace under the High-Speed Research (HSR) program. The baseline for these optimization efforts has been the M2.4-7A configuration which represents an arrow-wing technology for the High-Speed Civil Transport (HSCT). Optimization work on this configuration began in early 1994 and continued into 1996. Initial work focused on optimization of the wing camber and twist on a wing/body configuration and reductions of 3.5 drag counts (Euler) were realized. The next phase of the optimization effort included fuselage camber along with the wing and a drag reduction of 5.0 counts was achieved. Including the effects of the nacelles and diverters into the optimization problem became the next focus where a reduction of 6.6 counts (Euler W/B/N/D) was eventually realized. The final two phases of the effort included a large set of constraints designed to make the final optimized configuration more realistic and they were successful albeit with a loss of performance.

Improved linearity in AlGaN/GaN metal-insulator-semiconductor high electron mobility transistors with nonlinear polarization dielectric

NASA Astrophysics Data System (ADS)

Gao, Tao; Xu, Ruimin; Kong, Yuechan; Zhou, Jianjun; Kong, Cen; Dong, Xun; Chen, Tangsheng

2015-06-01

We demonstrate highly improved linearity in a nonlinear ferroelectric of Pb(Zr0.52Ti0.48)-gated AlGaN/GaN metal-insulator-semiconductor high electron mobility transistor (MIS-HEMT). Distinct double-hump feature in the transconductance-gate voltage (gm-Vg) curve is observed, yielding remarkable enhancement in gate voltage swing as compared to MIS-HEMT with conventional linear gate dielectric. By incorporating the ferroelectric polarization into a self-consistent calculation, it is disclosed that in addition to the common hump corresponding to the onset of electron accumulation, the second hump at high current level is originated from the nonlinear polar nature of ferroelectric, which enhances the gate capacitance by increasing equivalent dielectric constant nonlinearly. This work paves a way for design of high linearity GaN MIS-HEMT by exploiting the nonlinear properties of dielectric.

Laser And Nonlinear Optical Materials For Laser Remote Sensing

NASA Technical Reports Server (NTRS)

Barnes, Norman P.

2005-01-01

NASA remote sensing missions involving laser systems and their economic impact are outlined. Potential remote sensing missions include: green house gasses, tropospheric winds, ozone, water vapor, and ice cap thickness. Systems to perform these measurements use lanthanide series lasers and nonlinear devices including second harmonic generators and parametric oscillators. Demands these missions place on the laser and nonlinear optical materials are discussed from a materials point of view. Methods of designing new laser and nonlinear optical materials to meet these demands are presented.

A Green's function formulation for a nonlinear potential flow solution applicable to transonic flow

NASA Technical Reports Server (NTRS)

Baker, A. J.; Fox, C. H., Jr.

1977-01-01

Routine determination of inviscid subsonic flow fields about wing-body-tail configurations employing a Green's function approach for numerical solution of the perturbation velocity potential equation is successfully extended into the high subsonic subcritical flow regime and into the shock-free supersonic flow regime. A modified Green's function formulation, valid throughout a range of Mach numbers including transonic, that takes an explicit accounting of the intrinsic nonlinearity in the parent governing partial differential equations is developed. Some considerations pertinent to flow field predictions in the transonic flow regime are discussed.

Precluding nonlinear ISI in direct detection long-haul fiber optic systems

NASA Technical Reports Server (NTRS)

Swenson, Norman L.; Shoop, Barry L.; Cioffi, John M.

1991-01-01

Long-distance, high-rate fiber optic systems employing directly modulated 1.55-micron single-mode lasers and conventional single-mode fiber suffer severe intersymbol interference (ISI) with a large nonlinear component. A method of reducing the nonlinearity of the ISI, thereby making linear equalization more viable, is investigated. It is shown that the degree of nonlinearity is highly dependent on the choice of laser bias current, and that in some cases the ISI nonlinearity can be significantly reduced by biasing the laser substantially above threshold. Simulation results predict that an increase in signal-to-nonlinear-distortion ratio as high as 25 dB can be achieved for synchronously spaced samples at an optimal sampling phase by increasing the bias current from 1.2 times threshold to 3.5 times threshold. The high SDR indicates that a linear tapped delay line equalizer could be used to mitigate ISI. Furthermore, the shape of the pulse response suggests that partial response precoding and digital feedback equalization would be particularly effective for this channel.

Elliptical As2Se3 filled core ultra-high-nonlinearity and polarization-maintaining photonic crystal fiber with double hexagonal lattice cladding

NASA Astrophysics Data System (ADS)

Li, Feng; He, Menghui; Zhang, Xuedian; Chang, Min; Wu, Zhizheng; Liu, Zheng; Chen, Hua

2018-05-01

A high birefringence and ultra-high nonlinearity photonic crystal fiber (PCF) is proposed, which is composed of an elliptical As2Se3-doped core and an inner cladding with hexagonal lattice. Optical properties of the PCF are simulated by the full-vector finite element method. The simulation results show that the high birefringence of ∼0.33, ultra-high-nonlinearity coefficient of 300757 W-1km-1 and the low confinement loss can be achieved in the proposed PCF simultaneously at the wavelength of 1.55 μm. Furthermore, by comparison with the other two materials (80PbO•20Ga2O3, As2S3) filled in the core, the As2Se3-doped PCF is found to have the highest birefringence and nonlinearity due to its higher refractive index and nonlinear refractive index. The flattened dispersion feature, as well as the low confinement loss of the proposed PCF structure make it suitable as a wide range of applications, such as the coherent optical communications, polarization-maintaining and nonlinear optics, etc.

The anharmonic quartic force field infrared spectra of five non-linear polycyclic aromatic hydrocarbons: Benz[a]anthracene, chrysene, phenanthrene, pyrene, and triphenylene

NASA Astrophysics Data System (ADS)

Mackie, Cameron J.; Candian, Alessandra; Huang, Xinchuan; Maltseva, Elena; Petrignani, Annemieke; Oomens, Jos; Mattioda, Andrew L.; Buma, Wybren Jan; Lee, Timothy J.; Tielens, Alexander G. G. M.

2016-08-01

The study of interstellar polycyclic aromatic hydrocarbons (PAHs) relies heavily on theoretically predicted infrared spectra. Most earlier studies use scaled harmonic frequencies for band positions and the double harmonic approximation for intensities. However, recent high-resolution gas-phase experimental spectroscopic studies have shown that the harmonic approximation is not sufficient to reproduce experimental results. In our previous work, we presented the anharmonic theoretical spectra of three linear PAHs, showing the importance of including anharmonicities into the theoretical calculations. In this paper, we continue this work by extending the study to include five non-linear PAHs (benz[a]anthracene, chrysene, phenanthrene, pyrene, and triphenylene), thereby allowing us to make a full assessment of how edge structure, symmetry, and size influence the effects of anharmonicities. The theoretical anharmonic spectra are compared to spectra obtained under matrix isolation low-temperature conditions, low-resolution, high-temperature gas-phase conditions, and high-resolution, low-temperature gas-phase conditions. Overall, excellent agreement is observed between the theoretical and experimental spectra although the experimental spectra show subtle but significant differences.

High temperature composite analyzer (HITCAN) user's manual, version 1.0

NASA Technical Reports Server (NTRS)

Lackney, J. J.; Singhal, S. N.; Murthy, P. L. N.; Gotsis, P.

1993-01-01

This manual describes 'how-to-use' the computer code, HITCAN (HIgh Temperature Composite ANalyzer). HITCAN is a general purpose computer program for predicting nonlinear global structural and local stress-strain response of arbitrarily oriented, multilayered high temperature metal matrix composite structures. This code combines composite mechanics and laminate theory with an internal data base for material properties of the constituents (matrix, fiber and interphase). The thermo-mechanical properties of the constituents are considered to be nonlinearly dependent on several parameters including temperature, stress and stress rate. The computation procedure for the analysis of the composite structures uses the finite element method. HITCAN is written in FORTRAN 77 computer language and at present has been configured and executed on the NASA Lewis Research Center CRAY XMP and YMP computers. This manual describes HlTCAN's capabilities and limitations followed by input/execution/output descriptions and example problems. The input is described in detail including (1) geometry modeling, (2) types of finite elements, (3) types of analysis, (4) material data, (5) types of loading, (6) boundary conditions, (7) output control, (8) program options, and (9) data bank.

The anharmonic quartic force field infrared spectra of five non-linear polycyclic aromatic hydrocarbons: Benz[a]anthracene, chrysene, phenanthrene, pyrene, and triphenylene.

PubMed

Mackie, Cameron J; Candian, Alessandra; Huang, Xinchuan; Maltseva, Elena; Petrignani, Annemieke; Oomens, Jos; Mattioda, Andrew L; Buma, Wybren Jan; Lee, Timothy J; Tielens, Alexander G G M

2016-08-28

The study of interstellar polycyclic aromatic hydrocarbons (PAHs) relies heavily on theoretically predicted infrared spectra. Most earlier studies use scaled harmonic frequencies for band positions and the double harmonic approximation for intensities. However, recent high-resolution gas-phase experimental spectroscopic studies have shown that the harmonic approximation is not sufficient to reproduce experimental results. In our previous work, we presented the anharmonic theoretical spectra of three linear PAHs, showing the importance of including anharmonicities into the theoretical calculations. In this paper, we continue this work by extending the study to include five non-linear PAHs (benz[a]anthracene, chrysene, phenanthrene, pyrene, and triphenylene), thereby allowing us to make a full assessment of how edge structure, symmetry, and size influence the effects of anharmonicities. The theoretical anharmonic spectra are compared to spectra obtained under matrix isolation low-temperature conditions, low-resolution, high-temperature gas-phase conditions, and high-resolution, low-temperature gas-phase conditions. Overall, excellent agreement is observed between the theoretical and experimental spectra although the experimental spectra show subtle but significant differences.

Experimental study on nonlinear vibrating of aluminum foam using electronic speckle pattern interferometry

NASA Astrophysics Data System (ADS)

Yang, Fujun; Ma, Yinhang; Tao, Nan; He, Xiaoyuan

2017-06-01

Due to its multi properties, including excellent stiffness-to-weight and strength-to-weight ratios, closed-cell aluminum and its alloy foams become candidate materials for use in many high-technology industries, such as the automotive and aerospace industries. For the efficient use of closed-cell foams in structural applications, it is necessary and important to detailly understand their mechanical characteristics. In this paper, the nonlinear vibration responses of the cantilever beams of closed-cell aluminum foams were investigated by use of electronic speckle pattern interferometry (ESPI). The nonlinear resonant mode shapes of testing specimens under harmonic excitation were measured. It is first time to obtain from the experimental results that there exist super-harmonic responses when the cantilever beams of closed-cell aluminum foam were forced to vibrate, which was caused by its specific cellular structures.

Nonlinear pulse propagation and phase velocity of laser-driven plasma waves

NASA Astrophysics Data System (ADS)

Benedetti, Carlo; Rossi, Francesco; Schroeder, Carl; Esarey, Eric; Leemans, Wim

2014-10-01

We investigate and characterize the laser evolution and plasma wave excitation by a relativistically intense, short-pulse laser propagating in a preformed parabolic plasma channel, including the effects of pulse steepening, frequency redshifting, and energy depletion. We derived in 3D, and in the weakly relativistic intensity regime, analytical expressions for the laser energy depletion, the pulse self-steepening rate, the laser intensity centroid velocity, and the phase velocity of the plasma wave. Analytical results have been validated numerically using the 2D-cylindrical, ponderomotive code INF&RNO. We also discuss the extension of these results to the nonlinear regime, where an analytical theory of the nonlinear wake phase velocity is lacking. Work supported by the Office of Science, Office of High Energy Physics, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium

NASA Astrophysics Data System (ADS)

Hussain, Q.; Latif, T.; Alvi, N.; Asghar, S.

2018-06-01

The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study). Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters.

Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems

NASA Astrophysics Data System (ADS)

Williams, Rube B.

2004-02-01

Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.

Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts

NASA Technical Reports Server (NTRS)

Hilburger, Mark W.; Starnes, James H., Jr.

2002-01-01

Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.

LDV measurement of small nonlinearities in flat and curved membranes. A model for eardrum nonlinear acoustic behaviour

NASA Astrophysics Data System (ADS)

Kilian, Gladiné; Pieter, Muyshondt; Joris, Dirckx

2016-06-01

Laser Doppler Vibrometry is an intrinsic highly linear measurement technique which makes it a great tool to measure extremely small nonlinearities in the vibration response of a system. Although the measurement technique is highly linear, other components in the experimental setup may introduce nonlinearities. An important source of artificially introduced nonlinearities is the speaker, which generates the stimulus. In this work, two correction methods to remove the effects of stimulus nonlinearity are investigated. Both correction methods were found to give similar results but have different pros and cons. The aim of this work is to investigate the importance of the conical shape of the eardrum as a source of nonlinearity in hearing. We present measurements on flat and indented membranes. The data shows that the curved membrane exhibit slightly higher levels of nonlinearity compared to the flat membrane.

Active Nonlinear Feedback Control for Aerospace Systems. Processor

DTIC Science & Technology

1990-12-01

relating to the role of nonlinearities in feedback control. These area include Lyapunov function theory, chaotic controllers, statistical energy analysis , phase robustness, and optimal nonlinear control theory.

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.

Nonlinear dissipative devices in structural vibration control: A review

NASA Astrophysics Data System (ADS)

Lu, Zheng; Wang, Zixin; Zhou, Ying; Lu, Xilin

2018-06-01

Structural vibration is a common phenomenon existing in various engineering fields such as machinery, aerospace, and civil engineering. It should be noted that the effective suppression of structural vibration is conducive to enhancing machine performance, prolonging the service life of devices, and promoting the safety and comfort of structures. Conventional linear energy dissipative devices (linear dampers) are largely restricted for wider application owing to their low performance under certain conditions, such as the detuning effect of tuned mass dampers subjected to nonstationary excitations and the excessively large forces generated in linear viscous dampers at high velocities. Recently, nonlinear energy dissipative devices (nonlinear dampers) with broadband response and high robustness are being increasingly used in practical engineering. At the present stage, nonlinear dampers can be classified into three groups, namely nonlinear stiffness dampers, nonlinear-stiffness nonlinear-damping dampers, and nonlinear damping dampers. Corresponding to each nonlinear group, three types of nonlinear dampers that are widely utilized in practical engineering are reviewed in this paper: the nonlinear energy sink (NES), particle impact damper (PID), and nonlinear viscous damper (NVD), respectively. The basic concepts, research status, engineering applications, and design approaches of these three types of nonlinear dampers are summarized. A comparison between their advantages and disadvantages in practical engineering applications is also conducted, to provide a reference source for practical applications and new research.

A sub-cc nonlinear piezoelectric energy harvester for powering leadless pacemakers

PubMed Central

Ansari, MH; Karami, M Amin

2018-01-01

A miniature nonlinear piezoelectric energy harvester is developed to power state of the art leadless cardiac pacemakers from cardiac motions. The energy harvester is integrated in the leadless pacemaker and is connected to the myocardium. The energy harvester converts myocardial motions to electricity to power leadless pacemakers. The energy is stored in a battery or supercapacitor and is used for pacing. The device is composed of a bimorph piezoelectric beam confined in a gray iron frame. The system is assembled at high temperature and operated at the body temperature. The mismatch in the coefficients of thermal expansion of the beam and the frame causes the beam to buckle in body temperature. This intentional buckling makes the beam unstable and improves the power production and robustness of the device. Having high natural frequency is a major problem in microelectromechanical systems energy harvesters. Considering the small size of the energy harvester, 0.5 cm3, the natural frequency is expected to be high. In our design, the natural frequency is lowered significantly using a buckled beam and a proof mass. Since the beam is buckled, the design is bistable and nonlinear, which could increase the output power. In this article, the device is analytically modeled, and the natural frequencies and mode shapes of the energy harvester are analytically derived. The terms corresponding to geometric nonlinearities are included in the electromechanical coupled governing equations. The simulations show that the device generates sufficient electricity to power leadless pacemakers. PMID:29674842

A Collection of Nonlinear Aircraft Simulations in MATLAB

NASA Technical Reports Server (NTRS)

Garza, Frederico R.; Morelli, Eugene A.

2003-01-01

Nonlinear six degree-of-freedom simulations for a variety of aircraft were created using MATLAB. Data for aircraft geometry, aerodynamic characteristics, mass / inertia properties, and engine characteristics were obtained from open literature publications documenting wind tunnel experiments and flight tests. Each nonlinear simulation was implemented within a common framework in MATLAB, and includes an interface with another commercially-available program to read pilot inputs and produce a three-dimensional (3-D) display of the simulated airplane motion. Aircraft simulations include the General Dynamics F-16 Fighting Falcon, Convair F-106B Delta Dart, Grumman F-14 Tomcat, McDonnell Douglas F-4 Phantom, NASA Langley Free-Flying Aircraft for Sub-scale Experimental Research (FASER), NASA HL-20 Lifting Body, NASA / DARPA X-31 Enhanced Fighter Maneuverability Demonstrator, and the Vought A-7 Corsair II. All nonlinear simulations and 3-D displays run in real time in response to pilot inputs, using contemporary desktop personal computer hardware. The simulations can also be run in batch mode. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. Since all the nonlinear simulations are implemented entirely in MATLAB, user-defined control laws can be added in a straightforward fashion, and the simulations are portable across various computing platforms. Routines for trim, linearization, and numerical integration are included. The general nonlinear simulation framework and the specifics for each particular aircraft are documented.

Vertically homogeneous stationary tornado-type vortex

NASA Astrophysics Data System (ADS)

Rutkevich, P. B.; Rutkevych, P. P.

2010-05-01

Tornado is regarded as one of the most dangerous atmosphere phenomena. The tornado phenomenon has been intensively studied so far, however, there is still no established and accepted theory of how tornadoes form, an uncertainty still exists concerning extreme winds and pressure drops in tornadoes. It is commonly accepted that it is possible to describe tornado from the set of nonlinear hydrodynamical equations, however, it is still unclear which non-linear processes are responsible for its formation. Nonlinear terms in the system are associated with either centrifugal force, or entropy transport, or transport of humidity. It appears that the amount and spatial distribution of precipitation with the convection are important indicators of the weather phenomena associated with a particular storm. The low-precipitation supercells that produce relatively little precipitation and yet show clear visual signs of rotation. Low-precipitation supercells occur most often near the surface dryline and, owing to the sparse precipitation and relatively dry environments with little cloudiness. Low-precipitation storms are frequently non-tornadic and many are non-severe despite exhibiting persistent rotation. On the other hand, the so-called high-precipitation storms are characterized by substantial precipitation within their mesocyclonic circulations. When high-precipitation storms have a recognizable hook radar echo, reflectivity in the hook is comparable to those in the precipitation core. High-precipitation supercells are probably the most common form of supercell and produce severe weather of all types including tornadoes. Therefore, in this work we consider a hydrodynamic system with only one nonlinear term associated with atmosphere humidity, which yields energy to the system. The tornado vortex is usually to a good approximation cylindrical so we use cylindrical geometry and homogeneity in vertical direction. In this case the problem reduces to a system of ordinary differential equations. Rotation in the vortex is associated with compressibility so we also take into account the compressibility of the gas. Under certain approximations the problem reduces to a single high-order nonlinear equation. Numerical solution of the obtained high-order equation describes all three velocity components and all thermodynamic parameters in the system. The system exhibits high rotation and strong vertical air flow in the middle part of the vortex.

Nonlinear optical transmittance of semiconductors in the presence of high-intensity radiation fields

NASA Astrophysics Data System (ADS)

Dong, H. M.; Han, F. W.; Duan, Y. F.; Huang, F.; Liu, J. L.

2018-04-01

We developed a systematic theoretical study of nonlinear optical properties of semiconductors. The eight-band kṡp model and the energy-balance equation are employed to calculate the transmission and optical absorption coefficients in the presence of both the linear one-photon absorption and the nonlinear two-photon absorption (TPA) processes. A substantial reduction of the optical transmittance far below the band-gap can be observed under relatively high-intensity radiation fields due to the nonlinear TPA. The TPA-induced optical transmittance decreases with increasing intensity of the radiation fields. Our theoretical results are in line with those observed experimentally. The theoretical approach can be applied to understand the nonlinear optical properties of semiconductors under high-field conditions.

General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.

Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice

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

Hong QIn, Ronald Davidson

2011-07-18

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant.more » This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation, and reduces beam pulsation.« less

Generalized Courant-Snyder theory and Kapchinskij-Vladimirskij distribution for high-intensity beams in a coupled transverse focusing lattice

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

Qin Hong; Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026; Davidson, Ronald C.

2011-05-15

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in an uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are noncommutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant.more » This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation and reduces beam pulsation.« less

Nonlinear analysis of heart rate variability within independent frequency components during the sleep-wake cycle.

PubMed

Vigo, Daniel E; Dominguez, Javier; Guinjoan, Salvador M; Scaramal, Mariano; Ruffa, Eduardo; Solernó, Juan; Siri, Leonardo Nicola; Cardinali, Daniel P

2010-04-19

Heart rate variability (HRV) is a complex signal that results from the contribution of different sources of oscillation related to the autonomic nervous system activity. Although linear analysis of HRV has been applied to sleep studies, the nonlinear dynamics of HRV underlying frequency components during sleep is less known. We conducted a study to evaluate nonlinear HRV within independent frequency components in wake status, slow-wave sleep (SWS, stages III or IV of non-rapid eye movement sleep), and rapid-eye-movement sleep (REM). The sample included 10 healthy adults. Polysomnography was performed to detect sleep stages. HRV was studied globally during each phase and then very low frequency (VLF), low frequency (LF) and high frequency (HF) components were separated by means of the wavelet transform algorithm. HRV nonlinear dynamics was estimated with sample entropy (SampEn). A higher SampEn was found when analyzing global variability (Wake: 1.53+/-0.28, SWS: 1.76+/-0.32, REM: 1.45+/-0.19, p=0.005) and VLF variability (Wake: 0.13+/-0.03, SWS: 0.19+/-0.03, REM: 0.14+/-0.03, p<0.001) at SWS. REM was similar to wake status regarding nonlinear HRV. We propose nonlinear HRV is a useful index of the autonomic activity that characterizes the different sleep-wake cycle stages. 2009 Elsevier B.V. All rights reserved.

Guided wave methods and apparatus for nonlinear frequency generation

DOEpatents

Durfee, III, Charles G.; Rundquist, Andrew; Kapteyn, Henry C.; Murnane, Margaret M.

2000-01-01

Methods and apparatus are disclosed for the nonlinear generation of sum and difference frequencies of electromagnetic radiation propagating in a nonlinear material. A waveguide having a waveguide cavity contains the nonlinear material. Phase matching of the nonlinear generation is obtained by adjusting a waveguide propagation constant, the refractive index of the nonlinear material, or the waveguide mode in which the radiation propagates. Phase matching can be achieved even in isotropic nonlinear materials. A short-wavelength radiation source uses phase-matched nonlinear generation in a waveguide to produce high harmonics of a pulsed laser.

Spectral element modelling of seismic wave propagation in visco-elastoplastic media including excess-pore pressure development

NASA Astrophysics Data System (ADS)

Oral, Elif; Gélis, Céline; Bonilla, Luis Fabián; Delavaud, Elise

2017-12-01

Numerical modelling of seismic wave propagation, considering soil nonlinearity, has become a major topic in seismic hazard studies when strong shaking is involved under particular soil conditions. Indeed, when strong ground motion propagates in saturated soils, pore pressure is another important parameter to take into account when successive phases of contractive and dilatant soil behaviour are expected. Here, we model 1-D seismic wave propagation in linear and nonlinear media using the spectral element numerical method. The study uses a three-component (3C) nonlinear rheology and includes pore-pressure excess. The 1-D-3C model is used to study the 1987 Superstition Hills earthquake (ML 6.6), which was recorded at the Wildlife Refuge Liquefaction Array, USA. The data of this event present strong soil nonlinearity involving pore-pressure effects. The ground motion is numerically modelled for different assumptions on soil rheology and input motion (1C versus 3C), using the recorded borehole signals as input motion. The computed acceleration-time histories show low-frequency amplification and strong high-frequency damping due to the development of pore pressure in one of the soil layers. Furthermore, the soil is found to be more nonlinear and more dilatant under triaxial loading compared to the classical 1C analysis, and significant differences in surface displacements are observed between the 1C and 3C approaches. This study contributes to identify and understand the dominant phenomena occurring in superficial layers, depending on local soil properties and input motions, conditions relevant for site-specific studies.

Fluid equations with nonlinear wave-particle resonances^

NASA Astrophysics Data System (ADS)

Mattor, Nathan

1997-11-01

We have derived fluid equations that include linear and nonlinear wave-particle resonance effects. This greatly extends previous ``Landau-fluid'' closures, which include linear Landau damping. (G.W. Hammett and F.W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990).^, (Z. Chang and J. D. Callen, Phys. Fluids B 4,) 1167 (1992). The new fluid equations are derived with no approximation regarding nonlinear kinetic interaction, and so additionally include numerous nonlinear kinetic effects. The derivation starts with the electrostatic drift kinetic equation for simplicity, with a Maxwellian distribution function. Fluid closure is accomplished through a simple integration trick applied to the drift kinetic equation, using the property that the nth moment of Maxwellian distribution is related to the nth derivative. The result is a compact closure term appearing in the highest moment equation, a term which involves a plasma dispersion function of the electrostatic field and its derivatives. The new term reduces to the linear closures in appropriate limits, so both approaches retain linear Landau damping. But the nonlinearly closed equations have additional desirable properties. Unlike linear closures, the nonlinear closure retains the time-reversibility of the original kinetic equation. We have shown directly that the nonlinear closure retains at least two nonlinear resonance effects: wave-particle trapping and Compton scattering. Other nonlinear kinetic effects are currently under investigation. The new equations correct two previous discrepancies between kinetic and Landau-fluid predictions, including a propagator discrepancy (N. Mattor, Phys. Fluids B 4,) 3952 (1992). and a numerical discrepancy for the 3-mode shearless bounded slab ITG problem. (S. E. Parker et al.), Phys. Plasmas 1, 1461 (1994). ^* In collaboration with S. E. Parker, Department of Physics, University of Colorado, Boulder. ^ Work performed at LLNL under DoE contract No. W7405-ENG-48.

Nonlinear bending-torsional vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1986-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by comparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Nonlinear vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1987-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Broadband unidirectional ultrasound propagation

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

Sinha, Dipen N.; Pantea, Cristian

A passive, linear arrangement of a sonic crystal-based apparatus and method including a 1D sonic crystal, a nonlinear medium, and an acoustic low-pass filter, for permitting unidirectional broadband ultrasound propagation as a collimated beam for underwater, air or other fluid communication, are described. The signal to be transmitted is first used to modulate a high-frequency ultrasonic carrier wave which is directed into the sonic crystal side of the apparatus. The apparatus processes the modulated signal, whereby the original low-frequency signal exits the apparatus as a collimated beam on the side of the apparatus opposite the sonic crystal. The sonic crystalmore » provides a bandpass acoustic filter through which the modulated high-frequency ultrasonic signal passes, and the nonlinear medium demodulates the modulated signal and recovers the low-frequency sound beam. The low-pass filter removes remaining high-frequency components, and contributes to the unidirectional property of the apparatus.« less

High power pumped MID-IR wavelength devices using nonlinear frequency mixing (NFM)

NASA Technical Reports Server (NTRS)

Sanders, Steven (Inventor); Lang, Robert J. (Inventor); Waarts, Robert G. (Inventor)

2001-01-01

Laser diode pumped mid-IR wavelength sources include at least one high power, near-IR wavelength, injection and/or sources wherein one or both of such sources may be tunable providing a pump wave output beam to a quasi-phase matched (QPM) nonlinear frequency mixing (NFM) device. The NFM device may be a difference frequency mixing (DFM) device or an optical parametric oscillation (OPO) device. Wavelength tuning of at least one of the sources advantageously provides the ability for optimizing pump or injection wavelengths to match the QPM properties of the NFM device enabling a broad range of mid-IR wavelength selectivity. Also, pump powers are gain enhanced by the addition of a rare earth amplifier or oscillator, or a Raman/Brillouin amplifier or oscillator between the high power source and the NFM device. Further, polarization conversion using Raman or Brillouin wavelength shifting is provided to optimize frequency conversion efficiency in the NFM device.

High power pumped mid-IR wavelength systems using nonlinear frequency mixing (NFM) devices

NASA Technical Reports Server (NTRS)

Sanders, Steven (Inventor); Lang, Robert J. (Inventor); Waarts, Robert G. (Inventor)

1999-01-01

Laser diode pumped mid-IR wavelength systems include at least one high power, near-IR wavelength, injection and/or sources wherein one or both of such sources may be tunable providing a pump wave output beam to a quasi-phase matched (QPM) nonlinear frequency mixing (NFM) device. The NFM device may be a difference frequency mixing (DFM) device or an optical parametric oscillation (OPO) device. Wavelength tuning of at least one of the sources advantageously provides the ability for optimizing pump or injection wavelengths to match the QPM properties of the NFM device enabling a broad range of mid-IR wavelength selectivity. Also, pump powers are gain enhanced by the addition of a rare earth amplifier or oscillator, or a Raman/Brillouin amplifier or oscillator between the high power source and the NFM device. Further, polarization conversion using Raman or Brillouin wavelength shifting is provided to optimize frequency conversion efficiency in the NFM device.

High Power, Pulsed, RF Generation from Nonlinear Lumped Element Transmission Lines (NLETLs)

DTIC Science & Technology

2011-02-05

specific to solitons. including both overtaking and head on collision interactions and the Fermi- Pasta -Ulam recurrence phenomenon [50]. Contributions by...simulation has indicated the initiation of this curious effect. The Fernii- Pasta -Ulain recurrence phenomena, whereby a sinusoidal excitation applied to a

Equivalent reduced model technique development for nonlinear system dynamic response

NASA Astrophysics Data System (ADS)

Thibault, Louis; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2013-04-01

The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.

Vectorial control of nonlinear emission via chiral butterfly nanoantennas: generation of pure high order nonlinear vortex beams.

PubMed

Lesina, Antonino Cala'; Berini, Pierre; Ramunno, Lora

2017-02-06

We report on a chiral gap-nanostructure, which we term a "butterfly nanoantenna," that offers full vectorial control over nonlinear emission. The field enhancement in its gap occurs for only one circular polarization but for every incident linear polarization. As the polarization, phase and amplitude of the linear field in the gap are highly controlled, the linear field can drive nonlinear emitters within the gap, which behave as an idealized Huygens source. A general framework is thereby proposed wherein the butterfly nanoantennas can be arranged in a metasurface, and the nonlinear Huygens sources exploited to produce a highly structured far-field optical beam. Nonlinearity allows us to shape the light at shorter wavelengths, not accessible by linear plasmonics, and resulting in high purity beams. The chirality of the butterfly allows us to create orbital angular momentum states using a linearly polarized excitation. A third harmonic Laguerre-Gauss beam carrying an optical orbital angular momentum of 41 is demonstrated as an example, through large-scale simulations on a high-performance computing platform of the full plasmonic metasurface with an area large enough to contain up to 3600 nanoantennas.

Improved linearity in AlGaN/GaN metal-insulator-semiconductor high electron mobility transistors with nonlinear polarization dielectric

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

Gao, Tao; Science and Technology on Monolithic Integrated Circuits and Modules Laboratory, Nanjing Electronic Devices Institute, Nanjing 210016; Xu, Ruimin

2015-06-15

We demonstrate highly improved linearity in a nonlinear ferroelectric of Pb(Zr{sub 0.52}Ti{sub 0.48})-gated AlGaN/GaN metal-insulator-semiconductor high electron mobility transistor (MIS-HEMT). Distinct double-hump feature in the transconductance-gate voltage (g{sub m}-V{sub g}) curve is observed, yielding remarkable enhancement in gate voltage swing as compared to MIS-HEMT with conventional linear gate dielectric. By incorporating the ferroelectric polarization into a self-consistent calculation, it is disclosed that in addition to the common hump corresponding to the onset of electron accumulation, the second hump at high current level is originated from the nonlinear polar nature of ferroelectric, which enhances the gate capacitance by increasing equivalent dielectricmore » constant nonlinearly. This work paves a way for design of high linearity GaN MIS-HEMT by exploiting the nonlinear properties of dielectric.« less

Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities.

PubMed

Zeng, Xianglong; Guo, Hairun; Zhou, Binbin; Bache, Morten

2012-11-19

We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency. Numerical results show that compressed pulses with less than three-cycle duration can be achieved even when the compression factor is very large, and in contrast to standard soliton compression, these compressed pulses have minimal pedestal and high quality factor.

Investigation on nonlinear optical properties of MoS2 nanoflake, grown on silicon and quartz substrates

NASA Astrophysics Data System (ADS)

Bayesteh, S.; Mortazavi, S. Z.; Reyhani, A.

2018-03-01

In this study, MoS2 was directly synthesized by one-step thermal chemical vapour deposition (TCVD), on different substrates including Si/SiO2 and quartz, using MoO3 and sulfide powders as precursor. The XRD patterns demonstrate the high crystallinity of MoS2 on Si/SiO2 and quartz substrates. SEM confirmed the formation of MoS2 grown on both substrates. According to line width and frequency difference between the E1 2g and A1g in Raman spectroscopy, it is inferred that the MoS2 grown on Si/SiO2 substrate is monolayer and the MoS2 grown on quartz substrate is multilayer. Moreover, by assessment of MoS2 nanoflake band gap via UV-visible analysis, it verified the formation of few layer structures. In addition, the open-aperture and close-aperture Z-scan techniques were employed to study the nonlinear optical properties including nonlinear absorption and nonlinear refraction of the synthesized MoS2. All experiments were performed using a diode laser with a wavelength of 532 nm as light source. The monolayer MoS2 synthesized on Si/SiO2, display considerable two-photon absorption. However, the multilayer MoS2 synthesized on quartz displayed saturable absorption (SA). It is noticeable that both samples demonstrate obvious self-defocusing behaviour.

Mode Identification of High-Amplitude Pressure Waves in Liquid Rocket Engines

NASA Astrophysics Data System (ADS)

EBRAHIMI, R.; MAZAHERI, K.; GHAFOURIAN, A.

2000-01-01

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure amplitude histories and phase diagrams along the tube are computed. To determine the validity of the presented method for steep non-linear waves, the Euler equations are numerically solved for non-linear waves, and negligible interactions between these waves are observed. To show the applicability of this method, other's experimental results in which modes were identified are used. Results indicate that this simple method can be used in analyzing complicated pressure signal measurements.

Experimental and numerical investigation of the nonlinear dynamics of compliant mechanisms for deployable structures

NASA Astrophysics Data System (ADS)

Dewalque, Florence; Schwartz, Cédric; Denoël, Vincent; Croisier, Jean-Louis; Forthomme, Bénédicte; Brüls, Olivier

2018-02-01

This paper studies the dynamics of tape springs which are characterised by a highly geometrical nonlinear behaviour including buckling, the formation of folds and hysteresis. An experimental set-up is designed to capture these complex nonlinear phenomena. The experimental data are acquired by the means of a 3D motion analysis system combined with a synchronised force plate. Deployment tests show that the motion can be divided into three phases characterised by different types of folds, frequencies of oscillation and damping behaviours. Furthermore, the reproducibility quality of the dynamic and quasi-static results is validated by performing a large number of tests. In parallel, a nonlinear finite element model is developed. The required model parameters are identified based on simple experimental tests such as static deformed configurations and small amplitude vibration tests. In the end, the model proves to be well correlated with the experimental results in opposite sense bending, while in equal sense, both the experimental set-up and the numerical model are particularly sensitive to the initial conditions.

Nonlinear Tracking Control of a Conductive Supercoiled Polymer Actuator.

PubMed

Luong, Tuan Anh; Cho, Kyeong Ho; Song, Min Geun; Koo, Ja Choon; Choi, Hyouk Ryeol; Moon, Hyungpil

2018-04-01

Artificial muscle actuators made from commercial nylon fishing lines have been recently introduced and shown as a new type of actuator with high performance. However, the actuators also exhibit significant nonlinearities, which make them difficult to control, especially in precise trajectory-tracking applications. In this article, we present a nonlinear mathematical model of a conductive supercoiled polymer (SCP) actuator driven by Joule heating for model-based feedback controls. Our efforts include modeling of the hysteresis behavior of the actuator. Based on nonlinear modeling, we design a sliding mode controller for SCP actuator-driven manipulators. The system with proposed control law is proven to be asymptotically stable using the Lyapunov theory. The control performance of the proposed method is evaluated experimentally and compared with that of a proportional-integral-derivative (PID) controller through one-degree-of-freedom SCP actuator-driven manipulators. Experimental results show that the proposed controller's performance is superior to that of a PID controller, such as the tracking errors are nearly 10 times smaller compared with those of a PID controller, and it is more robust to external disturbances such as sensor noise and actuator modeling error.

Simulation and measurement of nonlinear behavior in a high-power test cell.

PubMed

Harvey, Gerald; Gachagan, Anthony

2011-04-01

High-power ultrasound has many diverse uses in process applications in industries ranging from food to pharmaceutical. Because cavitation is frequently a desirable effect within many high-power, low-frequency systems, these systems are commonly expected to feature highly nonlinear acoustic propagation because of the high input levels employed. This generation of harmonics significantly alters the field profile compared with that of a linear system, making accurate field modeling difficult. However, when the short propagation distances involved are considered, it is not unreasonable to assume that these systems may remain largely linear until the onset of cavitation, in terms of classical acoustic propagation. The purpose of this paper is to investigate the possible nonlinear effects within such systems before the onset of cavitation. A theoretical description of nonlinear propagation will be presented and the merits of common analytical models will be discussed. Following this, a numerical model of nonlinearity will be outlined and the advantages it presents for representing nonlinear effects in bounded fields will be discussed. Next, the driving equipment and transducers will be evaluated for linearity to disengage any effects from those formed in the transmission load. Finally, the linearity of the system will be measured using an acoustic hydrophone and compared with finite element analysis to confirm that nonlinear effects are not prevalent in such systems at the onset of cavitation. © 2011 IEEE

Nonlinear Large Deflection Theory with Modified Aeroelastic Lifting Line Aerodynamics for a High Aspect Ratio Flexible Wing

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Chaparro, Daniel

2017-01-01

This paper investigates the effect of nonlinear large deflection bending on the aerodynamic performance of a high aspect ratio flexible wing. A set of nonlinear static aeroelastic equations are derived for the large bending deflection of a high aspect ratio wing structure. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields lower lift and span efficiency than the linear bending theory. A coupled aerodynamic-nonlinear finite element model is developed to implement the nonlinear bending theory for a Common Research Model (CRM) flexible wing wind tunnel model to be tested in the University of Washington Aeronautical Laboratory (UWAL). The structural stiffness of the model is designed to give about 10% wing tip deflection which is large enough that could cause the nonlinear deflection effect to become significant. The computational results show that the nonlinear bending theory yields slightly less lift than the linear bending theory for this wind tunnel model. As a result, the linear bending theory is deemed adequate for the CRM wind tunnel model.

Efficient, nonlinear phase estimation with the nonmodulated pyramid wavefront sensor

NASA Astrophysics Data System (ADS)

Frazin, Richard A.

2018-04-01

The sensitivity of the the pyramid wavefront sensor (PyWFS) has made it a popular choice for astronomical adaptive optics (AAO) systems, and it is at its most sensitive when it is used without modulation of the input beam. In non-modulated mode, the device is highly nonlinear. Hence, all PyWFS implementations on current AAO systems employ modulation to make the device more linear. The upcoming era of 30-m class telescopes and the demand for ultra-precise wavefront control stemming from science objectives that include direct imaging of exoplanets make using the PyWFS without modulation desirable. This article argues that nonlinear estimation based on Newton's method for nonlinear optimization can be useful for mitigating the effects of nonlinearity in the non-modulated PyWFS. The proposed approach requires all optical modeling to be pre-computed, which has the advantage of avoiding real-time simulations of beam propagation. Further, the required real-time calculations are amenable to massively parallel computation. Numerical experiments simulate a currently operational PyWFS. A singular value analysis shows that the common practice of calculating two "slope" images from the four PyWFS pupil images discards critical information and is unsuitable for the non-modulated PyWFS simulated here. Instead, this article advocates estimators that use the raw pixel values not only from the four geometrical images of the pupil, but from surrounding pixels as well. The simulations indicate that nonlinear estimation can be effective when the Strehl ratio of the input beam is greater than 0.3, and the improvement relative to linear estimation tends to increase at larger Strehl ratios. At Strehl ratios less than about 0.5, the performances of both the nonlinear and linear estimators are relatively insensitive to noise, since they are dominated by nonlinearity error.

Topological nature of nonlinear optical effects in solids.

PubMed

Morimoto, Takahiro; Nagaosa, Naoto

2016-05-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials.

Topological nature of nonlinear optical effects in solids

PubMed Central

Morimoto, Takahiro; Nagaosa, Naoto

2016-01-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials. PMID:27386523

New Materials Directions for the Realization of Ultra-High Performance 3rd Order Non-Linear Optical Organics

DTIC Science & Technology

2015-03-13

Nowacki, H.S. Oh, C. Zanlorenzi, H.S. Jee, A. Baev, P.N. Prasad, and L. Akcelrud, "Design and synthesis of polymers for chiral photonics ...rationally design and create organic materials with high nonlinear refractive index and low single· and two- photon absorption at wavelengths relevant to...can also enhance 3rd-order NLO response through microscopic cascading of 2nd-order nonlinearity. Chiral control of nonlinearity bas also been

GHM method for obtaining rationalsolutions of nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

2015-01-01

In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

Self-adaptive predictor-corrector algorithm for static nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Padovan, J.

1981-01-01

A multiphase selfadaptive predictor corrector type algorithm was developed. This algorithm enables the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as pro/post buckling behavior. The strategy involves three main phases: (1) the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive incremental Newton Ramphson (INR) type iterations; (20 uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior; (3) the use of quality of convergence checks which enable various self adaptive modifications of the algorithmic structure when necessary. The restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels to improve the convergence process. The capabilities of the procedure to handle various types of static nonlinear structural behavior are illustrated.

Static DC to DC Power Conditioning-Active Ripple Filter, 1 MHZ DC to DC Conversion, and Nonlinear Analysis. Ph.D. Thesis; [voltage regulation and conversion circuitry for spacecraft power supplies

NASA Technical Reports Server (NTRS)

Sander, W. A., III

1973-01-01

Dc to dc static power conditioning systems on unmanned spacecraft have as their inputs highly fluctuating dc voltages which they condition to regulated dc voltages. These input voltages may be less than or greater than the desired regulated voltages. The design of two circuits which address specific problems in the design of these power conditioning systems and a nonlinear analysis of one of the circuits are discussed. The first circuit design is for a nondissipative active ripple filter which uses an operational amplifier to amplify and cancel the sensed ripple voltage. A dc to dc converter operating at a switching frequency of 1 MHz is the second circuit discussed. A nonlinear analysis of the type of dc to dc converter utilized in designing the 1 MHz converter is included.

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

Bose, Benjamin; Koyama, Kazuya, E-mail: benjamin.bose@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

We develop a code to produce the power spectrum in redshift space based on standard perturbation theory (SPT) at 1-loop order. The code can be applied to a wide range of modified gravity and dark energy models using a recently proposed numerical method by A.Taruya to find the SPT kernels. This includes Horndeski's theory with a general potential, which accommodates both chameleon and Vainshtein screening mechanisms and provides a non-linear extension of the effective theory of dark energy up to the third order. Focus is on a recent non-linear model of the redshift space power spectrum which has been shownmore » to model the anisotropy very well at relevant scales for the SPT framework, as well as capturing relevant non-linear effects typical of modified gravity theories. We provide consistency checks of the code against established results and elucidate its application within the light of upcoming high precision RSD data.« less

Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability

PubMed Central

Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.

2016-01-01

Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose–Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics. PMID:27991513

Voltage-Induced Nonlinear Conduction Properties of Epoxy Resin/Micron-Silver Particles Composites

NASA Astrophysics Data System (ADS)

Qu, Zhaoming; Lu, Pin; Yuan, Yang; Wang, Qingguo

2018-01-01

The nonlinear conduction properties of epoxy resin (ER)/micron-silver particles (MP) composites were investigated. Under sufficient high intensity applied constant voltage, the obvious nonlinear conduction properties of the samples with volume fraction 25% were found. With increments in the voltage, the conductive switching effect was observed. The nonlinear conduction mechanism of the ER/MP composites under high applied voltages could be attributed to the electrical current conducted via discrete paths of conductive particles induced by the electric field. The test results show that the ER/MP composites with nonlinear conduction properties are of great potential application in electromagnetic protection of electron devices and systems.

Nonlinear Constitutive Relations for High Temperature Applications, 1986

NASA Technical Reports Server (NTRS)

1988-01-01

The purpose of the symposium was to review the state-of-the-art in nonlinear constitutive modeling of high temperature materials for aeronautics applications and to identify the need for future research and development efforts in this area. Through this symposium, it was recognized that considerable research efforts are urgently needed in the development of nonlinear constitutive relations for high temperature applications. In the aerospace industry this need is further prompted by recent advances in high temperature materials technology and new demands on material and component performance.

Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios

NASA Astrophysics Data System (ADS)

Liu, F.; Huijsmans, G. T. A.; Loarte, A.; Garofalo, A. M.; Solomon, W. M.; Hoelzl, M.; Nkonga, B.; Pamela, S.; Becoulet, M.; Orain, F.; Van Vugt, D.

2018-01-01

In nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated kink-peeling mode. The features of the dominant saturated KPMs, which are localised toroidally by nonlinear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the edge harmonic oscillation typically present in DIII-D QH-mode experiments. The nonlinear evolution of MHD modes including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E × B flow and its shear on the QH-mode plasma has been investigated. E × B flow shear has a strong stabilisation effect on the medium to high-n modes but is destabilising for the n = 2 mode. The QH-mode extrapolation results of an ITER Q = 10 plasma show that the pedestal currents are large enough to destabilise n = 1-5 KPMs, leading to a stationary saturated kink-peeling mode.

An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Casper, Jay; Baysal, Oktay

1997-01-01

Topics covered include: Low-dispersion scheme for nonlinear acoustic waves in nonuniform flow; Computation of acoustic scattering by a low-dispersion scheme; Algorithmic extension of low-dispersion scheme and modeling effects for acoustic wave simulation; The accuracy of shock capturing in two spatial dimensions; Using high-order methods on lower-order geometries; and Computational considerations for the simulation of discontinuous flows.

Wind energy system time-domain (WEST) analyzers

NASA Technical Reports Server (NTRS)

Dreier, M. E.; Hoffman, J. A.

1981-01-01

A portable analyzer which simulates in real time the complex nonlinear dynamics of horizontal axis wind energy systems was constructed. Math models for an aeroelastic rotor featuring nonlinear aerodynamic and inertial terms were implemented with high speed digital controllers and analog calculation. This model was combined with other math models of elastic supports, control systems, a power train and gimballed rotor kinematics. A stroboscopic display system graphically depicting distributed blade loads, motion, and other aerodynamic functions on a cathode ray tube is included. Limited correlation efforts showed good comparison between the results of this analyzer and other sophisticated digital simulations. The digital simulation results were successfully correlated with test data.

Time-optimal Aircraft Pursuit-evasion with a Weapon Envelope Constraint

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1990-01-01

The optimal pursuit-evasion problem between two aircraft including a realistic weapon envelope is analyzed using differential game theory. Six order nonlinear point mass vehicle models are employed and the inclusion of an arbitrary weapon envelope geometry is allowed. The performance index is a linear combination of flight time and the square of the vehicle acceleration. Closed form solution to this high-order differential game is then obtained using feedback linearization. The solution is in the form of a feedback guidance law together with a quartic polynomial for time-to-go. Due to its modest computational requirements, this nonlinear guidance law is useful for on-board real-time implementation.

Further Results of Soft-Inplane Tiltrotor Aeromechanics Investigation Using Two Multibody Analyses

NASA Technical Reports Server (NTRS)

Masarati, Pierangelo; Quaranta, Giuseppe; Piatak, David J.; Singleton, Jeffrey D.

2004-01-01

This investigation focuses on the development of multibody analytical models to predict the dynamic response, aeroelastic stability, and blade loading of a soft-inplane tiltrotor wind-tunnel model. Comprehensive rotorcraft-based multibody analyses enable modeling of the rotor system to a high level of detail such that complex mechanics and nonlinear effects associated with control system geometry and joint deadband may be considered. The influence of these and other nonlinear effects on the aeromechanical behavior of the tiltrotor model are examined. A parametric study of the design parameters which may have influence on the aeromechanics of the soft-inplane rotor system are also included in this investigation.

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

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

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

2011-05-15

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

Nonlinear association criterion, nonlinear Granger causality and related issues with applications to neuroimage studies.

PubMed

Tao, Chenyang; Feng, Jianfeng

2016-03-15

Quantifying associations in neuroscience (and many other scientific disciplines) is often challenged by high-dimensionality, nonlinearity and noisy observations. Many classic methods have either poor power or poor scalability on data sets of the same or different scales such as genetical, physiological and image data. Based on the framework of reproducing kernel Hilbert spaces we proposed a new nonlinear association criteria (NAC) with an efficient numerical algorithm and p-value approximation scheme. We also presented mathematical justification that links the proposed method to related methods such as kernel generalized variance, kernel canonical correlation analysis and Hilbert-Schmidt independence criteria. NAC allows the detection of association between arbitrary input domain as long as a characteristic kernel is defined. A MATLAB package was provided to facilitate applications. Extensive simulation examples and four real world neuroscience examples including functional MRI causality, Calcium imaging and imaging genetic studies on autism [Brain, 138(5):13821393 (2015)] and alcohol addiction [PNAS, 112(30):E4085-E4093 (2015)] are used to benchmark NAC. It demonstrates the superior performance over the existing procedures we tested and also yields biologically significant results for the real world examples. NAC beats its linear counterparts when nonlinearity is presented in the data. It also shows more robustness against different experimental setups compared with its nonlinear counterparts. In this work we presented a new and robust statistical approach NAC for measuring associations. It could serve as an interesting alternative to the existing methods for datasets where nonlinearity and other confounding factors are present. Copyright © 2016 Elsevier B.V. All rights reserved.

Nonlinear analysis of structures. [within framework of finite element method

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.

1974-01-01

The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.

Reconstruction of nonlinear wave propagation

DOEpatents

Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie

2013-04-23

Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.

Optical soliton solutions of the cubic-quintic non-linear Schrödinger's equation including an anti-cubic term

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Hosseini, Kamyar; Samadani, Farzan; Raza, Nauman

2018-07-01

A wide range of problems in different fields of the applied sciences especially non-linear optics is described by non-linear Schrödinger's equations (NLSEs). In the present paper, a specific type of NLSEs known as the cubic-quintic non-linear Schrödinger's equation including an anti-cubic term has been studied. The generalized Kudryashov method along with symbolic computation package has been exerted to carry out this objective. As a consequence, a series of optical soliton solutions have formally been retrieved. It is corroborated that the generalized form of Kudryashov method is a direct, effectual, and reliable technique to deal with various types of non-linear Schrödinger's equations.

Genetic Wild Card: A Marker for Learners at Risk.

ERIC Educational Resources Information Center

Williams, Christine A.

This paper surveys past and current theories about the workings of the mind, current brain research and psychological applications of non-linear dynamics. Parallels are drawn between the world of high-functioning autism, gifted individuals with learning disabilities, and aspects of genius. An organizing theory is presented, which includes these…

The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Interface Technology for Geometrically Nonlinear Analysis of Multiple Connected Subdomains

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

1997-01-01

Interface technology for geometrically nonlinear analysis is presented and demonstrated. This technology is based on an interface element which makes use of a hybrid variational formulation to provide for compatibility between independently modeled connected subdomains. The interface element developed herein extends previous work to include geometric nonlinearity and to use standard linear and nonlinear solution procedures. Several benchmark nonlinear applications of the interface technology are presented and aspects of the implementation are discussed.

Continuous-wave supercontinuum laser based on an erbium-doped fiber ring cavity incorporating a highly nonlinear optical fiber.

PubMed

Lee, Ju Han; Takushima, Yuichi; Kikuchi, Kazuro

2005-10-01

We experimentally demonstrate a novel erbium-doped fiber based continuous-wave (cw) supercontinuum laser. The laser has a simple ring-cavity structure incorporating an erbium-doped fiber and a highly nonlinear dispersion-shifted fiber (HNL-DSF). Differently from previously demonstrated cw supercontinuum sources based on single propagation of a strong Raman pump laser beam through a highly nonlinear fiber, erbium gain inside the cavity generates a seed light oscillation, and the oscillated light subsequently evolves into a supercontinuum by nonlinear effects such as modulation instability and stimulated Raman scattering in the HNL-DSF. High quality of the depolarized supercontinuum laser output with a spectral bandwidth larger than 250 nm is readily achieved.

Integrated method for chaotic time series analysis

DOEpatents

Hively, Lee M.; Ng, Esmond G.

1998-01-01

Methods and apparatus for automatically detecting differences between similar but different states in a nonlinear process monitor nonlinear data. Steps include: acquiring the data; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; and determining by comparison whether differences between similar but different states are indicated.

A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

PubMed

Xu, Zhengfu; Bao, Gang

2010-11-01

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

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.

Study on the near-field non-linearity (SMILE) of high power diode laser arrays

NASA Astrophysics Data System (ADS)

Zhang, Hongyou; Jia, Yangtao; Li, Changxuan; Zah, Chung-en; Liu, Xingsheng

2018-02-01

High power laser diodes have been found a wide range of industrial, space, medical applications, characterized by high conversion efficiency, small size, light weight and a long lifetime. However, due to thermal induced stress, each emitter in a semiconductor laser bar or array is displaced along p-n junction, resulting of each emitter is not in a line, called Near-field Non-linearity. Near-field Non-linearity along laser bar (also known as "SMILE") determines the outcome of optical coupling and beam shaping [1]. The SMILE of a laser array is the main obstacle to obtain good optical coupling efficiency and beam shaping from a laser array. Larger SMILE value causes a larger divergence angle and a wider line after collimation and focusing, respectively. In this letter, we simulate two different package structures based on MCC (Micro Channel Cooler) with Indium and AuSn solders, including the distribution of normal stress and the SMILE value. According to the theoretical results, we found the distribution of normal stress on laser bar shows the largest in the middle and drops rapidly near both ends. At last, we did another experiment to prove that the SMILE value of a laser bar was mainly affected by the die bonding process, rather than the operating condition.

Photonic Switching Devices Using Light Bullets

NASA Technical Reports Server (NTRS)

Goorjian, Peter M. (Inventor)

1997-01-01

The present invention is directed toward a unique ultra-fast, all-optical switching device or switch made with readily available, relatively inexpensive, highly nonlinear photonic glasses. These photonic glasses have a sufficiently negative group velocity dispersion and high nonlinear index of refraction to support stable light bullets. The light bullets counterpropagate through, and interact within the waveguide to selectively change each others' directions of propagation into predetermined channels. In one embodiment, the switch utilizes a rectangularly planar slab waveguide, and further includes two central channels and a plurality of lateral channels for guiding the light bullets into and out of the waveguide. One advantage presented by the present all-optical switching device lies in its practical use of light bullets, thus preventing the degeneration of the pulses due to dispersion and diffraction at the front and back of the pulses. Another feature of the switching device is the relative insensitivity of the collision process to the time difference in which the counter-propagating pulses enter the waveguide. since. contrary to conventional co-propagating spatial solitons, the relative phase of the colliding pulses does not affect the interaction of these pulses. Yet another feature of the present all-optical switching device is the selection of the light pulse parameters which enables the generation of light bullets in highly nonlinear glasses.

Relativistic cosmic-ray spectra in the fully nonlinear theory of shock acceleration

NASA Technical Reports Server (NTRS)

Ellison, D. C.; Eichler, D.

1985-01-01

The non-linear theory of shock acceleration was generalized to include wave dynamics. In the limit of rapid wave damping, it is found that a finite wave velocity tempers the acceleration of high Mach number shocks and limits the maximum compression ratio even when energy loss is important. For a given spectrum, the efficiency of relativistic particle production is essentially independent of v sub Ph. For the three families shown, the percentage of kinetic energy flux going into relativistic particles is (1) 72 percent, (2) 44 percent, and (3) 26 percent (this includes the energy loss at the upper energy cutoff). Even small v sub ph, typical of the HISM, produce quasi-universal spectra that depend only weakly on the acoustic Mach number. These spectra should be close enough to e(-2) to satisfy cosmic ray source requirements.

Application of dynamical systems theory to the high angle of attack dynamics of the F-14

NASA Technical Reports Server (NTRS)

Jahnke, Craig C.; Culick, Fred E. C.

1990-01-01

Dynamical systems theory has been used to study the nonlinear dynamics of the F-14. An eight degree of freedom model that does not include the control system present in operational F-14s has been analyzed. The aerodynamic model, supplied by NASA, includes nonlinearities as functions of the angles of attack and sideslip, the rotation rate, and the elevator deflection. A continuation method has been used to calculate the steady states of the F-14 as continuous functions of the control surface deflections. Bifurcations of these steady states have been used to predict the onset of wing rock, spiral divergence, and jump phenomena which cause the aircraft to enter a spin. A simple feedback control system was designed to eliminate the wing rock and spiral divergence instabilities. The predictions were verified with numerical simulations.

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.

Independence screening for high dimensional nonlinear additive ODE models with applications to dynamic gene regulatory networks.

PubMed

Xue, Hongqi; Wu, Shuang; Wu, Yichao; Ramirez Idarraga, Juan C; Wu, Hulin

2018-05-02

Mechanism-driven low-dimensional ordinary differential equation (ODE) models are often used to model viral dynamics at cellular levels and epidemics of infectious diseases. However, low-dimensional mechanism-based ODE models are limited for modeling infectious diseases at molecular levels such as transcriptomic or proteomic levels, which is critical to understand pathogenesis of diseases. Although linear ODE models have been proposed for gene regulatory networks (GRNs), nonlinear regulations are common in GRNs. The reconstruction of large-scale nonlinear networks from time-course gene expression data remains an unresolved issue. Here, we use high-dimensional nonlinear additive ODEs to model GRNs and propose a 4-step procedure to efficiently perform variable selection for nonlinear ODEs. To tackle the challenge of high dimensionality, we couple the 2-stage smoothing-based estimation method for ODEs and a nonlinear independence screening method to perform variable selection for the nonlinear ODE models. We have shown that our method possesses the sure screening property and it can handle problems with non-polynomial dimensionality. Numerical performance of the proposed method is illustrated with simulated data and a real data example for identifying the dynamic GRN of Saccharomyces cerevisiae. Copyright © 2018 John Wiley & Sons, Ltd.

Derivation of an applied nonlinear Schroedinger equation

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

Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens

We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

Subcritical transition scenarios via linear and nonlinear localized optimal perturbations in plane Poiseuille flow

NASA Astrophysics Data System (ADS)

Farano, Mirko; Cherubini, Stefania; Robinet, Jean-Christophe; De Palma, Pietro

2016-12-01

Subcritical transition in plane Poiseuille flow is investigated by means of a Lagrange-multiplier direct-adjoint optimization procedure with the aim of finding localized three-dimensional perturbations optimally growing in a given time interval (target time). Space localization of these optimal perturbations (OPs) is achieved by choosing as objective function either a p-norm (with p\\gg 1) of the perturbation energy density in a linear framework; or the classical (1-norm) perturbation energy, including nonlinear effects. This work aims at analyzing the structure of linear and nonlinear localized OPs for Poiseuille flow, and comparing their transition thresholds and scenarios. The nonlinear optimization approach provides three types of solutions: a weakly nonlinear, a hairpin-like and a highly nonlinear optimal perturbation, depending on the value of the initial energy and the target time. The former shows localization only in the wall-normal direction, whereas the latter appears much more localized and breaks the spanwise symmetry found at lower target times. Both solutions show spanwise inclined vortices and large values of the streamwise component of velocity already at the initial time. On the other hand, p-norm optimal perturbations, although being strongly localized in space, keep a shape similar to linear 1-norm optimal perturbations, showing streamwise-aligned vortices characterized by low values of the streamwise velocity component. When used for initializing direct numerical simulations, in most of the cases nonlinear OPs provide the most efficient route to transition in terms of time to transition and initial energy, even when they are less localized in space than the p-norm OP. The p-norm OP follows a transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases of streak saturation, providing a contemporary growth of all of the velocity components due to strong nonlinear coupling.

Tidal alignment of galaxies

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

Blazek, Jonathan; Vlah, Zvonimir; Seljak, Uroš

We develop an analytic model for galaxy intrinsic alignments (IA) based on the theory of tidal alignment. We calculate all relevant nonlinear corrections at one-loop order, including effects from nonlinear density evolution, galaxy biasing, and source density weighting. Contributions from density weighting are found to be particularly important and lead to bias dependence of the IA amplitude, even on large scales. This effect may be responsible for much of the luminosity dependence in IA observations. The increase in IA amplitude for more highly biased galaxies reflects their locations in regions with large tidal fields. We also consider the impact ofmore » smoothing the tidal field on halo scales. We compare the performance of this consistent nonlinear model in describing the observed alignment of luminous red galaxies with the linear model as well as the frequently used "nonlinear alignment model," finding a significant improvement on small and intermediate scales. We also show that the cross-correlation between density and IA (the "GI" term) can be effectively separated into source alignment and source clustering, and we accurately model the observed alignment down to the one-halo regime using the tidal field from the fully nonlinear halo-matter cross correlation. Inside the one-halo regime, the average alignment of galaxies with density tracers no longer follows the tidal alignment prediction, likely reflecting nonlinear processes that must be considered when modeling IA on these scales. Finally, we discuss tidal alignment in the context of cosmic shear measurements.« less

Tidal alignment of galaxies

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

Blazek, Jonathan; Vlah, Zvonimir; Seljak, Uroš, E-mail: blazek@berkeley.edu, E-mail: zvlah@stanford.edu, E-mail: useljak@berkeley.edu

We develop an analytic model for galaxy intrinsic alignments (IA) based on the theory of tidal alignment. We calculate all relevant nonlinear corrections at one-loop order, including effects from nonlinear density evolution, galaxy biasing, and source density weighting. Contributions from density weighting are found to be particularly important and lead to bias dependence of the IA amplitude, even on large scales. This effect may be responsible for much of the luminosity dependence in IA observations. The increase in IA amplitude for more highly biased galaxies reflects their locations in regions with large tidal fields. We also consider the impact ofmore » smoothing the tidal field on halo scales. We compare the performance of this consistent nonlinear model in describing the observed alignment of luminous red galaxies with the linear model as well as the frequently used 'nonlinear alignment model,' finding a significant improvement on small and intermediate scales. We also show that the cross-correlation between density and IA (the 'GI' term) can be effectively separated into source alignment and source clustering, and we accurately model the observed alignment down to the one-halo regime using the tidal field from the fully nonlinear halo-matter cross correlation. Inside the one-halo regime, the average alignment of galaxies with density tracers no longer follows the tidal alignment prediction, likely reflecting nonlinear processes that must be considered when modeling IA on these scales. Finally, we discuss tidal alignment in the context of cosmic shear measurements.« less

Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

NASA Astrophysics Data System (ADS)

Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.

2012-12-01

In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (< 10-6), the nonlinear classical theory issued from a Taylor decomposition can explain the harmonic content. For higher strain, harmonic content becomes richer and the material exhibits more hysteretic behaviors, i.e. strain rate dependencies. Such observations have been made in the past (e.g., Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.

Optics and Nonlinear Buckling Mechanics in Large-Area, Highly Stretchable Arrays of Plasmonic Nanostructures.

PubMed

Gao, Li; Zhang, Yihui; Zhang, Hui; Doshay, Sage; Xie, Xu; Luo, Hongying; Shah, Deesha; Shi, Yan; Xu, Siyi; Fang, Hui; Fan, Jonathan A; Nordlander, Peter; Huang, Yonggang; Rogers, John A

2015-06-23

Large-scale, dense arrays of plasmonic nanodisks on low-modulus, high-elongation elastomeric substrates represent a class of tunable optical systems, with reversible ability to shift key optical resonances over a range of nearly 600 nm at near-infrared wavelengths. At the most extreme levels of mechanical deformation (strains >100%), nonlinear buckling processes transform initially planar arrays into three-dimensional configurations, in which the nanodisks rotate out of the plane to form linear arrays with "wavy" geometries. Analytical, finite-element, and finite-difference time-domain models capture not only the physics of these buckling processes, including all of the observed modes, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, particularly to soft optical sensors that integrate on or in the human body.

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

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Dynamical Approach Study of Spurious Numerics in Nonlinear Computations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi (Technical Monitor)

2002-01-01

The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

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

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. Themore » goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.« less

Integrated method for chaotic time series analysis

DOEpatents

Hively, L.M.; Ng, E.G.

1998-09-29

Methods and apparatus for automatically detecting differences between similar but different states in a nonlinear process monitor nonlinear data are disclosed. Steps include: acquiring the data; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; and determining by comparison whether differences between similar but different states are indicated. 8 figs.

Stability Analysis of a High-Speed Seal Test Rotor With Marginal and Extended Squeeze-Film Dampers: Theoretical and Experimental Results

NASA Technical Reports Server (NTRS)

Proctor, Margaret P.; Gunter, Edgar J.

2007-01-01

A case study of a high-speed seal test rotor shows how rotor dynamic analysis can be used to diagnose the source of high vibrations and evaluate a proposed remedy. Experimental results are compared with the synchronous and non-synchronous whirl response analysis of a double overhung, high-speed seal test rotor with ball bearings supported in 5.84- and 12.7-mm-long, un-centered squeeze-film oil dampers. Test performance with the original damper of length 5.84 mm was marginal. Non-synchronous whirling occurred at the overhung seal test disk and there was a high amplitude synchronous response near the drive spline above 32,000 rpm. Nonlinear synchronous unbalance and time transient whirl studies were conducted on the seal test rotor with the original and extended damper lengths. With the original damper design, the nonlinear synchronous response showed that unbalance could cause damper lockup at 33,000 rpm. Alford cross-coupling forces were also included at the overhung seal test disk for the whirl analysis. Sub-synchronous whirling at the seal test disk was observed in the nonlinear time transient analysis. With the extended damper length of 12.7 mm, the sub-synchronous motion was eliminated and the rotor unbalance response was acceptable to 45,000 rpm with moderate rotor unbalance. Seal test rotor orbits and vibration levels with the extended squeeze film dampers showed smooth operation to 40,444 rpm.

Mid-infrared supercontinuum generation in multimode step index chalcogenide fiber

NASA Astrophysics Data System (ADS)

Ben Khalifa, Ameni; Ben Salem, Amine; Cherif, Rim; Zghal, Mourad

2016-09-01

In this paper, we propose a design of a high numerical aperture multimode hybrid step-index fiber for mid-infrared (mid- IR) supercontinuum generation (SCG) where two chalcogenide glass compositions As40Se60 and Ge10As23.4Se66.6 for the core and the cladding are selected, respectively. Aiming to get accurate modeling of the SCG by the fundamental mode, we solve the multimode generalized nonlinear Schrödinger equations and demonstrate nonlinear coupling and energy transfer between high order modes. The proposed study points out the impact of nonlinear mode coupling that should be taken into account in order to successfully predict the mid-infrared supercontinuum generation in highly nonlinear multimode fibers.

Evaluation of a Highly Anticlastic Panel with Tow Overlaps

NASA Technical Reports Server (NTRS)

Wu, K. Chauncey; Gurdal, Zafer

2007-01-01

A rectangular, variable-stiffness panel with tow overlaps was manufactured using an advanced tow placement machine. The cured panel had large anticlastic imperfections, with measured amplitudes of over two times the average panel thickness. These imperfections were not due to the overall steered-fiber layup or the tow overlaps, but instead resulted from local asymmetries in the laminate that were caused by a manufacturing oversight. In the nominal panel layup, fiber angles vary linearly from 60 degrees on the panel axial centerline to 30 degrees on the parallel edges. A geometrically nonlinear analysis was performed with a -280 degree Fahrenheit thermal load to simulate the postcure cooldown to room temperature. The predicted geometric imperfections correlated well with the measured panel shape. Unique structural test fixtures were then developed which greatly reduced these imperfections, but they also caused prestresses in the panel. Surface imperfections measured after the panel was installed in the test fixtures were used with nonlinear finite element analyses to predict these fixturing-induced prestresses. These prestresses were also included in structural analyses of panel end compression to failure, and the analytical results compared well with test data when both geometric and material nonlinearities were included.

A semi-active H∞ control strategy with application to the vibration suppression of nonlinear high-rise building under earthquake excitations.

PubMed

Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong

2016-01-01

Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibration. In this strategy, a modified Kalman-Bucy observer which is suitable for the proposed semi-active strategy is developed to obtain the state vector from the measured semi-active control force and acceleration feedback, taking into account of the effects of nonlinearity, disturbance and uncertainty of controlled system parameters by the observed nonlinear accelerations. Then, the proposed semi-active H∞ control strategy is applied to the ASCE 20-story benchmark building when subjected to earthquake excitation and compared with the other control approaches by some control criteria. It is indicated that the proposed semi-active H∞ control strategy provides much better control performances by comparison with the semi-active MPC and Clipped-LQG control approaches, and can reduce nonlinear seismic response and minimize the damage in the buildings. Besides, it enhances the reliability of the control performance when compared with the active control strategy. Thus, the proposed semi-active H∞ control strategy is suitable for suppressing the nonlinear vibration of high-rise buildings.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Reduced nonlinear prognostic model construction from high-dimensional data

NASA Astrophysics Data System (ADS)

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

2017-04-01

Construction of a data-driven model of evolution operator using universal approximating functions can only be statistically justified when the dimension of its phase space is small enough, especially in the case of short time series. At the same time in many applications real-measured data is high-dimensional, e.g. it is space-distributed and multivariate in climate science. Therefore it is necessary to use efficient dimensionality reduction methods which are also able to capture key dynamical properties of the system from observed data. To address this problem we present a Bayesian approach to an evolution operator construction which incorporates two key reduction steps. First, the data is decomposed into a set of certain empirical modes, such as standard empirical orthogonal functions or recently suggested nonlinear dynamical modes (NDMs) [1], and the reduced space of corresponding principal components (PCs) is obtained. Then, the model of evolution operator for PCs is constructed which maps a number of states in the past to the current state. The second step is to reduce this time-extended space in the past using appropriate decomposition methods. Such a reduction allows us to capture only the most significant spatio-temporal couplings. The functional form of the evolution operator includes separately linear, nonlinear (based on artificial neural networks) and stochastic terms. Explicit separation of the linear term from the nonlinear one allows us to more easily interpret degree of nonlinearity as well as to deal better with smooth PCs which can naturally occur in the decompositions like NDM, as they provide a time scale separation. Results of application of the proposed method to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

Temperature-dependent Sellmeier equations for rare-earth sesquioxides.

PubMed

Zelmon, David E; Northridge, Jessica M; Haynes, Nicholas D; Perlov, Dan; Petermann, Klaus

2013-06-01

High-power lasers are making increasing demands on laser hosts especially in the area of thermal management. Traditional hosts, such as YAG, are unsuitable for many high-power applications and therefore, new hosts are being developed including rare-earth sesquioxides. We report new measurements of the refractive indices of these materials as functions of wavelength and temperature, which will aid in the design of laser cavities and other nonlinear optical elements.

Engineered second-harmonic diffraction from highly transmissive metasurfaces composed of complementary split-ring resonators.

PubMed

Yang, Xin; Zhang, Chi; Wan, Mingjie; Chen, Zhuo; Wang, Zhenlin

2016-07-01

We theoretically and experimentally investigated the optical second-harmonic (SH) diffraction from metasurfaces based on gold complementary split-ring resonators (CSRRs). We have demonstrated that the generated SH currents are mostly parallel to the incident polarization and are asymmetric with respect to the base of a CSRR, thus allowing us to impose the phase change of π on the SH radiation by reversing the CSRR's orientation. We verified this concept of geometry-induced nonlinear phase by designing and fabricating a nonlinear metasurface consisting of supercells of CSRRs with opposite orientations that can function as a SH beam splitter. The ability to control the phase of the local nonlinearity coupled with the high transmittance at both fundamental and SHG wavelengths makes the CSRRs good candidates for the construction of highly efficient three-dimensional nonlinear metamaterials and suitable for applications in nonlinear beam shaping.

Attosecond nonlinear optics using gigawatt-scale isolated attosecond pulses

PubMed Central

Takahashi, Eiji J.; Lan, Pengfei; Mücke, Oliver D.; Nabekawa, Yasuo; Midorikawa, Katsumi

2013-01-01

High-energy isolated attosecond pulses required for the most intriguing nonlinear attosecond experiments as well as for attosecond-pump/attosecond-probe spectroscopy are still lacking at present. Here we propose and demonstrate a robust generation method of intense isolated attosecond pulses, which enable us to perform a nonlinear attosecond optics experiment. By combining a two-colour field synthesis and an energy-scaling method of high-order harmonic generation, the maximum pulse energy of the isolated attosecond pulse reaches as high as 1.3 μJ. The generated pulse with a duration of 500 as, as characterized by a nonlinear autocorrelation measurement, is the shortest and highest-energy pulse ever with the ability to induce nonlinear phenomena. The peak power of our tabletop light source reaches 2.6 GW, which even surpasses that of an extreme-ultraviolet free-electron laser. PMID:24158092

Three-dimensional femtosecond laser processing for lab-on-a-chip applications

NASA Astrophysics Data System (ADS)

Sima, Felix; Sugioka, Koji; Vázquez, Rebeca Martínez; Osellame, Roberto; Kelemen, Lóránd; Ormos, Pal

2018-02-01

The extremely high peak intensity associated with ultrashort pulse width of femtosecond laser allows us to induce nonlinear interaction such as multiphoton absorption and tunneling ionization with materials that are transparent to the laser wavelength. More importantly, focusing the femtosecond laser beam inside the transparent materials confines the nonlinear interaction only within the focal volume, enabling three-dimensional (3D) micro- and nanofabrication. This 3D capability offers three different schemes, which involve undeformative, subtractive, and additive processing. The undeformative processing preforms internal refractive index modification to construct optical microcomponents including optical waveguides. Subtractive processing can realize the direct fabrication of 3D microfluidics, micromechanics, microelectronics, and photonic microcomponents in glass. Additive processing represented by two-photon polymerization enables the fabrication of 3D polymer micro- and nanostructures for photonic and microfluidic devices. These different schemes can be integrated to realize more functional microdevices including lab-on-a-chip devices, which are miniaturized laboratories that can perform reaction, detection, analysis, separation, and synthesis of biochemical materials with high efficiency, high speed, high sensitivity, low reagent consumption, and low waste production. This review paper describes the principles and applications of femtosecond laser 3D micro- and nanofabrication for lab-on-a-chip applications. A hybrid technique that promises to enhance functionality of lab-on-a-chip devices is also introduced.

High-Alpha Handling Qualities Flight Research on the NASA F/A-18 High Alpha Research Vehicle

NASA Technical Reports Server (NTRS)

Wichman, Keith D.; Pahle, Joseph W.; Bahm, Catherine; Davidson, John B.; Bacon, Barton J.; Murphy, Patrick C.; Ostroff, Aaron J.; Hoffler, Keith D.

1996-01-01

A flight research study of high-angle-of-attack handling qualities has been conducted at the NASA Dryden Flight Research Center using the F/A-18 High Alpha Research Vehicle (HARV). The objectives were to create a high-angle-of-attack handling qualities flight database, develop appropriate research evaluation maneuvers, and evaluate high-angle-of-attack handling qualities guidelines and criteria. Using linear and nonlinear simulations and flight research data, the predictions from each criterion were compared with the pilot ratings and comments. Proposed high-angle-of-attack nonlinear design guidelines and proposed handling qualities criteria and guidelines developed using piloted simulation were considered. Recently formulated time-domain Neal-Smith guidelines were also considered for application to high-angle-of-attack maneuvering. Conventional envelope criteria were evaluated for possible extension to the high-angle-of-attack regime. Additionally, the maneuvers were studied as potential evaluation techniques, including a limited validation of the proposed standard evaluation maneuver set. This paper gives an overview of these research objectives through examples and summarizes result highlights. The maneuver development is described briefly, the criteria evaluation is emphasized with example results given, and a brief discussion of the database form and content is presented.

Design and implementation of non-linear image processing functions for CMOS image sensor

NASA Astrophysics Data System (ADS)

Musa, Purnawarman; Sudiro, Sunny A.; Wibowo, Eri P.; Harmanto, Suryadi; Paindavoine, Michel

2012-11-01

Today, solid state image sensors are used in many applications like in mobile phones, video surveillance systems, embedded medical imaging and industrial vision systems. These image sensors require the integration in the focal plane (or near the focal plane) of complex image processing algorithms. Such devices must meet the constraints related to the quality of acquired images, speed and performance of embedded processing, as well as low power consumption. To achieve these objectives, low-level analog processing allows extracting the useful information in the scene directly. For example, edge detection step followed by a local maxima extraction will facilitate the high-level processing like objects pattern recognition in a visual scene. Our goal was to design an intelligent image sensor prototype achieving high-speed image acquisition and non-linear image processing (like local minima and maxima calculations). For this purpose, we present in this article the design and test of a 64×64 pixels image sensor built in a standard CMOS Technology 0.35 μm including non-linear image processing. The architecture of our sensor, named nLiRIC (non-Linear Rapid Image Capture), is based on the implementation of an analog Minima/Maxima Unit. This MMU calculates the minimum and maximum values (non-linear functions), in real time, in a 2×2 pixels neighbourhood. Each MMU needs 52 transistors and the pitch of one pixel is 40×40 mu m. The total area of the 64×64 pixels is 12.5mm2. Our tests have shown the validity of the main functions of our new image sensor like fast image acquisition (10K frames per second), minima/maxima calculations in less then one ms.

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint

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

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

2016-01-01

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

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

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

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

2015-10-01

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

Nonlinear Analysis of Airfoil High-Intensity Gust Response Using a High-Order Prefactored Compact Code

NASA Technical Reports Server (NTRS)

Crivellini, A.; Golubev, V.; Mankbadi, R.; Scott, J. R.; Hixon, R.; Povinelli, L.; Kiraly, L. James (Technical Monitor)

2002-01-01

The nonlinear response of symmetric and loaded airfoils to an impinging vortical gust is investigated in the parametric space of gust dimension, intensity, and frequency. The study, which was designed to investigate the validity limits for a linear analysis, is implemented by applying a nonlinear high-order prefactored compact code and comparing results with linear solutions from the GUST3D frequency-domain solver. Both the unsteady aerodynamic and acoustic gust responses are examined.

Characterization of a Multi-element Clinical HIFU System Using Acoustic Holography and Nonlinear Modeling

PubMed Central

Kreider, Wayne; Yuldashev, Petr V.; Sapozhnikov, Oleg A.; Farr, Navid; Partanen, Ari; Bailey, Michael R.; Khokhlova, Vera A.

2014-01-01

High-intensity focused ultrasound (HIFU) is a treatment modality that relies on the delivery of acoustic energy to remote tissue sites to induce thermal and/or mechanical tissue ablation. To ensure the safety and efficacy of this medical technology, standard approaches are needed for accurately characterizing the acoustic pressures generated by clinical ultrasound sources under operating conditions. Characterization of HIFU fields is complicated by nonlinear wave propagation and the complexity of phased-array transducers. Previous work has described aspects of an approach that combines measurements and modeling, and here we demonstrate this approach for a clinical phased array transducer. First, low-amplitude hydrophone measurements were performed in water over a scan plane between the array and the focus. Second, these measurements were used to holographically reconstruct the surface vibrations of the transducer and to set a boundary condition for a 3-D acoustic propagation model. Finally, nonlinear simulations of the acoustic field were carried out over a range of source power levels. Simulation results were compared to pressure waveforms measured directly by hydrophone at both low and high power levels, demonstrating that details of the acoustic field including shock formation are quantitatively predicted. PMID:25004539

Two-step sensitivity testing of parametrized and regionalized life cycle assessments: methodology and case study.

PubMed

Mutel, Christopher L; de Baan, Laura; Hellweg, Stefanie

2013-06-04

Comprehensive sensitivity analysis is a significant tool to interpret and improve life cycle assessment (LCA) models, but is rarely performed. Sensitivity analysis will increase in importance as inventory databases become regionalized, increasing the number of system parameters, and parametrized, adding complexity through variables and nonlinear formulas. We propose and implement a new two-step approach to sensitivity analysis. First, we identify parameters with high global sensitivities for further examination and analysis with a screening step, the method of elementary effects. Second, the more computationally intensive contribution to variance test is used to quantify the relative importance of these parameters. The two-step sensitivity test is illustrated on a regionalized, nonlinear case study of the biodiversity impacts from land use of cocoa production, including a worldwide cocoa products trade model. Our simplified trade model can be used for transformable commodities where one is assessing market shares that vary over time. In the case study, the highly uncertain characterization factors for the Ivory Coast and Ghana contributed more than 50% of variance for almost all countries and years examined. The two-step sensitivity test allows for the interpretation, understanding, and improvement of large, complex, and nonlinear LCA systems.

Beam optical design of in-flight fragment separator for high-power heavy ion beam

NASA Astrophysics Data System (ADS)

Yun, C. C.; Kim, Mi-Jung; Kim, D. G.; Song, J. S.; Kim, Myeong-Jin; Kim, J. W.; Kim, J. R.; Wan, W.

2013-12-01

An in-flight fragment separator has been designed for the rare isotope science project (RISP) in Korea. A beam used for the design is 238U in the energy of 200 MeV/u with the maximum beam power of 400 kW. The use of high-power beam requires careful removal of the primary beam by pre-separator, for which its configuration was revised to employ four dipole magnets instead of two. Different configurations of the separator have been tested in search of optimal design in non-linear optics, which was complicated by the space needed for the target, beam dump and radiation shielding. Non-linear optical calculations have been carried out using GICOSY and COSY Infinity including the fringe fields of large-aperture quadrupole magnets. Correction of non-linear terms is made with multipole coils located inside the superconducting quadrupole magnets and by external multipole magnets. Beam simulations using LISE++ and MOCADI have been performed to consider the effects of multiple charge states of the primary and isotope beams produced at the target. Layout of the separator is being finalized, and detailed optics simulation will continue to refine its design.

Fully 3D modeling of tokamak vertical displacement events with realistic parameters

NASA Astrophysics Data System (ADS)

Pfefferle, David; Ferraro, Nathaniel; Jardin, Stephen; Bhattacharjee, Amitava

2016-10-01

In this work, we model the complex multi-domain and highly non-linear physics of Vertical Displacement Events (VDEs), one of the most damaging off-normal events in tokamaks, with the implicit 3D extended MHD code M3D-C1. The code has recently acquired the capability to include finite thickness conducting structures within the computational domain. By exploiting the possibility of running a linear 3D calculation on top of a non-linear 2D simulation, we monitor the non-axisymmetric stability and assess the eigen-structure of kink modes as the simulation proceeds. Once a stability boundary is crossed, a fully 3D non-linear calculation is launched for the remainder of the simulation, starting from an earlier time of the 2D run. This procedure, along with adaptive zoning, greatly increases the efficiency of the calculation, and allows to perform VDE simulations with realistic parameters and high resolution. Simulations are being validated with NSTX data where both axisymmetric (toroidally averaged) and non-axisymmetric induced and conductive (halo) currents have been measured. This work is supported by US DOE Grant DE-AC02-09CH11466.

Implementation of Improved Transverse Shear Calculations and Higher Order Laminate Theory Into Strain Rate Dependent Analyses of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Zhu, Lin-Fa; Kim, Soo; Chattopadhyay, Aditi; Goldberg, Robert K.

2004-01-01

A numerical procedure has been developed to investigate the nonlinear and strain rate dependent deformation response of polymer matrix composite laminated plates under high strain rate impact loadings. A recently developed strength of materials based micromechanics model, incorporating a set of nonlinear, strain rate dependent constitutive equations for the polymer matrix, is extended to account for the transverse shear effects during impact. Four different assumptions of transverse shear deformation are investigated in order to improve the developed strain rate dependent micromechanics model. The validities of these assumptions are investigated using numerical and theoretical approaches. A method to determine through the thickness strain and transverse Poisson's ratio of the composite is developed. The revised micromechanics model is then implemented into a higher order laminated plate theory which is modified to include the effects of inelastic strains. Parametric studies are conducted to investigate the mechanical response of composite plates under high strain rate loadings. Results show the transverse shear stresses cannot be neglected in the impact problem. A significant level of strain rate dependency and material nonlinearity is found in the deformation response of representative composite specimens.

Comparison of HF radar measurements with Eulerian and Lagrangian surface currents

NASA Astrophysics Data System (ADS)

Röhrs, Johannes; Sperrevik, Ann Kristin; Christensen, Kai Håkon; Broström, Göran; Breivik, Øyvind

2015-05-01

High-frequency (HF) radar-derived ocean currents are compared with in situ measurements to conclude if the radar observations include effects of surface waves that are of second order in the wave amplitude. Eulerian current measurements from a high-resolution acoustic Doppler current profiler and Lagrangian measurements from surface drifters are used as references. Directional wave spectra are obtained from a combination of pressure sensor data and a wave model. Our analysis shows that the wave-induced Stokes drift is not included in the HF radar-derived currents, that is, HF radars measure the Eulerian current. A disputed nonlinear correction to the phase velocity of surface gravity waves, which may affect HF radar signals, has a magnitude of about half the Stokes drift at the surface. In our case, this contribution by nonlinear dispersion would be smaller than the accuracy of the HF radar currents, hence no conclusion can be made. Finally, the analysis confirms that the HF radar data represent an exponentially weighted vertical average where the decay scale is proportional to the wavelength of the transmitted signal.

Nonlinear vibration of a coupled high- Tc superconducting levitation system

NASA Astrophysics Data System (ADS)

Sugiura, T.; Inoue, T.; Ura, H.

2004-10-01

High- Tc superconducting levitation can be applied to electro-mechanical systems, such as flywheel energy storage and linear-drive transportation. Such a system can be modeled as a magnetically coupled system of many permanent magnets and high- Tc superconducting bulks. It is a multi-degree-of-freedom dynamical system coupled by nonlinear interaction between levitated magnets and superconducting bulks. This nonlinearly coupled system, with small damping due to no contact support, can easily show complicated phenomena of nonlinear dynamics. In mechanical design, it is important to evaluate this nonlinear dynamics, though it has not been well studied so far. This research deals with forced vibration of a coupled superconducting levitation system. As a simple modeling of a coupled system, a permanent magnet levitated above a superconducting bulk is placed between two fixed permanent magnets without contact. Frequency response of the levitated magnet under excitation of one of the fixed magnets was examined theoretically. The results show typical nonlinear vibration, such as jump, hysteresis, and parametric resonance, which were confirmed in our numerical analyses and experiments.

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Bayesian framework for modeling diffusion processes with nonlinear drift based on nonlinear and incomplete observations.

PubMed

Wu, Hao; Noé, Frank

2011-03-01

Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.

The role of nonlinear effects in the propagation of noise from high-power jet aircraft.

PubMed

Gee, Kent L; Sparrow, Victor W; James, Michael M; Downing, J Micah; Hobbs, Christopher M; Gabrielson, Thomas B; Atchley, Anthony A

2008-06-01

To address the question of the role of nonlinear effects in the propagation of noise radiated by high-power jet aircraft, extensive measurements were made of the F-22A Raptor during static engine run-ups. Data were acquired at low-, intermediate-, and high-thrust engine settings with microphones located 23-305 m from the aircraft along several angles. Comparisons between the results of a generalized-Burgers-equation-based nonlinear propagation model and the measurements yield favorable agreement, whereas application of a linear propagation model results in spectral predictions that are much too low at high frequencies. The results and analysis show that significant nonlinear propagation effects occur for even intermediate-thrust engine conditions and at angles well away from the peak radiation angle. This suggests that these effects are likely to be common in the propagation of noise radiated by high-power aircraft.

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

PubMed

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

Engineered Multifunctional Nanophotonic Materials for Ultrafast Optical Switching

DTIC Science & Technology

2012-11-02

and Co3 + placed at tetrahedral and octahedral sites, respectively. Single -layer thin films of Co3O4 nanoparticles have large optical nonlinearity and...the first two methodologies in systems having weakly resonant structures, including 3-D and/or 1-D photonic crystal structures (i.e. nonlinear Bragg...Nonlinear optical transmission of lead phthalocyanine-doped nematic liquid crystal composites for multiscale nonlinear switching from nanosecond to

Theoretical investigation of the force and dynamically coupled torsional-axial-lateral dynamic response of eared rotors

NASA Technical Reports Server (NTRS)

David, J. W.; Mitchell, L. D.

1982-01-01

Difficulties in solution methodology to be used to deal with the potentially higher nonlinear rotor equations when dynamic coupling is included. A solution methodology is selected to solve the nonlinear differential equations. The selected method was verified to give good results even at large nonlinearity levels. The transfer matrix methodology is extended to the solution of nonlinear problems.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

PubMed

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series

NASA Astrophysics Data System (ADS)

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Embedded algorithms within an FPGA-based system to process nonlinear time series data

NASA Astrophysics Data System (ADS)

Jones, Jonathan D.; Pei, Jin-Song; Tull, Monte P.

2008-03-01

This paper presents some preliminary results of an ongoing project. A pattern classification algorithm is being developed and embedded into a Field-Programmable Gate Array (FPGA) and microprocessor-based data processing core in this project. The goal is to enable and optimize the functionality of onboard data processing of nonlinear, nonstationary data for smart wireless sensing in structural health monitoring. Compared with traditional microprocessor-based systems, fast growing FPGA technology offers a more powerful, efficient, and flexible hardware platform including on-site (field-programmable) reconfiguration capability of hardware. An existing nonlinear identification algorithm is used as the baseline in this study. The implementation within a hardware-based system is presented in this paper, detailing the design requirements, validation, tradeoffs, optimization, and challenges in embedding this algorithm. An off-the-shelf high-level abstraction tool along with the Matlab/Simulink environment is utilized to program the FPGA, rather than coding the hardware description language (HDL) manually. The implementation is validated by comparing the simulation results with those from Matlab. In particular, the Hilbert Transform is embedded into the FPGA hardware and applied to the baseline algorithm as the centerpiece in processing nonlinear time histories and extracting instantaneous features of nonstationary dynamic data. The selection of proper numerical methods for the hardware execution of the selected identification algorithm and consideration of the fixed-point representation are elaborated. Other challenges include the issues of the timing in the hardware execution cycle of the design, resource consumption, approximation accuracy, and user flexibility of input data types limited by the simplicity of this preliminary design. Future work includes making an FPGA and microprocessor operate together to embed a further developed algorithm that yields better computational and power efficiency.

On the Modeling of Shells in Multibody Dynamics

NASA Technical Reports Server (NTRS)

Bauchau, Olivier A.; Choi, Jou-Young; Bottasso, Carlo L.

2000-01-01

Energy preserving/decaying schemes are presented for the simulation of the nonlinear multibody systems involving shell components. The proposed schemes are designed to meet four specific requirements: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material nonlinearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. The kinematic nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous manner, and the material nonlinearities can be handled when the, constitutive laws stem from the existence of a strain energy density function. The efficiency and robustness of the proposed approach is illustrated with specific numerical examples that also demonstrate the need for integration schemes possessing high frequency numerical dissipation.

Numerical study of electromagnetic scattering from one-dimensional nonlinear fractal sea surface

NASA Astrophysics Data System (ADS)

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

2010-02-01

In recent years, linear fractal sea surface models have been developed for the sea surface in order to establish an electromagnetic backscattering model. Unfortunately, the sea surface is always nonlinear, particularly at high sea states. We present a nonlinear fractal sea surface model and derive an electromagnetic backscattering model. Using this model, we numerically calculate the normalized radar cross section (NRCS) of a nonlinear sea surface. Comparing the averaged NRCS between linear and nonlinear fractal models, we show that the NRCS of a linear fractal sea surface underestimates the NRCS of the real sea surface, especially for sea states with high fractal dimensions, and for dominant ocean surface gravity waves that are either very short or extremely long.

Nonlinear dielectric thin films for high-power electric storage with energy density comparable with electrochemical supercapacitors.

PubMed

Yao, Kui; Chen, Shuting; Rahimabady, Mojtaba; Mirshekarloo, Meysam Sharifzadeh; Yu, Shuhui; Tay, Francis Eng Hock; Sritharan, Thirumany; Lu, Li

2011-09-01

Although batteries possess high energy storage density, their output power is limited by the slow movement of charge carriers, and thus capacitors are often required to deliver high power output. Dielectric capacitors have high power density with fast discharge rate, but their energy density is typically much lower than electrochemical supercapacitors. Increasing the energy density of dielectric materials is highly desired to extend their applications in many emerging power system applications. In this paper, we review the mechanisms and major characteristics of electric energy storage with electrochemical supercapacitors and dielectric capacitors. Three types of in-house-produced ferroic nonlinear dielectric thin film materials with high energy density are described, including (Pb(0.97)La(0.02))(Zr(0.90)Sn(0.05)Ti(0.05))O(3) (PLZST) antiferroelectric ceramic thin films, Pb(Zn(1/3)Nb(2/3))O(3-)Pb(Mg(1/3)Nb(2/3))O(3-)PbTiO(3) (PZN-PMN-PT) relaxor ferroelectric ceramic thin films, and poly(vinylidene fluoride) (PVDF)-based polymer blend thin films. The results showed that these thin film materials are promising for electric storage with outstandingly high power density and fairly high energy density, comparable with electrochemical supercapacitors.

Hydrostatic Stress Effects Incorporated Into the Analysis of the High-Strain-Rate Deformation of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.

2003-01-01

Procedures for modeling the effect of high strain rate on composite materials are needed for designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and strain rate dependence of the composite response is primarily due to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. An experimental program has been carried out through a university grant with the Ohio State University to obtain tensile and shear deformation data for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. This information has been used at the NASA Glenn Research Center to develop, characterize, and correlate a material model in which the strain rate dependence and nonlinearity (including hydrostatic stress effects) of the polymer are correctly analyzed. To obtain the material data, Glenn s researchers designed and fabricated test specimens of a representative toughened epoxy resin. Quasi-static tests at low strain rates and split Hopkinson bar tests at high strain rates were then conducted at the Ohio State University. The experimental data confirmed the strong effects of strain rate on both the tensile and shear deformation of the polymer. For the analytical model, Glenn researchers modified state variable constitutive equations previously used for the viscoplastic analysis of metals to allow for the analysis of the nonlinear, strain-rate-dependent polymer deformation. Specifically, we accounted for the effects of hydrostatic stresses. An important discovery in the course of this work was that the hydrostatic stress effects varied during the loading process, which needed to be accounted for within the constitutive equations. The model is characterized primarily by shear data, with tensile data used to characterize the hydrostatic stress effects.

Classical and quantum non-linear optical applications using the Mach-Zehnder interferometer

NASA Astrophysics Data System (ADS)

Prescod, Andru

Mach Zehnder (MZ) modulators are widely employed in a variety of applications, such as optical communications, optical imaging, metrology and encryption. In this dissertation, we explore two non-linear MZ applications; one classified as classical and one as quantum, in which the Mach Zehnder interferometer is used. In the first application, a classical non-linear application, we introduce and study a new electro-optic highly linear (e.g., >130 dB) modulator configuration. This modulator makes use of a phase modulator (PM) in one arm of the MZ interferometer (MZI) and a ring resonator (RR) located on the other arm. The modulator performance is obtained through the control of a combination of internal and external parameters. These parameters include the RR-coupling ratio (internal parameter); the RF power split ratio and the RF phase bias (external parameters). Results show the unique and superior features, such as high linearity (SFDR˜133 dB), modulation bandwidth extension (as much as 70%) over the previously proposed and demonstrated Resonator-Assisted Mach Zehnder (RAMZ) design. Furthermore the proposed electro-optic modulator of this dissertation also provides an inherent SFDR compensation capability, even in cases where a significant waveguide optical loss exists. This design also shows potential for increased flexibility, practicality and ease of use. In the second application, a quantum non-linear application, we experimentally demonstrate quantum optical coherence tomography (QOCT) using a type II non-linear crystal (periodically-poled potassium titanyl phosphate (KTiOPO4) or PPKTP). There have been several publications discussing the merits and disadvantages of QOCT compared to OCT and other imaging techniques. First, we discuss the issues and solutions for increasing the efficiency of the quantum entangled photons. Second, we use a free space QOCT experiment to generate a high flux of these quantum entangled photons in two orthogonal polarizations, by parametric down-conversion. Third, by ensuring that these down-converted photons have the same frequency, spatial-temporal mode, and the same polarization when they interfere at a beam splitter, quantum interference should occur. Quantum interference of these entangled photons enables high resolution probing of dispersive samples.

Chip-Scale Architectures for Precise Optical Frequency Synthesis

NASA Astrophysics Data System (ADS)

Yang, Jinghui

Scientists and engineers have investigated various types of stable and accurate optical synthesizers, where mode-locked laser based optical frequency comb synthesizers have been widely investigated. These frequency combs bridge the frequencies from optical domain to microwave domain with orders of magnitude difference, providing a metrological tool for various platforms. The demand for highly robust, scalable, compact and cost-effective femtosecond-laser synthesizers, however, are of great importance for applications in air- or space-borne platforms, where low cost and rugged packaging are particularly required. This has been afforded in the past several years due to breakthroughs in chip-scale nanofabrication, bringing advances in optical frequency combs down to semiconductor chips. These platforms, with significantly enhanced light-matter interaction, provide a fertile sandbox for research rich in nonlinear dynamics, and offer a reliable route towards low-phase noise photonic oscillators, broadband optical frequency synthesizers, miniaturized optical clockwork, and coherent terabit communications. The dissertation explores various types of optical frequency comb synthesizers based on nonlinear microresonators. Firstly, the fundamental mechanism of mode-locking in a high-quality factor microresonator is examined, supported by ultrafast optical characterizations, analytical closed-form solutions and numerical modeling. In the evolution of these frequency microcombs, the key nonlinear dynamical effect governing the comb state coherence is rigorously analyzed. Secondly, a prototype of chip-scale optical frequency synthesizer is demonstrated, with the laser frequency comb stabilized down to instrument-limited 50-mHz RF frequency inaccuracies and 10-16 fractional frequency inaccuracies, near the fundamental limits. Thirdly, a globally stable Turing pattern is achieved and characterized in these nonlinear resonators with high-efficiency conversion, subsequently generating coherent high-power terahertz radiation via plasmonic photomixers. Finally, a new universal modality of frequency combs is discussed, including satellite states, dynamical tunability, and high efficiency conversion towards direct chip-scale optical frequency synthesis at the precision metrology frontiers.

Structural Dynamic Analyses And Test Predictions For Spacecraft Structures With Non-Linearities

NASA Astrophysics Data System (ADS)

Vergniaud, Jean-Baptiste; Soula, Laurent; Newerla, Alfred

2012-07-01

The overall objective of the mechanical development and verification process is to ensure that the spacecraft structure is able to sustain the mechanical environments encountered during launch. In general the spacecraft structures are a-priori assumed to behave linear, i.e. the responses to a static load or dynamic excitation, respectively, will increase or decrease proportionally to the amplitude of the load or excitation induced. However, past experiences have shown that various non-linearities might exist in spacecraft structures and the consequences of their dynamic effects can significantly affect the development and verification process. Current processes are mainly adapted to linear spacecraft structure behaviour. No clear rules exist for dealing with major structure non-linearities. They are handled outside the process by individual analysis and margin policy, and analyses after tests to justify the CLA coverage. Non-linearities can primarily affect the current spacecraft development and verification process on two aspects. Prediction of flights loads by launcher/satellite coupled loads analyses (CLA): only linear satellite models are delivered for performing CLA and no well-established rules exist how to properly linearize a model when non- linearities are present. The potential impact of the linearization on the results of the CLA has not yet been properly analyzed. There are thus difficulties to assess that CLA results will cover actual flight levels. Management of satellite verification tests: the CLA results generated with a linear satellite FEM are assumed flight representative. If the internal non- linearities are present in the tested satellite then there might be difficulties to determine which input level must be passed to cover satellite internal loads. The non-linear behaviour can also disturb the shaker control, putting the satellite at risk by potentially imposing too high levels. This paper presents the results of a test campaign performed in the frame of an ESA TRP study [1]. A bread-board including typical non-linearities has been designed, manufactured and tested through a typical spacecraft dynamic test campaign. The study has demonstrate the capabilities to perform non-linear dynamic test predictions on a flight representative spacecraft, the good correlation of test results with respect to Finite Elements Model (FEM) prediction and the possibility to identify modal behaviour and to characterize non-linearities characteristics from test results. As a synthesis for this study, overall guidelines have been derived on the mechanical verification process to improve level of expertise on tests involving spacecraft including non-linearity.

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.

Nonlinear optical properties of organic materials V; Proceedings of the 5th Meeting, San Diego, CA, July 22-24, 1992

NASA Astrophysics Data System (ADS)

Williams, David J.

The present volume on nonlinear optical properties of organic materials discusses organic nonlinear optics, polymers for nonlinear optics, characterization of nonlinear properties, photorefractive and second-order materials, harmonic generation in organic materials, and devices and applications. Particular attention is given to organic semiconductor-doped polymer glasses as novel nonlinear media, heterocyclic nonlinear optical materials, loss measurements in electrooptic polymer waveguides, the phase-matched second-harmonic generation in planar waveguides, electrooptic measurements in poled polymers, transient effects in spatial light modulation by nonlinearity-absorbing molecules, the electrooptic effects in organic single crystals, surface acoustic wave propagation in an organic nonlinear optical crystal, nonlinear optics of astaxanthin thin films; and advanced high-temperature polymers for integrated optical waveguides. (No individual items are abstracted in this volume)

Selector-free resistive switching memory cell based on BiFeO3 nano-island showing high resistance ratio and nonlinearity factor

PubMed Central

Jeon, Ji Hoon; Joo, Ho-Young; Kim, Young-Min; Lee, Duk Hyun; Kim, Jin-Soo; Kim, Yeon Soo; Choi, Taekjib; Park, Bae Ho

2016-01-01

Highly nonlinear bistable current-voltage (I–V) characteristics are necessary in order to realize high density resistive random access memory (ReRAM) devices that are compatible with cross-point stack structures. Up to now, such I–V characteristics have been achieved by introducing complex device structures consisting of selection elements (selectors) and memory elements which are connected in series. In this study, we report bipolar resistive switching (RS) behaviours of nano-crystalline BiFeO3 (BFO) nano-islands grown on Nb-doped SrTiO3 substrates, with large ON/OFF ratio of 4,420. In addition, the BFO nano-islands exhibit asymmetric I–V characteristics with high nonlinearity factor of 1,100 in a low resistance state. Such selector-free RS behaviours are enabled by the mosaic structures and pinned downward ferroelectric polarization in the BFO nano-islands. The high resistance ratio and nonlinearity factor suggest that our BFO nano-islands can be extended to an N × N array of N = 3,740 corresponding to ~107 bits. Therefore, our BFO nano-island showing both high resistance ratio and nonlinearity factor offers a simple and promising building block of high density ReRAM. PMID:27001415

Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.

ERIC Educational Resources Information Center

Raw, Cecil J. G.; Stacey, Larry M.

1989-01-01

Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…

Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations

NASA Astrophysics Data System (ADS)

Demina, Maria V.; Kudryashov, Nikolay A.

2011-03-01

Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational, periodic, elliptic) are found for a wide class of autonomous nonlinear ordinary differential equations.

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.

Four wave mixing as a probe of the vacuum

NASA Astrophysics Data System (ADS)

Tennant, Daniel M.

2016-06-01

Much attention has been paid to the quantum structure of the vacuum. Higher order processes in quantum electrodynamics are strongly believed to cause polarization and even breakdown of the vacuum in the presence of strong fields soon to be accessible in high intensity laser experiments. Less explored consequences of strong field electrodynamics include effects from Born-Infeld type of electromagnetic theories, a nonlinear electrodynamics that follows from classical considerations as opposed to coupling to virtual fluctuations. In this article, I will demonstrate how vacuum four wave mixing has the possibility to differentiate between these two types of vacuum responses: quantum effects on one hand and nonlinear classical extensions on the other.

Full potential methods for analysis/design of complex aerospace configurations

NASA Technical Reports Server (NTRS)

Shankar, Vijaya; Szema, Kuo-Yen; Bonner, Ellwood

1986-01-01

The steady form of the full potential equation, in conservative form, is employed to analyze and design a wide variety of complex aerodynamic shapes. The nonlinear method is based on the theory of characteristic signal propagation coupled with novel flux biasing concepts and body-fitted mapping procedures. The resulting codes are vectorized for the CRAY XMP and the VPS-32 supercomputers. Use of the full potential nonlinear theory is demonstrated for a single-point supersonic wing design and a multipoint design for transonic maneuver/supersonic cruise/maneuver conditions. Achievement of high aerodynamic efficiency through numerical design is verified by wind tunnel tests. Other studies reported include analyses of a canard/wing/nacelle fighter geometry.

Direct modeling parameter signature analysis and failure mode prediction of physical systems using hybrid computer optimization

NASA Technical Reports Server (NTRS)

Drake, R. L.; Duvoisin, P. F.; Asthana, A.; Mather, T. W.

1971-01-01

High speed automated identification and design of dynamic systems, both linear and nonlinear, are discussed. Special emphasis is placed on developing hardware and techniques which are applicable to practical problems. The basic modeling experiment and new results are described. Using the improvements developed successful identification of several systems, including a physical example as well as simulated systems, was obtained. The advantages of parameter signature analysis over signal signature analysis in go-no go testing of operational systems were demonstrated. The feasibility of using these ideas in failure mode prediction in operating systems was also investigated. An improved digital controlled nonlinear function generator was developed, de-bugged, and completely documented.

Finite element modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, A. K.; Andersen, C. M.

1983-01-01

Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

Automatic control: the vertebral column of dogfish sharks behaves as a continuously variable transmission with smoothly shifting functions.

PubMed

Porter, Marianne E; Ewoldt, Randy H; Long, John H

2016-09-15

During swimming in dogfish sharks, Squalus acanthias, both the intervertebral joints and the vertebral centra undergo significant strain. To investigate this system, unique among vertebrates, we cyclically bent isolated segments of 10 vertebrae and nine joints. For the first time in the biomechanics of fish vertebral columns, we simultaneously characterized non-linear elasticity and viscosity throughout the bending oscillation, extending recently proposed techniques for large-amplitude oscillatory shear (LAOS) characterization to large-amplitude oscillatory bending (LAOB). The vertebral column segments behave as non-linear viscoelastic springs. Elastic properties dominate for all frequencies and curvatures tested, increasing as either variable increases. Non-linearities within a bending cycle are most in evidence at the highest frequency, 2.0 Hz, and curvature, 5 m -1 Viscous bending properties are greatest at low frequencies and high curvatures, with non-linear effects occurring at all frequencies and curvatures. The range of mechanical behaviors includes that of springs and brakes, with smooth transitions between them that allow for continuously variable power transmission by the vertebral column to assist in the mechanics of undulatory propulsion. © 2016. Published by The Company of Biologists Ltd.

Second harmonic generation by self-focusing of intense hollow Gaussian laser beam in collisionless plasma

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

Purohit, Gunjan, E-mail: gunjan75@gmail.com; Rawat, Priyanka; Gauniyal, Rakhi

2016-01-15

The effect of self focused hollow Gaussian laser beam (HGLB) (carrying null intensity in center) on the excitation of electron plasma wave (EPW) and second harmonic generation (SHG) has been investigated in collisionless plasma, where relativistic-ponderomotive and only relativistic nonlinearities are operative. The relativistic change of electron mass and the modification of the background electron density due to ponderomotive nonlinearity lead to self-focusing of HGLB in plasma. Paraxial ray theory has been used to derive coupled equations for the self focusing of HGLB in plasma, generation of EPW, and second harmonic. These coupled equations are solved analytically and numerically tomore » study the laser intensity in the plasma, electric field associated with the excited EPW, and the power of SHG. Second harmonic emission is generated due to nonlinear coupling between incident HGLB and EPW satisfying the proper phase matching conditions. The results show that the effect of including the ponderomotive nonlinearity is significant on the generation of EPW and second harmonic. The electric field associated with EPW and the power of SHG are found to be highly sensitive to the order of the hollow Gaussian beam.« less

Simulation of ion-temperature-gradient turbulence in tokamaks

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

Cohen, B I; Dimits, A M; Kim, C

Results are presented from nonlinear gyrokinetic simulations of toroidal ion temperature gradient (ITG) turbulence and transport. The gyrokinetic simulations are found to yield values of the thermal diffusivity significantly lower than gyrofluid or IFS-PPPL-model predictions. A new phenomenon of nonlinear effective critical gradients larger than the linear instability threshold gradients is observed, and is associated with undamped flux-surface-averaged shear flows. The nonlinear gyrokineic codes have passed extensive validity tests which include comparison against independent linear calculations, a series of nonlinear convergence tests, and a comparison between two independent nonlinear gyrokinetic codes. Our most realistic simulations to date have actual reconstructedmore » equilibria from experiments and a model for dilution by impurity and beam ions. These simulations highlight the need for still more physics to be included in the simulations« less

Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Wu, Xinyuan

2017-07-01

In this paper we explore arbitrarily high-order Lagrange collocation-type time-stepping schemes for effectively solving high-dimensional nonlinear Klein-Gordon equations with different boundary conditions. We begin with one-dimensional periodic boundary problems and first formulate an abstract ordinary differential equation (ODE) on a suitable infinity-dimensional function space based on the operator spectrum theory. We then introduce an operator-variation-of-constants formula which is essential for the derivation of our arbitrarily high-order Lagrange collocation-type time-stepping schemes for the nonlinear abstract ODE. The nonlinear stability and convergence are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix under some suitable smoothness assumptions. With regard to the two dimensional Dirichlet or Neumann boundary problems, our new time-stepping schemes coupled with discrete Fast Sine / Cosine Transformation can be applied to simulate the two-dimensional nonlinear Klein-Gordon equations effectively. All essential features of the methodology are present in one-dimensional and two-dimensional cases, although the schemes to be analysed lend themselves with equal to higher-dimensional case. The numerical simulation is implemented and the numerical results clearly demonstrate the advantage and effectiveness of our new schemes in comparison with the existing numerical methods for solving nonlinear Klein-Gordon equations in the literature.

Investigation of broadband terahertz generation from metasurface

NASA Astrophysics Data System (ADS)

Fang, Ming; Niu, Kaikun; Huang, Zhiaxiang; Sha, Wei E. I.; Wu, Xianliang; Koschny, Thomas; Soukoulis, Costas M.

2018-05-01

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designing nonlinear plasmonic metamaterials.

Investigation of broadband terahertz generation from metasurface.

PubMed

Fang, Ming; Niu, Kaikun; Huang, Zhiaxiang; Sha, Wei E I; Wu, Xianliang; Koschny, Thomas; Soukoulis, Costas M

2018-05-28

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designing nonlinear plasmonic metamaterials.

Computational aspects in high intensity ultrasonic surgery planning.

PubMed

Pulkkinen, A; Hynynen, K

2010-01-01

Therapeutic ultrasound treatment planning is discussed and computational aspects regarding it are reviewed. Nonlinear ultrasound simulations were solved with a combined frequency domain Rayleigh and KZK model. Ultrasonic simulations were combined with thermal simulations and were used to compute heating of muscle tissue in vivo for four different focused ultrasound transducers. The simulations were compared with measurements and good agreement was found for large F-number transducers. However, at F# 1.9 the simulated rate of temperature rise was approximately a factor of 2 higher than the measured ones. The power levels used with the F# 1 transducer were too low to show any nonlinearity. The simulations were used to investigate the importance of nonlinarities generated in the coupling water, and also the importance of including skin in the simulations. Ignoring either of these in the model would lead to larger errors. Most notably, the nonlinearities generated in the water can enhance the focal temperature by more than 100%. The simulations also demonstrated that pulsed high power sonications may provide an opportunity to significantly (up to a factor of 3) reduce the treatment time. In conclusion, nonlinear propagation can play an important role in shaping the energy distribution during a focused ultrasound treatment and it should not be ignored in planning. However, the current simulation methods are accurate only with relatively large F-numbers and better models need to be developed for sharply focused transducers. Copyright 2009 Elsevier Ltd. All rights reserved.

A Reconfiguration Scheme for Accommodating Actuator Failures in Multi-Input, Multi-Output Flight Control Systems

NASA Technical Reports Server (NTRS)

Siwakosit, W.; Hess, R. A.; Bacon, Bart (Technical Monitor); Burken, John (Technical Monitor)

2000-01-01

A multi-input, multi-output reconfigurable flight control system design utilizing a robust controller and an adaptive filter is presented. The robust control design consists of a reduced-order, linear dynamic inversion controller with an outer-loop compensation matrix derived from Quantitative Feedback Theory (QFT). A principle feature of the scheme is placement of the adaptive filter in series with the QFT compensator thus exploiting the inherent robustness of the nominal flight control system in the presence of plant uncertainties. An example of the scheme is presented in a pilot-in-the-loop computer simulation using a simplified model of the lateral-directional dynamics of the NASA F18 High Angle of Attack Research Vehicle (HARV) that included nonlinear anti-wind up logic and actuator limitations. Prediction of handling qualities and pilot-induced oscillation tendencies in the presence of these nonlinearities is included in the example.

Stable diffraction-management soliton in a periodic structure with alternating left-handed and right-handed media

NASA Astrophysics Data System (ADS)

Zhang, Jinggui

2017-09-01

In this paper, we first derive a modified two-dimensional non-linear Schrödinger equation including high-order diffraction (HOD) suitable for the propagation of optical beam near the low-diffraction regime in Kerr non-linear media with spatial dispersion. Then, we apply our derived physical model to a designed two-dimensional configuration filled with alternate layers of a left-handed material (LHM) and a right-handed media by employing the mean-field theory. It is found that the periodic structure including LHM may experience diminished, cancelled, and even reversed diffraction behaviours through engineering the relative thickness between both media. In particular, the variational method analytically predicts that close to the zero-diffraction regime, such periodic structure can support stable diffraction-management solitons whose beamwidth and peak amplitude evolve periodically with the help of HOD effect. Numerical simulation based on the split-step Fourier method confirms the analytical results.

Gain scheduled linear quadratic control for quadcopter

NASA Astrophysics Data System (ADS)

Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.

2017-12-01

This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.

Combined feedforward and feedback control of a redundant, nonlinear, dynamic musculoskeletal system.

PubMed

Blana, Dimitra; Kirsch, Robert F; Chadwick, Edward K

2009-05-01

A functional electrical stimulation controller is presented that uses a combination of feedforward and feedback for arm control in high-level injury. The feedforward controller generates the muscle activations nominally required for desired movements, and the feedback controller corrects for errors caused by muscle fatigue and external disturbances. The feedforward controller is an artificial neural network (ANN) which approximates the inverse dynamics of the arm. The feedback loop includes a PID controller in series with a second ANN representing the nonlinear properties and biomechanical interactions of muscles and joints. The controller was designed and tested using a two-joint musculoskeletal model of the arm that includes four mono-articular and two bi-articular muscles. Its performance during goal-oriented movements of varying amplitudes and durations showed a tracking error of less than 4 degrees in ideal conditions, and less than 10 degrees even in the case of considerable fatigue and external disturbances.

Nonlinear synthesis of infrasound propagation through an inhomogeneous, absorbing atmosphere.

PubMed

de Groot-Hedlin, C D

2012-08-01

An accurate and efficient method to predict infrasound amplitudes from large explosions in the atmosphere is required for diverse source types, including bolides, volcanic eruptions, and nuclear and chemical explosions. A finite-difference, time-domain approach is developed to solve a set of nonlinear fluid dynamic equations for total pressure, temperature, and density fields rather than acoustic perturbations. Three key features for the purpose of synthesizing nonlinear infrasound propagation in realistic media are that it includes gravitational terms, it allows for acoustic absorption, including molecular vibration losses at frequencies well below the molecular vibration frequencies, and the environmental models are constrained to have axial symmetry, allowing a three-dimensional simulation to be reduced to two dimensions. Numerical experiments are performed to assess the algorithm's accuracy and the effect of source amplitudes and atmospheric variability on infrasound waveforms and shock formation. Results show that infrasound waveforms steepen and their associated spectra are shifted to higher frequencies for nonlinear sources, leading to enhanced infrasound attenuation. Results also indicate that nonlinear infrasound amplitudes depend strongly on atmospheric temperature and pressure variations. The solution for total field variables and insertion of gravitational terms also allows for the computation of other disturbances generated by explosions, including gravity waves.

Nonlinear acoustics in biomedical ultrasound

NASA Astrophysics Data System (ADS)

Cleveland, Robin O.

2015-10-01

Ultrasound is widely used to image inside the body; it is also used therapeutically to treat certain medical conditions. In both imaging and therapy applications the amplitudes employed in biomedical ultrasound are often high enough that nonlinear acoustic effects are present in the propagation: the effects have the potential to be advantageous in some scenarios but a hindrance in others. In the case of ultrasound imaging the nonlinearity produces higher harmonics that result in images of greater quality. However, nonlinear effects interfere with the imaging of ultrasound contrast agents (typically micron sized bubbles with a strong nonlinear response of their own) and nonlinear effects also result in complications when derating of pressure measurements in water to in situ values in tissue. High intensity focused ultrasound (HIFU) is emerging as a non-invasive therapeutic modality which can result in thermal ablation of tissue. For thermal ablation, the extra effective attenuation resulting from nonlinear effects can result in enhanced heating of tissue if shock formation occurs in the target region for ablation - a highly desirable effect. However, if nonlinearity is too strong it can also result in undesired near-field heating and reduced ablation in the target region. The disruption of tissue (histotripsy) and fragmentation of kidney stones (lithotripsy) exploits shock waves to produce mechanically based effects, with minimal heating present. In these scenarios it is necessary for the waves to be of sufficient amplitude that a shock exists when the waveform reaches the target region. This talk will discuss how underlying nonlinear phenomenon act in all the diagnostic and therapeutic applications described above.

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Application of an Ensemble Smoother to Precipitation Assimilation

NASA Technical Reports Server (NTRS)

Zhang, Sara; Zupanski, Dusanka; Hou, Arthur; Zupanski, Milija

2008-01-01

Assimilation of precipitation in a global modeling system poses a special challenge in that the observation operators for precipitation processes are highly nonlinear. In the variational approach, substantial development work and model simplifications are required to include precipitation-related physical processes in the tangent linear model and its adjoint. An ensemble based data assimilation algorithm "Maximum Likelihood Ensemble Smoother (MLES)" has been developed to explore the ensemble representation of the precipitation observation operator with nonlinear convection and large-scale moist physics. An ensemble assimilation system based on the NASA GEOS-5 GCM has been constructed to assimilate satellite precipitation data within the MLES framework. The configuration of the smoother takes the time dimension into account for the relationship between state variables and observable rainfall. The full nonlinear forward model ensembles are used to represent components involving the observation operator and its transpose. Several assimilation experiments using satellite precipitation observations have been carried out to investigate the effectiveness of the ensemble representation of the nonlinear observation operator and the data impact of assimilating rain retrievals from the TMI and SSM/I sensors. Preliminary results show that this ensemble assimilation approach is capable of extracting information from nonlinear observations to improve the analysis and forecast if ensemble size is adequate, and a suitable localization scheme is applied. In addition to a dynamically consistent precipitation analysis, the assimilation system produces a statistical estimate of the analysis uncertainty.

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse

NASA Astrophysics Data System (ADS)

Grishkov, V. E.; Uryupin, S. A.

2017-03-01

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron-ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse

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

Grishkov, V. E.; Uryupin, S. A., E-mail: uryupin@sci.lebedev.ru

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron–ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.

Energy and Transmissibility in Nonlinear Viscous Base Isolators

NASA Astrophysics Data System (ADS)

Markou, Athanasios A.; Manolis, George D.

2016-09-01

High damping rubber bearings (HDRB) are the most commonly used base isolators in buildings and are often combined with other systems, such as sliding bearings. Their mechanical behaviour is highly nonlinear and dependent on a number of factors. At first, a physical process is suggested here to explain the empirical formula introduced by J.M. Kelly in 1991, where the dissipated energy of a HDRB under cyclic testing, at constant frequency, is proportional to the amplitude of the shear strain, raised to a power of approximately 1.50. This physical process is best described by non-Newtonian fluid behaviour, originally developed by F.H. Norton in 1929 to describe creep in steel at high-temperatures. The constitutive model used includes a viscous term, that depends on the absolute value of the velocity, raised to a non-integer power. The identification of a three parameter Kelvin model, the simplest possible system with nonlinear viscosity, is also suggested here. Furthermore, a more advanced model with variable damping coefficient is implemented to better model in this complex mechanical process. Next, the assumption of strain-rate dependence in their rubber layers under cyclic loading is examined in order to best interpret experimental results on the transmission of motion between the upper and lower surfaces of HDRB. More specifically, the stress-relaxation phenomenon observed with time in HRDB can be reproduced numerically, only if the constitutive model includes a viscous term, that depends on the absolute value of the velocity raised to a non-integer power, i. e., the Norton fluid previously mentioned. Thus, it becomes possible to compute the displacement transmissibility function between the top and bottom surfaces of HDRB base isolator systems and to draw engineering-type conclusions, relevant to their design under time-harmonic loads.

Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model

NASA Astrophysics Data System (ADS)

Ngai, K. L.

2015-03-01

Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ1(f), the frequency dispersion of the third-order dielectric susceptibility, χ3(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ1(f) and χ3(f) is the characteristic of the many-body relaxation dynamics of interacting systems which are governed solely by the intermolecular potential, and thermodynamic condition plays no role in this respect. Although linked to χ3(f), dynamic heterogeneity is one of the parallel consequences of the many-body dynamics, and it should not be considered as the principal control parameter for the other dynamic properties of glassforming systems. Results same as χ3(f) at elevated pressures had been obtained before by molecular dynamics simulations from the four-points correlation function and the intermediate scattering function. Naturally all properties obtained from the computer experiment, including dynamics heterogeneity, frequency dispersion, the relation between the α- and JG β-relaxation, and the breakdown of the Stokes-Einstein relation, are parallel consequences of the many-body relaxation dynamics governed by the intermolecular potential.

Dynamics and control of quadcopter using linear model predictive control approach

NASA Astrophysics Data System (ADS)

Islam, M.; Okasha, M.; Idres, M. M.

2017-12-01

This paper investigates the dynamics and control of a quadcopter using the Model Predictive Control (MPC) approach. The dynamic model is of high fidelity and nonlinear, with six degrees of freedom that include disturbances and model uncertainties. The control approach is developed based on MPC to track different reference trajectories ranging from simple ones such as circular to complex helical trajectories. In this control technique, a linearized model is derived and the receding horizon method is applied to generate the optimal control sequence. Although MPC is computer expensive, it is highly effective to deal with the different types of nonlinearities and constraints such as actuators’ saturation and model uncertainties. The MPC parameters (control and prediction horizons) are selected by trial-and-error approach. Several simulation scenarios are performed to examine and evaluate the performance of the proposed control approach using MATLAB and Simulink environment. Simulation results show that this control approach is highly effective to track a given reference trajectory.

Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.

PubMed

Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang

2016-10-31

Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.

NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

NASA Astrophysics Data System (ADS)

Caplan, R. M.

2013-04-01

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files. Catalogue identifier: AEOJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOJ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 124453 No. of bytes in distributed program, including test data, etc.: 4728604 Distribution format: tar.gz Programming language: C, CUDA, MATLAB. Computer: PC, MAC. Operating system: Windows, MacOS, Linux. Has the code been vectorized or parallelized?: Yes. Number of processors used: Single CPU, number of GPU processors dependent on chosen GPU card (max is currently 3072 cores on GeForce GTX 690). Supplementary material: Setup guide, Installation guide. RAM: Highly dependent on dimensionality and grid size. For typical medium-large problem size in three dimensions, 4GB is sufficient. Keywords: Nonlinear Schröodinger Equation, GPU, high-order finite difference, Bose-Einstien condensates. Classification: 4.3, 7.7. Nature of problem: Integrate solutions of the time-dependent one-, two-, and three-dimensional cubic nonlinear Schrödinger equation. Solution method: The integrators utilize a fully-explicit fourth-order Runge-Kutta scheme in time and both second- and fourth-order differencing in space. The integrators are written to run on NVIDIA GPUs and are interfaced with MATLAB including built-in visualization and analysis tools. Restrictions: The main restriction for the GPU integrators is the amount of RAM on the GPU as the code is currently only designed for running on a single GPU. Unusual features: Ability to visualize real-time simulations through the interaction of MATLAB and the compiled GPU integrators. Additional comments: Setup guide and Installation guide provided. Program has a dedicated web site at www.nlsemagic.com. Running time: A three-dimensional run with a grid dimension of 87×87×203 for 3360 time steps (100 non-dimensional time units) takes about one and a half minutes on a GeForce GTX 580 GPU card.

Proposal of ultra-compact NAND/NOR/XNOR all-optical logic gates based on a nonlinear 3x1 multimode interference

NASA Astrophysics Data System (ADS)

Tajaldini, Mehdi; Mat Jafri, M. Z.

2014-05-01

We present a highly miniaturized multimode interference (MMI) coupler based on nonlinear modal propagation analysis (NMPA) method as a novel design method and potential application for optical NAND, NOR and XNOR logic gates for Boolean logic signal processing devices. Crystalline polydiacetylene is used to allow the appearances of nonlinear effects in low input intensities and ultra- short length to control the MMI coupler as an active device to access light switching due to its high nonlinear susceptibility. We consider a 10x33 μm2 MMI structure with three inputs and one output. Notably, the access facets are single-mode waveguides with sub-micron width. The center input contributes to control the induced light propagation in MMI by intensity variation whereas others could be launched by particular intensity when they are ON and 0 in OFF. Output intensity is analyzed in various sets of inputs to show the capability of Boolean logic gates, the contrast between ON and OFF is calculated on mentioned gates to present the efficiency. Good operation in low intensity and highly miniaturized MMI coupler is observed. Furthermore, nonlinear effects could be realized through the modal interferences. The issue of high insertion loss is addressed with a 3×3 upgraded coupler. Furthermore, the main significant aspect of this paper is simulating an MMI coupler that is launched by three nonlinear inputs, simultaneously, whereas last presents have never studied more than one input in nonlinear regimes.

Nonlinear Hysteretic Torsional Waves

NASA Astrophysics Data System (ADS)

Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.

2015-07-01

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

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

Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg; Zhou, Yu

2016-07-15

Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonantmore » frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.« less

Nonlinear dynamic response of a uni-directional model for the tile/pad space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1980-01-01

A unidirectional analysis of the nonlinear dynamic behavior of the space shuttle tile/pad thermal protection system is developed and examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. The analysis accounts for the highly nonlinear stiffening hysteresis and viscous behavior of the pad which joins the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude. Analytical studies indicate that with still higher amplitude the resonant frequency increases slowly. The nonlinear pad is also responsible for the analytically and experimentally observed distorted response wave shapes having high sharp peaks when the system is subject to sinusoidal loads. Furthermore, energy dissipation in the pad is studied analytically and it is found that the energy dissipated is sufficiently high to cause rapid decay of dynamic transients. Nevertheless, the sharp peaked nonlinear responses of the system lead to higher magnification factors than would be expected in such a highly damped linear system.

Modified Cheeger and Ratio Cut Methods Using the Ginzburg-Landau Functional for Classification of High-Dimensional Data

DTIC Science & Technology

2016-02-01

Modified Cheeger and Ratio Cut Methods Using the Ginzburg-Landau Functional for Classification of High-Dimensional Data Ekaterina Merkurjev*, Andrea...bertozzi@math.ucla.edu, xiaoran@isi.edu, lerman@isi.edu. Abstract Recent advances in clustering have included continuous relaxations of the Cheeger cut ...fully nonlinear Cheeger cut problem, as well as the ratio cut optimization task. Both problems are connected to total variation minimization, and the

Development of solution techniques for nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Vos, R. G.; Andrews, J. S.

1974-01-01

Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

Absorbing Boundary Conditions For Optical Pulses In Dispersive, Nonlinear Materials

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that provides absorbing boundary conditions for optical pulses in dispersive, nonlinear materials. A new numerical absorber at the boundaries has been developed that is responsive to the spectral content of the pulse. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of "light bullet" like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. Comparisons will be shown of calculations that use the standard boundary conditions and the new ones.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Non-linear optics of ultrastrongly coupled cavity polaritons

NASA Astrophysics Data System (ADS)

Crescimanno, Michael; Liu, Bin; McMaster, Michael; Singer, Kenneth

2016-05-01

Experiments at CWRU have developed organic cavity polaritons that display world-record vacuum Rabi splittings of more than an eV. This ultrastrongly coupled polaritonic matter is a new regime for exploring non-linear optical effects. We apply quantum optics theory to quantitatively determine various non-linear optical effects including types of low harmonic generation (SHG and THG) in single and double cavity polariton systems. Ultrastrongly coupled photon-matter systems such as these may be the foundation for technologies including low-power optical switching and computing.

Computational homogenisation for thermoviscoplasticity: application to thermally sprayed coatings

NASA Astrophysics Data System (ADS)

Berthelsen, Rolf; Denzer, Ralf; Oppermann, Philip; Menzel, Andreas

2017-11-01

Metal forming processes require wear-resistant tool surfaces in order to ensure a long life cycle of the expensive tools together with a constant high quality of the produced components. Thermal spraying is a relatively widely applied coating technique for the deposit of wear protection coatings. During these coating processes, heterogeneous coatings are deployed at high temperatures followed by quenching where residual stresses occur which strongly influence the performance of the coated tools. The objective of this article is to discuss and apply a thermo-mechanically coupled simulation framework which captures the heterogeneity of the deposited coating material. Therefore, a two-scale finite element framework for the solution of nonlinear thermo-mechanically coupled problems is elaborated and applied to the simulation of thermoviscoplastic material behaviour including nonlinear thermal softening in a geometrically linearised setting. The finite element framework and material model is demonstrated by means of numerical examples.

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; ...

2016-05-25

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility ofmore » PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.« less

A novel method to produce nonlinear empirical physical formulas for experimental nonlinear electro-optical responses of doped nematic liquid crystals: Feedforward neural network approach

NASA Astrophysics Data System (ADS)

Yildiz, Nihat; San, Sait Eren; Okutan, Mustafa; Kaya, Hüseyin

2010-04-01

Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.

Method and apparatus of highly linear optical modulation

DOEpatents

DeRose, Christopher; Watts, Michael R.

2016-05-03

In a new optical intensity modulator, a nonlinear change in refractive index is used to balance the nonlinearities in the optical transfer function in a way that leads to highly linear optical intensity modulation.

Finite difference time domain calculation of transients in antennas with nonlinear loads

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent

1991-01-01

In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Efficient, nonlinear phase estimation with the nonmodulated pyramid wavefront sensor.

PubMed

Frazin, Richard A

2018-04-01

The sensitivity of the pyramid wavefront sensor (PyWFS) has made it a popular choice for astronomical adaptive optics (AAO) systems. The PyWFS is at its most sensitive when it is used without modulation of the input beam. In nonmodulated mode, the device is highly nonlinear. Hence, all PyWFS implementations on current AAO systems employ modulation to make the device more linear. The upcoming era of 30-m class telescopes and the demand for ultra-precise wavefront control stemming from science objectives that include direct imaging of exoplanets make using the PyWFS without modulation desirable. This article argues that nonlinear estimation based on Newton's method for nonlinear optimization can be useful for mitigating the effects of nonlinearity in the nonmodulated PyWFS. The proposed approach requires all optical modeling to be pre-computed, which has the advantage of avoiding real-time simulations of beam propagation. Further, the required real-time calculations are amenable to massively parallel computation. Numerical experiments simulate a PyWFS with faces sloped 3.7° to the horizontal, operating at a wavelength of 0.85 μm, and with an index of refraction of 1.45. A singular value analysis shows that the common practice of calculating two "slope" images from the four PyWFS pupil images discards critical information and is unsuitable for the nonmodulated PyWFS simulated here. Instead, this article advocates estimators that use the raw pixel values not only from the four geometrical images of the pupil, but from surrounding pixels as well. The simulations indicate that nonlinear estimation can be effective when the Strehl ratio of the input beam is greater than 0.3, and the improvement relative to linear estimation tends to increase at larger Strehl ratios. At Strehl ratios less than about 0.5, the performances of both the nonlinear and linear estimators are relatively insensitive to noise since they are dominated by nonlinearity error.

Nonlinear dynamics of the human lumbar intervertebral disc.

PubMed

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J

2015-02-05

Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. Copyright © 2014 Elsevier Ltd. All rights reserved.

Advanced Ultrafast Spectroscopy for Chemical Detection of Nuclear Fuel Cycle Materials

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

Villa-Aleman, E.; Houk, A.; Spencer, W.

The development of new signatures and observables from processes related to proliferation activities are often related to the development of technologies. In our physical world, the intensity of observables is linearly related to the input drivers (light, current, voltage, etc.). Ultrafast lasers with high peak energies, opens the door to a new regime where the intensity of the observables is not necessarily linear with the laser energy. Potential nonlinear spectroscopic applications include chemical detection via remote sensing through filament generation, material characterization and processing, chemical reaction specificity, surface phenomena modifications, X-ray production, nuclear fusion, etc. The National Security Directorate lasermore » laboratory is currently working to develop new tools for nonproliferation research with femtosecond and picosecond lasers. Prior to this project, we could only achieve laser energies in the 5 nano-Joule range, preventing the study of nonlinear phenomena. To advance our nonproliferation research into the nonlinear regime we require laser pulses in the milli-Joule (mJ) energy range. We have procured and installed a 35 fs-7 mJ laser, operating at one-kilohertz repetition rate, to investigate elemental and molecular detection of materials in the laboratory with potential applications in remote sensing. Advanced, nonlinear Raman techniques will be used to study materials of interest that are in a matrix of many materials and currently with these nonlinear techniques we can achieve greater than three orders of magnitude signal enhancement. This work studying nuclear fuel cycle materials with nonlinear spectroscopies will advance SRNL research capabilities and grow a core capability within the DOE complex.« less

Investigation on the Nonlinear Control System of High-Pressure Common Rail (HPCR) System in a Diesel Engine

NASA Astrophysics Data System (ADS)

Cai, Le; Mao, Xiaobing; Ma, Zhexuan

2018-02-01

This study first constructed the nonlinear mathematical model of the high-pressure common rail (HPCR) system in the diesel engine. Then, the nonlinear state transformation was performed using the flow’s calculation and the standard state space equation was acquired. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrate that sliding-mode variable structure control algorithm shows favorable control performances and overcome the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.

Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: ultrawide bandwidth optical limiting.

PubMed

Scalora, Michael; Mattiucci, Nadia; D'Aguanno, Giuseppe; Larciprete, MariaCristina; Bloemer, Mark J

2006-01-01

We numerically study the nonlinear optical properties of metal-dielectric photonic band gap structures in the pulsed regime. We exploit the high chi3 of copper metal to induce nonlinear effects such as broadband optical limiting, self-phase modulation, and unusual spectral narrowing of high intensity pulses. We show that in a single pass through a typical, chirped multilayer stack nonlinear transmittance and peak powers can be reduced by nearly two orders of magnitude compared to low light intensity levels across the entire visible range. Chirping dielectric layer thickness dramatically improves the linear transmittance through the stack and achieves large fields inside the copper to access the large nonlinearity. At the same time, the linear properties of the stack block most of the remaining electromagnetic spectrum.

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

Non-linear dynamic compensation system

NASA Technical Reports Server (NTRS)

Lin, Yu-Hwan (Inventor); Lurie, Boris J. (Inventor)

1992-01-01

A non-linear dynamic compensation subsystem is added in the feedback loop of a high precision optical mirror positioning control system to smoothly alter the control system response bandwidth from a relatively wide response bandwidth optimized for speed of control system response to a bandwidth sufficiently narrow to reduce position errors resulting from the quantization noise inherent in the inductosyn used to measure mirror position. The non-linear dynamic compensation system includes a limiter for limiting the error signal within preselected limits, a compensator for modifying the limiter output to achieve the reduced bandwidth response, and an adder for combining the modified error signal with the difference between the limited and unlimited error signals. The adder output is applied to control system motor so that the system response is optimized for accuracy when the error signal is within the preselected limits, optimized for speed of response when the error signal is substantially beyond the preselected limits and smoothly varied therebetween as the error signal approaches the preselected limits.

Mapping nonlinear receptive field structure in primate retina at single cone resolution

PubMed Central

Li, Peter H; Greschner, Martin; Gunning, Deborah E; Mathieson, Keith; Sher, Alexander; Litke, Alan M; Paninski, Liam

2015-01-01

The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits. DOI: http://dx.doi.org/10.7554/eLife.05241.001 PMID:26517879

Measuring Ultrasonic Backscatter in the Presence of Nonlinear Propagation

NASA Astrophysics Data System (ADS)

Stiles, Timothy; Guerrero, Quinton

2011-11-01

A goal of medical ultrasound is the formation of quantitative ultrasound images in which contrast is determined by acoustic or physical properties of tissue rather than relative echo amplitude. Such images could greatly enhance early detection of many diseases, including breast cancer and liver cirrhosis. Accurate determination of the ultrasonic backscatter coefficient from patients remains a difficult task. One reason for this difficulty is the inherent nonlinear propagation of ultrasound at high intensities used for medical imaging. The backscatter coefficient from several tissue-mimicking samples were measured using the planar reflector method. In this method, the power spectrum from a sample is compared to the power spectrum of an optically flat sample of quartz. The results should be independent of incident pressure amplitude. Results demonstrate that backscatter coefficients can vary by more than an order of magnitude when ultrasound pressure varies from 0.1 MPa to 1.5 MPa at 5.0 MHz. A new method that incorporates nonlinear propagation is proposed to explain these discrepancies.

Gender classification of running subjects using full-body kinematics

NASA Astrophysics Data System (ADS)

Williams, Christina M.; Flora, Jeffrey B.; Iftekharuddin, Khan M.

2016-05-01

This paper proposes novel automated gender classification of subjects while engaged in running activity. The machine learning techniques include preprocessing steps using principal component analysis followed by classification with linear discriminant analysis, and nonlinear support vector machines, and decision-stump with AdaBoost. The dataset consists of 49 subjects (25 males, 24 females, 2 trials each) all equipped with approximately 80 retroreflective markers. The trials are reflective of the subject's entire body moving unrestrained through a capture volume at a self-selected running speed, thus producing highly realistic data. The classification accuracy using leave-one-out cross validation for the 49 subjects is improved from 66.33% using linear discriminant analysis to 86.74% using the nonlinear support vector machine. Results are further improved to 87.76% by means of implementing a nonlinear decision stump with AdaBoost classifier. The experimental findings suggest that the linear classification approaches are inadequate in classifying gender for a large dataset with subjects running in a moderately uninhibited environment.

Self-consistent projection operator theory in nonlinear quantum optical systems: A case study on degenerate optical parametric oscillators

NASA Astrophysics Data System (ADS)

Degenfeld-Schonburg, Peter; Navarrete-Benlloch, Carlos; Hartmann, Michael J.

2015-05-01

Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. We apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with a high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.

Nonlinear filtering techniques for noisy geophysical data: Using big data to predict the future

NASA Astrophysics Data System (ADS)

Moore, J. M.

2014-12-01

Chaos is ubiquitous in physical systems. Within the Earth sciences it is readily evident in seismology, groundwater flows and drilling data. Models and workflows have been applied successfully to understand and even to predict chaotic systems in other scientific fields, including electrical engineering, neurology and oceanography. Unfortunately, the high levels of noise characteristic of our planet's chaotic processes often render these frameworks ineffective. This contribution presents techniques for the reduction of noise associated with measurements of nonlinear systems. Our ultimate aim is to develop data assimilation techniques for forward models that describe chaotic observations, such as episodic tremor and slip (ETS) events in fault zones. A series of nonlinear filters are presented and evaluated using classical chaotic systems. To investigate whether the filters can successfully mitigate the effect of noise typical of Earth science, they are applied to sunspot data. The filtered data can be used successfully to forecast sunspot evolution for up to eight years (see figure).

The linear -- non-linear frontier for the Goldstone Higgs

DOE PAGES

Gavela, M. B.; Kanshin, K.; Machado, P. A. N.; ...

2016-12-01

The minimalmore » $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $$\\sigma$$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.« less

Frequency-domain nonlinear optics in two-dimensionally patterned quasi-phase-matching media.

PubMed

Phillips, C R; Mayer, B W; Gallmann, L; Keller, U

2016-07-11

Advances in the amplification and manipulation of ultrashort laser pulses have led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping via modulation of spatially-dispersed laser pulses, and efficient frequency-mixing in quasi-phase-matched nonlinear crystals to access new spectral regions. In this work, we introduce and demonstrate a new platform for nonlinear optics which has the potential to combine these separate functionalities (pulse amplification, frequency transfer, and pulse shaping) into a single monolithic device that is bandwidth- and power-scalable. The approach is based on two-dimensional (2D) patterning of quasi-phase-matching (QPM) gratings combined with optical parametric interactions involving spatially dispersed laser pulses. Our proof of principle experiment demonstrates this technique via mid-infrared optical parametric chirped pulse amplification of few-cycle pulses. Additionally, we present a detailed theoretical and numerical analysis of such 2D-QPM devices and how they can be designed.

Generalized Nonlinear Chirp Scaling Algorithm for High-Resolution Highly Squint SAR Imaging.

PubMed

Yi, Tianzhu; He, Zhihua; He, Feng; Dong, Zhen; Wu, Manqing

2017-11-07

This paper presents a modified approach for high-resolution, highly squint synthetic aperture radar (SAR) data processing. Several nonlinear chirp scaling (NLCS) algorithms have been proposed to solve the azimuth variance of the frequency modulation rates that are caused by the linear range walk correction (LRWC). However, the azimuth depth of focusing (ADOF) is not handled well by these algorithms. The generalized nonlinear chirp scaling (GNLCS) algorithm that is proposed in this paper uses the method of series reverse (MSR) to improve the ADOF and focusing precision. It also introduces a high order processing kernel to avoid the range block processing. Simulation results show that the GNLCS algorithm can enlarge the ADOF and focusing precision for high-resolution highly squint SAR data.

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.

Mastodon

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

Coleman, Justin Leigh; Veeraraghavan, Swetha; Bolisetti, Chandrakanth

MASTODON has the capability to model stochastic nonlinear soil-structure interaction (NLSSI) in a dynamic probabilistic risk assessment framework. The NLSSI simulations include structural dynamics, time integration, dynamic porous media flow, nonlinear hysteretic soil constitutive models, geometric nonlinearities (gapping, sliding, and uplift). MASTODON is also the MOOSE based master application for dynamic PRA of external hazards.

Advances in simultaneous atmospheric profile and cloud parameter regression based retrieval from high-spectral resolution radiance measurements

NASA Astrophysics Data System (ADS)

Weisz, Elisabeth; Smith, William L.; Smith, Nadia

2013-06-01

The dual-regression (DR) method retrieves information about the Earth surface and vertical atmospheric conditions from measurements made by any high-spectral resolution infrared sounder in space. The retrieved information includes temperature and atmospheric gases (such as water vapor, ozone, and carbon species) as well as surface and cloud top parameters. The algorithm was designed to produce a high-quality product with low latency and has been demonstrated to yield accurate results in real-time environments. The speed of the retrieval is achieved through linear regression, while accuracy is achieved through a series of classification schemes and decision-making steps. These steps are necessary to account for the nonlinearity of hyperspectral retrievals. In this work, we detail the key steps that have been developed in the DR method to advance accuracy in the retrieval of nonlinear parameters, specifically cloud top pressure. The steps and their impact on retrieval results are discussed in-depth and illustrated through relevant case studies. In addition to discussing and demonstrating advances made in addressing nonlinearity in a linear geophysical retrieval method, advances toward multi-instrument geophysical analysis by applying the DR to three different operational sounders in polar orbit are also noted. For any area on the globe, the DR method achieves consistent accuracy and precision, making it potentially very valuable to both the meteorological and environmental user communities.

Nonlinear Monte Carlo model of superdiffusive shock acceleration with magnetic field amplification

NASA Astrophysics Data System (ADS)

Bykov, Andrei M.; Ellison, Donald C.; Osipov, Sergei M.

2017-03-01

Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow into the hot downstream thermal plasma with a substantial fraction of energy going into a broad spectrum of superthermal charged particles and magnetic fluctuations. The superthermal particles can penetrate into the shock upstream region producing an extended shock precursor. The cold upstream plasma flow is decelerated by the force provided by the superthermal particle pressure gradient. In high Mach number collisionless shocks, efficient particle acceleration is likely coupled with turbulent magnetic field amplification (MFA) generated by the anisotropic distribution of accelerated particles. This anisotropy is determined by fast particle transport, making the problem strongly nonlinear and multiscale. Here, we present a nonlinear Monte Carlo model of collisionless shock structure with superdiffusive propagation of high-energy Fermi accelerated particles coupled to particle acceleration and MFA, which affords a consistent description of strong shocks. A distinctive feature of the Monte Carlo technique is that it includes the full angular anisotropy of the particle distribution at all precursor positions. The model reveals that the superdiffusive transport of energetic particles (i.e., Lévy-walk propagation) generates a strong quadruple anisotropy in the precursor particle distribution. The resultant pressure anisotropy of the high-energy particles produces a nonresonant mirror-type instability that amplifies compressible wave modes with wavelengths longer than the gyroradii of the highest-energy protons produced by the shock.

Measuring of nonlinear properties of spatial light modulator with different wavelengths

NASA Astrophysics Data System (ADS)

Khalid, Farah G.; Younis Al-Dabagh, Samar; Ahmed, Sudad S.; Mahmood, Aseel I.; Al-Naimee, Kais

2018-05-01

The non-linear optical properties of Spatial Light Modulator(SLM) represented by Nonlinear Refractive Index (NLR) and nonlinear Absorption coefficient has been measured in this work using highly sensitive method known as Z-scan technique for different wavelengths (red and green). The capability to do instant measurements of different nonlinear optical parameters lead to consider these techniques as a one of the most desired and effective methods that could apply for different materials. The results showed that the NLR were in the same power for the different wavelengths while the nonlinear absorption is higher in case of green laser.

Nonlinear hybridization of the fundamental eigenmodes of microscopic ferromagnetic ellipses.

PubMed

Demidov, V E; Buchmeier, M; Rott, K; Krzysteczko, P; Münchenberger, J; Reiss, G; Demokritov, S O

2010-05-28

We have studied experimentally with high spatial resolution the nonlinear eigenmodes of microscopic Permalloy elliptical elements. We show that the nonlinearity affects the frequencies of the edge and the center modes in an essentially different way. This leads to repulsion of corresponding resonances and to nonlinear mode hybridization resulting in qualitative modifications of the spatial characteristics of the modes. We find that the nonlinear counterparts of the edge and the center modes simultaneously exhibit features specific for both their linear analogues.

Recent Advances in Fiber Lasers for Nonlinear Microscopy

PubMed Central

Xu, C.; Wise, F. W.

2013-01-01

Nonlinear microscopy techniques developed over the past two decades have provided dramatic new capabilities for biological imaging. The initial demonstrations of nonlinear microscopies coincided with the development of solid-state femtosecond lasers, which continue to dominate applications of nonlinear microscopy. Fiber lasers offer attractive features for biological and biomedical imaging, and recent advances are leading to high-performance sources with the potential for robust, inexpensive, integrated instruments. This article discusses recent advances, and identifies challenges and opportunities for fiber lasers in nonlinear bioimaging. PMID:24416074

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

Power maximization of variable-speed variable-pitch wind turbines using passive adaptive neural fault tolerant control

NASA Astrophysics Data System (ADS)

Habibi, Hamed; Rahimi Nohooji, Hamed; Howard, Ian

2017-09-01

Power maximization has always been a practical consideration in wind turbines. The question of how to address optimal power capture, especially when the system dynamics are nonlinear and the actuators are subject to unknown faults, is significant. This paper studies the control methodology for variable-speed variable-pitch wind turbines including the effects of uncertain nonlinear dynamics, system fault uncertainties, and unknown external disturbances. The nonlinear model of the wind turbine is presented, and the problem of maximizing extracted energy is formulated by designing the optimal desired states. With the known system, a model-based nonlinear controller is designed; then, to handle uncertainties, the unknown nonlinearities of the wind turbine are estimated by utilizing radial basis function neural networks. The adaptive neural fault tolerant control is designed passively to be robust on model uncertainties, disturbances including wind speed and model noises, and completely unknown actuator faults including generator torque and pitch actuator torque. The Lyapunov direct method is employed to prove that the closed-loop system is uniformly bounded. Simulation studies are performed to verify the effectiveness of the proposed method.

Evaluation of polymer based third order nonlinear integrated optics devices

NASA Astrophysics Data System (ADS)

Driessen, A.; Hoekstra, H. J. W. M.; Blom, F. C.; Horst, F.; Krijnen, G. J. M.; van Schoot, J. B. P.; Lambeck, P. V.; Popma, Th. J. A.; Diemeer, M. B.

1998-01-01

Nonlinear polymers are promising materials for high speed active integrated optics devices. In this paper we evaluate the perspectives polymer based nonlinear optical devices can offer. Special attention is directed to the materials aspects. In our experimental work we applied mainly Akzo Nobel DANS side-chain polymer that exhibits large second and third order coefficients. This material has been characterized by third harmonic generation, z-scan and pump-probe measurements. In addition, various waveguiding structures have been used to measure the nonlinear absorption (two photon absorption) on a ps time-scale. Finally an integrated optics Mach Zehnder interferometer has been realized and evaluated. It is shown that the DANS side-chain polymer has many of the desired properties: the material is easily processable in high-quality optical waveguiding structures, has low linear absorption and its nonlinearity has a pure electronic origin. More materials research has to be done to arrive at materials with higher nonlinear coefficients to allow switching at moderate light intensity ( < 1 W peak power) and also with lower nonlinear absorption coefficients.

Application of multi-objective nonlinear optimization technique for coordinated ramp-metering

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

Haj Salem, Habib; Farhi, Nadir; Lebacque, Jean Patrick, E-mail: abib.haj-salem@ifsttar.fr, E-mail: nadir.frahi@ifsttar.fr, E-mail: jean-patrick.lebacque@ifsttar.fr

2015-03-10

This paper aims at developing a multi-objective nonlinear optimization algorithm applied to coordinated motorway ramp metering. The multi-objective function includes two components: traffic and safety. Off-line simulation studies were performed on A4 France Motorway including 4 on-ramps.

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.

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

NASA Astrophysics Data System (ADS)

Russell, Esra

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

Extreme Nonlinear Optics of High Intensity Laser Pulse Filamentation in Gases

DTIC Science & Technology

2016-05-12

of energy from femtosecond filaments. Published * absolute measurements of electronic, vibrational, and rotational nonlinear response in H2 and D2 ...coefficients in the fastest rotating molecules H2 and D2 , which can serve as a benchmark for theory of high field molecule interactions. One of the...17. Absolute measurement of the ultrafast nonlinear electronic and rovibrational response in H2 and D2 J. K. Wahlstrand, S. Zahedpour, Y.-H

Further results on global state feedback stabilization of nonlinear high-order feedforward systems.

PubMed

Xie, Xue-Jun; Zhang, Xing-Hui

2014-03-01

In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Investigation of broadband terahertz generation from metasurface

DOE PAGES

Fang, Ming; Niu, Kaikun; Huang, ZHixiang; ...

2018-01-01

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Investigation of broadband terahertz generation from metasurface

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

Fang, Ming; Niu, Kaikun; Huang, ZHixiang

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Investigation of broadband terahertz generation from metasurface

DOE PAGES

Fang, Ming; Niu, Kaikun; Huang, ZHixiang; ...

2018-05-21

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Direct application of Padé approximant for solving nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

METCAN demonstration manual, version 1.0

NASA Technical Reports Server (NTRS)

Lee, H.-J.; Murthy, P. L. N.

1992-01-01

The various features of the Metal Matrix Composite Analyzer (METCAN) computer program to simulate the high temperature nonlinear behavior of continuous fiber reinforced metal matrix composites are demonstrated. Different problems are used to demonstrate various capabilities of METCAN for both static and cyclic analyses. A complete description of the METCAN output file is also included to help interpret results.

A Numerical Approach to Solving the Hall MHD Equations Including Diamagnetic Drift (Preprint)

DTIC Science & Technology

2008-02-19

SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON Dr. Jean-Luc Cambier a. REPORT...1997. [3] L. Chacon and D.A. Knoll. A 2d high-beta hall mhd implicit nonlinear solver. Journal of Computational Physics, 188:573–592, 2003. [4] Tony F

Apparatus and method for epileptic seizure detection using non-linear techniques

DOEpatents

Hively, Lee M.; Clapp, Ned E.; Daw, C. Stuart; Lawkins, William F.

1998-01-01

Methods and apparatus for automatically detecting epileptic seizures by monitoring and analyzing brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; determining that one or more trends in the nonlinear measures indicate a seizure, and providing notification of seizure occurrence.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

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

Wang, Lei; Kruk, Sergey; Koshelev, Kirill

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Nonlinear Wavefront Control with All-Dielectric Metasurfaces.

PubMed

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; Kravchenko, Ivan; Luther-Davies, Barry; Kivshar, Yuri

2018-06-13

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront of parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Our nonlinear metasurfaces produce phase gradients over a full 0-2π phase range with a 92% diffraction efficiency.

Differences between direct current and alternating current capacitance nonlinearities in high-k dielectrics and their relation to hopping conduction

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

Khaldi, O.; Kassmi, M.; El Manar University, LMOP, 2092 Tunis

2014-08-28

Capacitance nonlinearities were studied in atomic layer deposited HfO{sub 2} films using two types of signals: a pure ac voltage of large magnitude (ac nonlinearities) and a small ac voltage superimposed to a large dc voltage (dc nonlinearities). In theory, ac and dc nonlinearities should be of the same order of magnitude. However, in practice, ac nonlinearities are found to be an order of magnitude higher than dc nonlinearities. Besides capacitance nonlinearities, hopping conduction is studied using low-frequency impedance measurements and is discussed through the correlated barrier hopping model. The link between hopping and nonlinearity is established. The ac nonlinearitiesmore » are ascribed to the polarization of isolated defect pairs, while dc nonlinearities are attributed to electrode polarization which originates from defect percolation paths. Both the ac and dc capacitance nonlinearities display an exponential variation with voltage, which results from field-induced lowering of the hopping barrier energy.« less

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE PAGES

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; ...

2018-05-11

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Linearizing an intermodulation radar transmitter by filtering switched tones

NASA Astrophysics Data System (ADS)

Mazzaro, Gregory J.; Sherbondy, Andrew J.; Ranney, Kenneth I.; Sherbondy, Kelly D.; Martone, Anthony F.

2017-05-01

For nonlinear radar, the transmit power required to measure a detectable response from a target is relatively high, and generating that high power is achieved at the cost of linearity. This paper applies the distortion mitigation technique Linearization by Time-Multiplexed Spectrum (LITMUS) to intermodulation radar, a type of nonlinear radar which receives spectral content produced by the mixing of multiple frequencies at a nonlinear target. By implementing LITMUS, an experimental detection system for an intermodulation radar achieves a signal-to-noise ratio up to 20 dB for a total transmit power of approximately 80 mW and nonlinear targets placed at a standoff distance of 2 meters.

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

Investigation of a stripline transmission line structure for gyromagnetic nonlinear transmission line high power microwave sources.

PubMed

Reale, D V; Parson, J M; Neuber, A A; Dickens, J C; Mankowski, J J

2016-03-01

A stripline gyromagnetic nonlinear transmission line (NLTL) was constructed out of yttrium iron garnet ferrite and tested at charge voltages of 35 kV-55 kV with bias fields ranging from 10 kA/m to 20 kA/m. Typically, high power gyromagnetic NLTLs are constructed in a coaxial geometry. While this approach has many advantages, including a uniform transverse electromagnetic (TEM) mode, simple interconnection between components, and the ability to use oil or pressurized gas as an insulator, the coaxial implementation suffers from complexity of construction, especially when using a solid insulator. By moving to a simpler transmission line geometry, NLTLs can be constructed more easily and arrayed on a single substrate. This work represents a first step in exploring the suitability of various transmission line structures, such as microstrips and coplanar waveguides. The resulting high power microwave (HPM) source operates in ultra high frequency (UHF) band with an average bandwidth of 40.1% and peak rf power from 2 MW to 12.7 MW.

Investigation of a stripline transmission line structure for gyromagnetic nonlinear transmission line high power microwave sources

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

Reale, D. V., E-mail: david.reale@ttu.edu; Parson, J. M.; Neuber, A. A.

2016-03-15

A stripline gyromagnetic nonlinear transmission line (NLTL) was constructed out of yttrium iron garnet ferrite and tested at charge voltages of 35 kV–55 kV with bias fields ranging from 10 kA/m to 20 kA/m. Typically, high power gyromagnetic NLTLs are constructed in a coaxial geometry. While this approach has many advantages, including a uniform transverse electromagnetic (TEM) mode, simple interconnection between components, and the ability to use oil or pressurized gas as an insulator, the coaxial implementation suffers from complexity of construction, especially when using a solid insulator. By moving to a simpler transmission line geometry, NLTLs can be constructedmore » more easily and arrayed on a single substrate. This work represents a first step in exploring the suitability of various transmission line structures, such as microstrips and coplanar waveguides. The resulting high power microwave (HPM) source operates in ultra high frequency (UHF) band with an average bandwidth of 40.1% and peak rf power from 2 MW to 12.7 MW.« less

Suppression and nonlinear excitation of parasitic modes in second harmonic gyrotrons operating in a very high order mode

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

Nusinovich, Gregory S.; Pu, Ruifeng; Granatstein, Victor L.

2015-07-06

In recent years, there was an active development of high-power, sub-terahertz (sub-THz) gyrotrons for numerous applications. For example, a 0.67 THz gyrotron delivering more than 200 kW with about 20% efficiency was developed. This record high efficiency was achieved because the gyrotron operated in a high-order TE{sub 31,8}-mode with the power of ohmic losses less than 10% of the power of outgoing radiation. That gyrotron operated at the fundamental cyclotron resonance, and a high magnetic field of about 27 T was created by a pulse solenoid. For numerous applications, it is beneficial to use gyrotrons at cyclotron harmonics which can operate inmore » available cryomagnets with fields not exceeding 15 T. However, typically, the gyrotron operation at harmonics faces severe competition from parasitic modes at the fundamental resonance. In the present paper, we consider a similar 0.67 THz gyrotron designed for operation in the same TE{sub 31,8}-mode, but at the second harmonic. We focus on two nonlinear effects typical for interaction between the fundamental and second harmonic modes, viz., the mode suppression and the nonlinear excitation of the mode at the fundamental harmonic by the second harmonic oscillations. Our study includes both the analytical theory and numerical simulations performed with the self-consistent code MAGY. The simulations show that stable second harmonic operation in the TE{sub 31,8} mode is possible with only modest sacrifice of efficiency and power.« less

Time-Domain Finite Element Analysis of Nonlinear Breakdown Problems in High-Power-Microwave Devices and Systems

DTIC Science & Technology

2015-12-24

simulation of the electromagnetic- plasma interaction and the high-power microwave breakdown in air. Under the high pressure and high frequency condition of...the high-power air breakdown, the physical phenomenon is described using a nonlinearly coupled full-wave Maxwell and fluid plasma system. This...Challenges ........................................................................... 3 3.1.1 Plasma Fluid Model

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

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

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

2014-02-01

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

On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.

2004-01-01

The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD.

Nonlinear Optics and Applications

NASA Technical Reports Server (NTRS)

Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)

2007-01-01

Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

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.)

Molecular orientation sensitive second harmonic microscopy by radially and azimuthally polarized light

PubMed Central

Ehmke, Tobias; Nitzsche, Tim Heiko; Knebl, Andreas; Heisterkamp, Alexander

2014-01-01

We demonstrate the possibility to switch the z-polarization component of the illumination in the vicinity of the focus of high-NA objective lenses by applying radially and azimuthally polarized incident light. The influence of the field distribution on nonlinear effects was first investigated by the means of simulations. These were performed for high-NA objective lenses commonly used in nonlinear microscopy. Special attention is paid to the influence of the polarization of the incoming field. For linearly, circularly and radially polarized light a considerable polarization component in z-direction is generated by high NA focusing. Azimuthal polarization is an exceptional case: even for strong focusing no z-component arises. Furthermore, the influence of the input polarization on the intensity contributing to the nonlinear signal generation was computed. No distinct difference between comparable input polarization states was found for chosen thresholds of nonlinear signal generation. Differences in signal generation for radially and azimuthally polarized vortex beams were experimentally evaluated in native collagen tissue (porcine cornea). The findings are in good agreement with the theoretical predictions and display the possibility to probe the molecular orientation along the optical axis of samples with known nonlinear properties. The combination of simulations regarding the nonlinear response of materials and experiments with different sample orientations and present or non present z-polarization could help to increase the understanding of nonlinear signal formation in yet unstudied materials. PMID:25071961

Nonlinear terms in storm surge predictions: Effect of tide and shelf geometry with case study from Hurricane Rita

NASA Astrophysics Data System (ADS)

Rego, JoãO. L.; Li, Chunyan

2010-06-01

This study applied the finite volume coastal ocean model (FVCOM) to the storm surge induced by Hurricane Rita along the Louisiana-Texas coast. The model was calibrated for tides and validated with observed water levels. Peak water levels were shown to be lower than expected for a landfall at high tide. For low- and high-tide landfalls, nonlinear effects due to tide-surge coupling were constructive and destructive to total storm tide, respectively, and their magnitude reached up to 70% of the tidal amplitude in the Rita application. Tide-surge interaction was further examined using a standard hurricane under idealized scenarios to evaluate the effects of various shelf geometries, tides, and landfall timings (relative to tide). Nonlinearity was important between landfall position and locations within 2.5 × radius of maximum winds. On an idealized wide continental shelf, nonlinear effects reached up to 80% of the tidal amplitude with an S2 tide and up to 47% with a K1 tide. Increasing average depths by 4 m reduced nonlinear effects to 41% of the tidal amplitude; increasing the slope by a factor of 3 produced nonlinearities of just 26% of tide (both with a K1 tide). The nonlinear effect was greatest for landfalls at low tide, followed by landfalls at high tide and then by landfalls at midebb or midflood.

Understanding climate impacts on vegetation using a spatiotemporal non-linear Granger causality framework

NASA Astrophysics Data System (ADS)

Papagiannopoulou, Christina; Decubber, Stijn; Miralles, Diego; Demuzere, Matthias; Dorigo, Wouter; Verhoest, Niko; Waegeman, Willem

2017-04-01

Satellite data provide an abundance of information about crucial climatic and environmental variables. These data - consisting of global records, spanning up to 35 years and having the form of multivariate time series with different spatial and temporal resolutions - enable the study of key climate-vegetation interactions. Although methods which are based on correlations and linear models are typically used for this purpose, their assumptions for linearity about the climate-vegetation relationships are too simplistic. Therefore, we adopt a recently proposed non-linear Granger causality analysis [1], in which we incorporate spatial information, concatenating data from neighboring pixels and training a joint model on the combined data. Experimental results based on global data sets show that considering non-linear relationships leads to a higher explained variance of past vegetation dynamics, compared to simple linear models. Our approach consists of several steps. First, we compile an extensive database [1], which includes multiple data sets for land surface temperature, near-surface air temperature, surface radiation, precipitation, snow water equivalents and surface soil moisture. Based on this database, high-level features are constructed and considered as predictors in our machine-learning framework. These high-level features include (de-trended) seasonal anomalies, lagged variables, past cumulative variables, and extreme indices, all calculated based on the raw climatic data. Second, we apply a spatiotemporal non-linear Granger causality framework - in which the linear predictive model is substituted for a non-linear machine learning algorithm - in order to assess which of these predictor variables Granger-cause vegetation dynamics at each 1° pixel. We use the de-trended anomalies of Normalized Difference Vegetation Index (NDVI) to characterize vegetation, being the target variable of our framework. Experimental results indicate that climate strongly (Granger-)causes vegetation dynamics in most regions globally. More specifically, water availability is the most dominant vegetation driver, being the dominant vegetation driver in 54% of the vegetated surface. Furthermore, our results show that precipitation and soil moisture have prolonged impacts on vegetation in semiarid regions, with up to 10% of additional explained variance on the vegetation dynamics occurring three months later. Finally, hydro-climatic extremes seem to have a remarkable impact on vegetation, since they also explain up to 10% of additional variance of vegetation in certain regions despite their infrequent occurrence. References [1] Papagiannopoulou, C., Miralles, D. G., Verhoest, N. E. C., Dorigo, W. A., and Waegeman, W.: A non-linear Granger causality framework to investigate climate-vegetation dynamics, Geosci. Model Dev. Discuss., doi:10.5194/gmd-2016-266, in review, 2016.

An experimental study of nonlinear dynamic system identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1990-01-01

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

A methodology for designing robust multivariable nonlinear control systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Grunberg, D. B.

1986-01-01

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1998-01-01

This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.

Do film soundtracks contain nonlinear analogues to influence emotion?

PubMed Central

Blumstein, Daniel T.; Davitian, Richard; Kaye, Peter D.

2010-01-01

A variety of vertebrates produce nonlinear vocalizations when they are under duress. By their very nature, vocalizations containing nonlinearities may sound harsh and are somewhat unpredictable; observations that are consistent with them being particularly evocative to those hearing them. We tested the hypothesis that humans capitalize on this seemingly widespread vertebrate response by creating nonlinear analogues in film soundtracks to evoke particular emotions. We used lists of highly regarded films to generate a set of highly ranked action/adventure, dramatic, horror and war films. We then scored the presence of a variety of nonlinear analogues in these film soundtracks. Dramatic films suppressed noise of all types, contained more abrupt frequency transitions and musical sidebands, and fewer noisy screams than expected. Horror films suppressed abrupt frequency transitions and musical sidebands, but had more non-musical sidebands, and noisy screams than expected. Adventure films had more male screams than expected. Together, our results suggest that film-makers manipulate sounds to create nonlinear analogues in order to manipulate our emotional responses. PMID:20504815

Do film soundtracks contain nonlinear analogues to influence emotion?

PubMed

Blumstein, Daniel T; Davitian, Richard; Kaye, Peter D

2010-12-23

A variety of vertebrates produce nonlinear vocalizations when they are under duress. By their very nature, vocalizations containing nonlinearities may sound harsh and are somewhat unpredictable; observations that are consistent with them being particularly evocative to those hearing them. We tested the hypothesis that humans capitalize on this seemingly widespread vertebrate response by creating nonlinear analogues in film soundtracks to evoke particular emotions. We used lists of highly regarded films to generate a set of highly ranked action/adventure, dramatic, horror and war films. We then scored the presence of a variety of nonlinear analogues in these film soundtracks. Dramatic films suppressed noise of all types, contained more abrupt frequency transitions and musical sidebands, and fewer noisy screams than expected. Horror films suppressed abrupt frequency transitions and musical sidebands, but had more non-musical sidebands, and noisy screams than expected. Adventure films had more male screams than expected. Together, our results suggest that film-makers manipulate sounds to create nonlinear analogues in order to manipulate our emotional responses.

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

Study of the use of a nonlinear, rate limited, filter on pilot control signals

NASA Technical Reports Server (NTRS)

Adams, J. J.

1977-01-01

The use of a filter on the pilot's control output could improve the performance of the pilot-aircraft system. What is needed is a filter with a sharp high frequency cut-off, no resonance peak, and a minimum of lag at low frequencies. The present investigation studies the usefulness of a nonlinear, rate limited, filter in performing the needed function. The nonlinear filter is compared with a linear, first order filter, and no filter. An analytical study using pilot models and a simulation study using experienced test pilots was performed. The results showed that the nonlinear filter does promote quick, steady maneuvering. It is shown that the nonlinear filter attenuates the high frequency remnant and adds less phase lag to the low frequency signal than does the linear filter. It is also shown that the rate limit in the nonlinear filter can be set to be too restrictive, causing an unstable pilot-aircraft system response.

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Spatial nonlinearities: Cascading effects in the earth system

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

2006-01-01

Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

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

PubMed

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

2011-02-01

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

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1986-01-01

The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.

Nonlinear air-coupled emission: The signature to reveal and image microdamage in solid materials

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

Solodov, Igor; Busse, Gerd

2007-12-17

It is shown that low-frequency elastic vibrations of near-surface planar defects cause high-frequency ultrasonic radiation in surrounding air. The frequency conversion mechanism is concerned with contact nonlinearity of the defect vibrations and provides efficient generation of air-coupled higher-order ultraharmonics, ultrasubharmonics, and combination frequencies. The nonlinear air-coupled ultrasonic emission is applied for location and high-resolution imaging of damage-induced defects in a variety of solid materials.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

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.

PREFACE: Ultrafast biophotonics Ultrafast biophotonics

NASA Astrophysics Data System (ADS)

Gu, Min; Reid, Derryck; Ben-Yakar, Adela

2010-08-01

The use of light to explore biology can be traced to the first observations of tissue made with early microscopes in the mid-seventeenth century, and has today evolved into the discipline which we now know as biophotonics. This field encompasses a diverse range of activities, each of which shares the common theme of exploiting the interaction of light with biological material. With the rapid advancement of ultrafast optical technologies over the last few decades, ultrafast lasers have increasingly found applications in biophotonics, to the extent that the distinctive new field of ultrafast biophotonics has now emerged, where robust turnkey ultrafast laser systems are facilitating cutting-edge studies in the life sciences to take place in everyday laboratories. The broad spectral bandwidths, precision timing resolution, low coherence and high peak powers of ultrafast optical pulses provide unique opportunities for imaging and manipulating biological systems. Time-resolved studies of bio-molecular dynamics exploit the short pulse durations from such lasers, while other applications such as optical coherence tomography benefit from the broad optical bandwidths possible by using super-continuum generation and additionally allowing for high speed imaging with speeds as high as 47 000 scans per second. Continuing progress in laser-system technology is accelerating the adoption of ultrafast techniques across the life sciences, both in research laboratories and in clinical applications, such as laser-assisted in situ keratomileusis (LASIK) eye surgery. Revolutionizing the field of optical microscopy, two-photon excitation fluorescence (TPEF) microscopy has enabled higher spatial resolution with improved depth penetration into biological specimens. Advantages of this nonlinear optical process include: reduced photo-interactions, allowing for extensive imaging time periods; simultaneously exciting multiple fluorescent molecules with only one excitation wavelength; and reduced chromatic aberration effects. These extensive advantages have led to further exploration of nonlinear processes including second-harmonic generation (SHG) microscopy and third-harmonic generation (THG) microscopy. Second-harmonic generation has provided biologists with an extremely powerful tool for generating contrast in biological imaging, with the additional benefit of non-invasive three-dimensional imaging. The recent popularity of THG microscopy is largely due to the fact that three-dimensional imaging is achievable without the need for any labels, but rather relying on the intrinsic properties of the biological specimen itself. This optical nonlinear technique has attracted much attention recently from the biological community due to its non-invasive capabilities. Users of ultrafast lasers in the biological and medical fields are becoming a fast-growing community, employing pulse-shaping microscopy, resolution-enhancing microscopy techniques, linear and nonlinear micro-spectroscopy, functional deep-tissue imaging, optical coherence tomography, nonlinear fluorescence microscopy, molecular imaging and control, harmonic microscopy and femtosecond lifetime imaging, for cutting-edge research concerning the interaction of light with biological dynamics. The adaptability of ultrafast lasers to interact with a large array of materials through nonlinear excitation has enabled precise control of laser fluence allowing for highly localized material interactions, permitting micro-structured fabricated surfaces. The resultant multi-dimensional fabricated micro-structures are capable of replicating and/or manipulating microenvironments for controlled cell biology. In this special issue of Journal of Optics readers have a chance to view a collection of new contributions to the growing research field of ultrafast biophotonics. They are presented with recent advances in ultrafast technology applied to biological and medical investigations, where topics include advances in the visualization and identification of photo-reaction dynamics of biological functions under relevant physiological conditions, theoretically proposed imaging designs for obtaining super-resolved optical sectioned images in single exposures and fabricated micro-structured surfaces for biological micro-environments. We hope the collection will stimulate innovative new research in this growing field by showcasing new techniques for the visualization and manipulation of complex biological systems using linear and and nonlinear optical processes. Professor Min Gu would like to acknowledge Dr Betty Kouskousis for her contribution and support towards this editorial.

Nonlinear dynamic phenomena in the space shuttle thermal protection system

NASA Technical Reports Server (NTRS)

Housner, J. M.; Edighoffer, H. H.; Park, K. C.

1981-01-01

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

NASA Astrophysics Data System (ADS)

Zhang, Dong; Kushibiki, Junichi; Zou, Wei

2006-10-01

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

Nonlinear oscillation of a rigid body over high- Tc superconductors supported by electro-magnetic forces

NASA Astrophysics Data System (ADS)

Sugiura, T.; Ogawa, S.; Ura, H.

2005-10-01

Characteristics of high- Tc superconducting levitation systems are no contact support and stable levitation without control. They can be applied to supporting mechanisms in machines, such as linear-drives and magnetically levitated trains. But small damping due to noncontact support and nonlinearity in the magnetic force can easily cause complicated phenomena of nonlinear dynamics. This research deals with nonlinear oscillation of a rigid bar supported at its both ends by electro-magnetic forces between superconductors and permanent magnets as a simple modeling of the above application. Deriving the equation of motion, we discussed an effect of nonlinearity in the magnetic force on dynamics of the levitated body: occurrence of combination resonance in the asymmetrical system. Numerical analyses and experiments were also carried out, and their results confirmed the above theoretical prediction.

Nonlinear threshold effect in the Z-scan method of characterizing limiters for high-intensity laser light

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

Tereshchenko, S. A., E-mail: tsa@miee.ru; Savelyev, M. S.; Podgaetsky, V. M.

A threshold model is described which permits one to determine the properties of limiters for high-powered laser light. It takes into account the threshold characteristics of the nonlinear optical interaction between the laser beam and the limiter working material. The traditional non-threshold model is a particular case of the threshold model when the limiting threshold is zero. The nonlinear characteristics of carbon nanotubes in liquid and solid media are obtained from experimental Z-scan data. Specifically, the nonlinear threshold effect was observed for aqueous dispersions of nanotubes, but not for nanotubes in solid polymethylmethacrylate. The threshold model fits the experimental Z-scanmore » data better than the non-threshold model. Output characteristics were obtained that integrally describe the nonlinear properties of the optical limiters.« less

Soliton production with nonlinear homogeneous lines

DOE PAGES

Elizondo-Decanini, Juan M.; Coleman, Phillip D.; Moorman, Matthew W.; ...

2015-11-24

Low- and high-voltage Soliton waves were produced and used to demonstrate collision and compression using diode-based nonlinear transmission lines. Experiments demonstrate soliton addition and compression using homogeneous nonlinear lines. We built the nonlinear lines using commercially available diodes. These diodes are chosen after their capacitance versus voltage dependence is used in a model and the line design characteristics are calculated and simulated. Nonlinear ceramic capacitors are then used to demonstrate high-voltage pulse amplification and compression. The line is designed such that a simple capacitor discharge, input signal, develops soliton trains in as few as 12 stages. We also demonstrated outputmore » voltages in excess of 40 kV using Y5V-based commercial capacitors. The results show some key features that determine efficient production of trains of solitons in the kilovolt range.« less

Technique for Very High Order Nonlinear Simulation and Validation

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2001-01-01

Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of 5 wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.

Short-term ECG recording for the identification of cardiac autonomic neuropathy in people with diabetes mellitus

NASA Astrophysics Data System (ADS)

Jelinek, Herbert F.; Pham, Phuong; Struzik, Zbigniew R.; Spence, Ian

2007-07-01

Diabetes mellitus (DM) is a serious and increasing health problem worldwide. Compared to non-diabetics, patients experience an increased risk of all cardiovascular diseases, including dysfunctional neural control of the heart. Poor diagnoses of cardiac autonomic neuropathy (CAN) may result in increased incidence of silent myocardial infarction and ischaemia, which can lead to sudden death. Traditionally the Ewing battery of tests is used to identify CAN. The purpose of this study is to examine the usefulness of heart rate variability (HRV) analyses of short-term ECG recordings as a method for detecting CAN. HRV may be able to identify asymptomatic individuals, which the Ewing battery is not able to do. Several HRV parameters are assessed, including time and frequency domain, as well as nonlinear parameters. Eighteen out of thirty-eight individuals with diabetes were positive for two or more of the Ewing battery of tests indicating CAN. Approximate Entropy (ApEn), log normalized total power (LnTP) and log normalized high frequency (LnHF) power demonstrate a significant difference at p < 0.05 between CAN+ and CAN-. This indicates that nonlinear scaling parameters are able to identify people with cardiac autonomic neuropathy in short ECG recordings. Our study paves the way to assess the utility of nonlinear parameters in identifying asymptomatic CAN.

On-line implementation of nonlinear parameter estimation for the Space Shuttle main engine

NASA Technical Reports Server (NTRS)

Buckland, Julia H.; Musgrave, Jeffrey L.; Walker, Bruce K.

1992-01-01

We investigate the performance of a nonlinear estimation scheme applied to the estimation of several parameters in a performance model of the Space Shuttle Main Engine. The nonlinear estimator is based upon the extended Kalman filter which has been augmented to provide estimates of several key performance variables. The estimated parameters are directly related to the efficiency of both the low pressure and high pressure fuel turbopumps. Decreases in the parameter estimates may be interpreted as degradations in turbine and/or pump efficiencies which can be useful measures for an online health monitoring algorithm. This paper extends previous work which has focused on off-line parameter estimation by investigating the filter's on-line potential from a computational standpoint. ln addition, we examine the robustness of the algorithm to unmodeled dynamics. The filter uses a reduced-order model of the engine that includes only fuel-side dynamics. The on-line results produced during this study are comparable to off-line results generated previously. The results show that the parameter estimates are sensitive to dynamics not included in the filter model. Off-line results using an extended Kalman filter with a full order engine model to address the robustness problems of the reduced-order model are also presented.

A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth

PubMed Central

Macklin, Paul

2011-01-01

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth. PMID:21331304

Obtaining high-energy responses of nonlinear piezoelectric energy harvester by voltage impulse perturbations

NASA Astrophysics Data System (ADS)

Lan, Chunbo; Tang, Lihua; Qin, Weiyang

2017-07-01

Nonlinear energy harvesters have attracted wide research attentions to achieve broadband performances in recent years. Nonlinear structures have multiple solutions in certain frequency region that contains high-energy and low-energy orbits. It is effectively the frequency region of capturing a high-energy orbit that determines the broadband performance. Thus, maintaining large-amplitude high-energy-orbit oscillations is highly desired. In this paper, a voltage impulse perturbation approach based on negative resistance is applied to trigger high-energy-orbit responses of piezoelectric nonlinear energy harvesters. First, the mechanism of the voltage impulse perturbation and the implementation of the synthetic negative resistance circuit are discussed in detail. Subsequently, numerical simulation and experiment are conducted and the results demonstrate that the high-energy-orbit oscillations can be triggered by the voltage impulse perturbation method for both monostable and bistable configurations given various scenarios. It is revealed that the perturbation levels required to trigger and maintain high-energy-orbit oscillations are different for various excitation frequencies in the region where multiple solutions exist. The higher gain in voltage output when high-energy-orbit oscillations are captured is accompanied with the demand of a higher voltage impulse perturbation level.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Nonlinear analysis of a rotor-bearing system using describing functions

NASA Astrophysics Data System (ADS)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Nonlinear optics quantum computing with circuit QED.

PubMed

Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M

2013-02-08

One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

NASA Astrophysics Data System (ADS)

Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.

2017-10-01

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.

The effect of system nonlinearities on system noise statistics

NASA Technical Reports Server (NTRS)

Robinson, L. H., Jr.

1971-01-01

The effects are studied of nonlinearities in a baseline communications system on the system noise amplitude statistics. So that a meaningful identification of system nonlinearities can be made, the baseline system is assumed to transmit a single biphase-modulated signal through a relay satellite to the receiving equipment. The significant nonlinearities thus identified include square-law or product devices (e.g., in the carrier reference recovery loops in the receivers), bandpass limiters, and traveling wave tube amplifiers.

Apparatus and method for epileptic seizure detection using non-linear techniques

DOEpatents

Hively, L.M.; Clapp, N.E.; Daw, C.S.; Lawkins, W.F.

1998-04-28

Methods and apparatus are disclosed for automatically detecting epileptic seizures by monitoring and analyzing brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; determining that one or more trends in the nonlinear measures indicate a seizure, and providing notification of seizure occurrence. 76 figs.

Generalized Nonlinear Chirp Scaling Algorithm for High-Resolution Highly Squint SAR Imaging

PubMed Central

He, Zhihua; He, Feng; Dong, Zhen; Wu, Manqing

2017-01-01

This paper presents a modified approach for high-resolution, highly squint synthetic aperture radar (SAR) data processing. Several nonlinear chirp scaling (NLCS) algorithms have been proposed to solve the azimuth variance of the frequency modulation rates that are caused by the linear range walk correction (LRWC). However, the azimuth depth of focusing (ADOF) is not handled well by these algorithms. The generalized nonlinear chirp scaling (GNLCS) algorithm that is proposed in this paper uses the method of series reverse (MSR) to improve the ADOF and focusing precision. It also introduces a high order processing kernel to avoid the range block processing. Simulation results show that the GNLCS algorithm can enlarge the ADOF and focusing precision for high-resolution highly squint SAR data. PMID:29112151

Nonlinear dynamic modeling of a V-shaped metal based thermally driven MEMS actuator for RF switches

NASA Astrophysics Data System (ADS)

Bakri-Kassem, Maher; Dhaouadi, Rached; Arabi, Mohamed; Estahbanati, Shahabeddin V.; Abdel-Rahman, Eihab

2018-05-01

In this paper, we propose a new dynamic model to describe the nonlinear characteristics of a V-shaped (chevron) metallic-based thermally driven MEMS actuator. We developed two models for the thermal actuator with two configurations. The first MEMS configuration has a small tip connected to the shuttle, while the second configuration has a folded spring and a wide beam attached to the shuttle. A detailed finite element model (FEM) and a lumped element model (LEM) are proposed for each configuration to completely characterize the electro-thermal and thermo-mechanical behaviors. The nonlinear resistivity of the polysilicon layer is extracted from the measured current-voltage (I-V) characteristics of the actuator and the simulated corresponding temperatures in the FEM model, knowing the resistivity of the polysilicon at room temperature from the manufacture’s handbook. Both developed models include the nonlinear temperature-dependent material properties. Numerical simulations in comparison with experimental data using a dedicated MEMS test apparatus verify the accuracy of the proposed LEM model to represent the complex dynamics of the thermal MEMS actuator. The LEM and FEM simulation results show an accuracy ranging from a maximum of 13% error down to a minimum of 1.4% error. The actuator with the lower thermal load to air that includes a folded spring (FS), also known as high surface area actuator is compared to the actuator without FS, also known as low surface area actuator, in terms of the I-V characteristics, power consumption, and experimental static and dynamic responses of the tip displacement.

Nonlinear thermotics: nonlinearity enhancement and harmonic generation in thermal metasurfaces

NASA Astrophysics Data System (ADS)

Dai, Gaole; Shang, Jin; Wang, Ruizhe; Huang, Jiping

2018-03-01

We propose and investigate a class of structural surfaces (metasurfaces). We develop the perturbation theory and the effective medium theory to study the thermal properties of the metasurface. We report that the coefficient of temperature-dependent (nonlinear) item in thermal conductivity can be enhanced under certain conditions. Furthermore, the existence of nonlinear item helps to generate high-order harmonic frequencies of heat flux in the presence of a heat source with periodic temperature. This work paves a different way to control and manipulate the transfer of heat, and it also makes it possible to develop nonlinear thermotics in the light of nonlinear optics.

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.

Prediction of jump phenomena in rotationally-coupled maneuvers of aircraft, including nonlinear aerodynamic effects

NASA Technical Reports Server (NTRS)

Young, J. W.; Schy, A. A.; Johnson, K. G.

1977-01-01

An analytical method has been developed for predicting critical control inputs for which nonlinear rotational coupling may cause sudden jumps in aircraft response. The analysis includes the effect of aerodynamics which are nonlinear in angle of attack. The method involves the simultaneous solution of two polynomials in roll rate, whose coefficients are functions of angle of attack and the control inputs. Results obtained using this procedure are compared with calculated time histories to verify the validity of the method for predicting jump-like instabilities.

A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

NASA Astrophysics Data System (ADS)

Sandhu, Amit

A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

Studies on spatial modes and the correlation anisotropy of entangled photons generated from 2D quadratic nonlinear photonic crystals

NASA Astrophysics Data System (ADS)

Luo, X. W.; Xu, P.; Sun, C. W.; Jin, H.; Hou, R. J.; Leng, H. Y.; Zhu, S. N.

2017-06-01

Concurrent spontaneous parametric down-conversion (SPDC) processes have proved to be an appealing approach for engineering the path-entangled photonic state with designable and tunable spatial modes. In this work, we propose a general scheme to construct high-dimensional path entanglement and demonstrate the basic properties of concurrent SPDC processes from domain-engineered quadratic nonlinear photonic crystals, including the spatial modes and the photon flux, as well as the anisotropy of spatial correlation under noncollinear quasi-phase-matching geometry. The overall understanding about the performance of concurrent SPDC processes will give valuable references to the construction of compact path entanglement and the development of new types of photonic quantum technologies.

Quantum information processing with a travelling wave of light

NASA Astrophysics Data System (ADS)

Serikawa, Takahiro; Shiozawa, Yu; Ogawa, Hisashi; Takanashi, Naoto; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We exploit quantum information processing on a traveling wave of light, expecting emancipation from thermal noise, easy coupling to fiber communication, and potentially high operation speed. Although optical memories are technically challenging, we have an alternative approach to apply multi-step operations on traveling light, that is, continuous-variable one-way computation. So far our achievement includes generation of a one-million-mode entangled chain in time-domain, mode engineering of nonlinear resource states, and real-time nonlinear feedforward. Although they are implemented with free space optics, we are also investigating photonic integration and performed quantum teleportation with a passive liner waveguide chip as a demonstration of entangling, measurement, and feedforward. We also suggest a loop-based architecture as another model of continuous-variable computing.

Experimental gaze at nonlinear phenomena

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

Libchaber, A.

1988-09-20

Experimental observations of nonlinear problems in physics are presented, including liquid crystal phase transformations, convection of mercury, and the transition to turbulence in helium gas thermal convection./aip/.

Nonlinear stability of the 1D Boltzmann equation in a periodic box

NASA Astrophysics Data System (ADS)

Wu, Kung-Chien

2018-05-01

We study the nonlinear stability of the Boltzmann equation in the 1D periodic box with size , where is the Knudsen number. The convergence rate is for small time region and exponential for large time region. Moreover, the exponential rate depends on the size of the domain (Knudsen number). This problem is highly nonlinear and hence we need more careful analysis to control the nonlinear term.

Design, synthesis and nonlinear optical properties of (E)-1-(4-substituted)-3-(4-hydroxy-3-nitrophenyl) prop-2-en-1-one compounds

NASA Astrophysics Data System (ADS)

Saha, Amrita; Shukla, Vijay; Choudhury, Sudip; Jayabalan, J.

2016-06-01

A new series of (E)-1-(4-substituted)-3-(4-hydroxy-3-nitrophenyl) prop-2-en-1-one compounds have been synthesized by Claisen-Schmidt condensation reaction. Nonlinear optical characterization were carried out using z-scan technique with nanosecond pulses. These samples are found to exhibit strong nonlinear absorption at 532 nm and the nonlinear absorption coefficient of these samples exponentially increases with the increase of phonon characteristic energy. This relation speaks the role of phonon in the origin of nonlinear absorption in these compounds. The reported dependence of optical nonlinearity of the chalcone derivatives on the phonon characteristic energy will help in designing similar class of new molecules with high nonlinear coefficients.

High-order rogue waves in vector nonlinear Schrödinger equations.

PubMed

Ling, Liming; Guo, Boling; Zhao, Li-Chen

2014-04-01

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

Bearing defect signature analysis using advanced nonlinear signal analysis in a controlled environment

NASA Technical Reports Server (NTRS)

Zoladz, T.; Earhart, E.; Fiorucci, T.

1995-01-01

Utilizing high-frequency data from a highly instrumented rotor assembly, seeded bearing defect signatures are characterized using both conventional linear approaches, such as power spectral density analysis, and recently developed nonlinear techniques such as bicoherence analysis. Traditional low-frequency (less than 20 kHz) analysis and high-frequency envelope analysis of both accelerometer and acoustic emission data are used to recover characteristic bearing distress information buried deeply in acquired data. The successful coupling of newly developed nonlinear signal analysis with recovered wideband envelope data from accelerometers and acoustic emission sensors is the innovative focus of this research.

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.

Development and Breakdown of Goertler Vortices in High Speed Boundary Layers

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan; Chang, Chau-Lyan; Wu, Minwei; Greene, Ptrick T.

2010-01-01

The nonlinear development of G rtler instability over a concave surface gives rise to a highly distorted stationary flow in the boundary layer that has strong velocity gradients in both spanwise and wall-normal directions. This distorted flow is susceptible to strong, high frequency secondary instability that leads to the onset of transition. For high Mach number flows, the boundary layer is also subject to the second mode instability. The nonlinear development of G rtler vortices and the ensuing growth and breakdown of secondary instability, the G rtler vortex interactions with second mode instabilities as well as oblique second mode interactions are examined in the context of both internal and external hypersonic configurations using nonlinear parabolized stability equations, 2-D eigenvalue analysis and direct numerical simulation. For G rtler vortex development inside the Purdue Mach 6 Ludwieg tube wind tunnel, multiple families of unstable secondary eigenmodes are identified and their linear and nonlinear evolution is examined. The computation of secondary instability is continued past the onset of transition to elucidate the physical mechanisms underlying the laminar breakdown process. Nonlinear breakdown scenarios associated with transition over a Mach 6 compression cone configuration are also explored.

Self-Organized Lattices of Nonlinear Optochemical Waves in Photopolymerizable Fluids: The Spontaneous Emergence of 3-D Order in a Weakly Correlated System.

PubMed

Ponte, Matthew R; Hudson, Alexander D; Saravanamuttu, Kalaichelvi

2018-03-01

Many of the extraordinary three-dimensional architectures that pattern our physical world emerge from complex nonlinear systems or dynamic populations whose individual constituents are only weakly correlated to each other. Shoals of fish, murmuration behaviors in birds, congestion patterns in traffic, and even networks of social conventions are examples of spontaneous pattern formation, which cannot be predicted from the properties of individual elements alone. Pattern formation at a different scale has been observed or predicted in weakly correlated systems including superconductors, atomic gases near Bose Einstein condensation, and incoherent optical fields. Understanding pattern formation in nonlinear weakly correlated systems, which are often unified through mathematical expression, could pave intelligent self-organizing pathways to functional materials, architectures, and computing technologies. However, it is experimentally difficult to directly visualize the nonlinear dynamics of pattern formation in most populations-especially in three dimensions. Here, we describe the collective behavior of large populations of nonlinear optochemical waves, which are poorly correlated in both space and time. The optochemical waves-microscopic filaments of white light entrapped within polymer channels-originate from the modulation instability of incandescent light traveling in photopolymerizable fluids. By tracing the three-dimensional distribution of optical intensity in the nascent polymerizing system, we find that populations of randomly distributed, optochemical waves synergistically and collectively shift in space to form highly ordered lattices of specific symmetries. These, to our knowledge, are the first three-dimensionally periodic structures to emerge from a system of weakly correlated waves. Their spontaneous formation in an incoherent and effectively chaotic field is counterintuitive, but the apparent contradiction of known behaviors of light including the laws of optical interference can be explained through the soliton-like interactions of optochemical waves with nearest neighbors. Critically, this work casts fundamentally new insight into the collective behaviors of poorly correlated nonlinear waves in higher dimensions and provides a rare, accessible platform for further experimental studies of these previously unexplored behaviors. Furthermore, it defines a self-organization paradigm that, unlike conventional counterparts, could generate polymer microstructures with symmetries spanning all the Bravais lattices.

Nonlinear system identification of smart structures under high impact loads

NASA Astrophysics Data System (ADS)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-05-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

Margin-maximizing feature elimination methods for linear and nonlinear kernel-based discriminant functions.

PubMed

Aksu, Yaman; Miller, David J; Kesidis, George; Yang, Qing X

2010-05-01

Feature selection for classification in high-dimensional spaces can improve generalization, reduce classifier complexity, and identify important, discriminating feature "markers." For support vector machine (SVM) classification, a widely used technique is recursive feature elimination (RFE). We demonstrate that RFE is not consistent with margin maximization, central to the SVM learning approach. We thus propose explicit margin-based feature elimination (MFE) for SVMs and demonstrate both improved margin and improved generalization, compared with RFE. Moreover, for the case of a nonlinear kernel, we show that RFE assumes that the squared weight vector 2-norm is strictly decreasing as features are eliminated. We demonstrate this is not true for the Gaussian kernel and, consequently, RFE may give poor results in this case. MFE for nonlinear kernels gives better margin and generalization. We also present an extension which achieves further margin gains, by optimizing only two degrees of freedom--the hyperplane's intercept and its squared 2-norm--with the weight vector orientation fixed. We finally introduce an extension that allows margin slackness. We compare against several alternatives, including RFE and a linear programming method that embeds feature selection within the classifier design. On high-dimensional gene microarray data sets, University of California at Irvine (UCI) repository data sets, and Alzheimer's disease brain image data, MFE methods give promising results.

Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows

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

Xu, X Q; Belli, E; Bodi, K

We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependencemore » of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.« less

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

NASA Technical Reports Server (NTRS)

Mei, Chuh; Moorthy, Jayashree

1995-01-01

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Augmented twin-nonlinear two-box behavioral models for multicarrier LTE power amplifiers.

PubMed

Hammi, Oualid

2014-01-01

A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Center for the Study of Plasma Microturbulence

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

Parker, Scott E.

We have discovered a possible "natural fueling" mechanism in tokamak fusion reactors using large scale gyrokinetic turbulence simulation. In the presence of a heat flux dominated tokamak plasma, cold ions naturally pinch radially inward. If cold DT fuel is introduced near the edge using shallow pellet injection, the cold fuel will pinch inward, at the expense of hot helium ash going radially outward. By adjusting the cold DT fuel concentration, the core DT density profiles can be maintained. We have also shown that cold source ions from edge recycling of cold neutrals are pinched radially inward. This mechanism may bemore » important for fully understanding the edge pedestal buildup after an ELM crash. Work includes benchmarking the gyrokinetic turbulence codes in the electromagnetic regime. This includes cyclone base case parameters with an increasing plasma beta. The code comparisons include GEM, GYRO and GENE. There is good linear agreement between the codes using the Cyclone base case, but including electromagnetics and scanning the plasma beta. All the codes have difficulty achieving nonlinear saturation as the kinetic ballooning limit is approached. GEM does not saturate well when beta gets above about 1/2 of the ideal ballooning limit. We find that the lack of saturation is due to the long wavelength k{sub y} modes being nonlinearly pumped to high levels. If the fundamental k{sub y} mode is zeroed out, higher values of beta nonlinearly saturate well. Additionally, there have been studies to better understand CTEM nonlinear saturation and the importance of zonal flows. We have continued our investigation of trapped electron mode (TEM) turbulence. More recently, we have focused on the nonlinear saturation of TEM turbulence. An important feature of TEM is that in many parameter regimes, the zonal flow is unimportant. We find that when zonal flows are unimportant, zonal density is the dominant saturation mechanism. We developed a simple theory that agrees with the simulation and predicts zonal density generation and feedback stabilization of the most unstable mode even in the absence of zonal flow. We are using GEM to simulate NSTX discharges. We have also done verification and validation on DIII-D. Good agreement with GYRO and DIII-D flux levels were reported in the core region.« less

Modulational instability of helicon waves in a magnetoactive semiconductor n-InSb

NASA Astrophysics Data System (ADS)

Salimullah, M.; Ferdous, T.

1984-03-01

In this paper the modulational instabilithy of a beam of high amplitude helicon wave in a magnetoactive piezoelectric semiconductor is studied. The nonlinear response of electrons in the semiconductor plasma has been found by following the fluid model of homogeneous plasmas. The low frequency nonlinearity has been taken through the ponderomotive force on electrons, whereas the nonlinearity in the scattered helicon waves arises through the nonlinear current densities of electrons. For typical plasma parameters in n-type indium antimonide and for a considerable power density (approximately 20 kW/sq cm) of the incident helicon beam, the growth rate of the modulational instability is quite high (approximately 10 to the 7th rad/s).

High-frequency solitons in media with induced scattering from damped low-frequency waves with nonuniform dispersion and nonlinearity

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

Aseeva, N. V., E-mail: vtyutin@hse.ru; Gromov, E. M.; Tyutin, V. V.

2015-12-15

The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrödinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of secondorder linear dispersion and cubic nonlinearity are also taken into account. It is shown that the shift in the 3D spectrum of soliton wavenumbers toward the short-wavelength region is due to nonlinearity increasing in coordinate and to decreasing dispersion. Analytic results are confirmed by numerical calculations.

Ultra-low loss Si3N4 waveguides with low nonlinearity and high power handling capability.

PubMed

Tien, Ming-Chun; Bauters, Jared F; Heck, Martijn J R; Blumenthal, Daniel J; Bowers, John E

2010-11-08

We investigate the nonlinearity of ultra-low loss Si3N4-core and SiO2-cladding rectangular waveguides. The nonlinearity is modeled using Maxwell's wave equation with a small amount of refractive index perturbation. Effective n2 is used to describe the third-order nonlinearity, which is linearly proportional to the optical intensity. The effective n2 measured using continuous-wave self-phase modulation shows agreement with the theoretical calculation. The waveguide with 2.8-μm wide and 80-nm thick Si3N4 core has low loss and high power handling capability, with an effective n2 of about 9×10(-16) cm2/W.

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

NASA Astrophysics Data System (ADS)

Falco, Lauren E.

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

Simulation of broadband ground motion including nonlinear soil effects for a magnitude 6.5 earthquake on the Seattle fault, Seattle, Washington

USGS Publications Warehouse

Hartzell, S.; Leeds, A.; Frankel, A.; Williams, R.A.; Odum, J.; Stephenson, W.; Silva, W.

2002-01-01

The Seattle fault poses a significant seismic hazard to the city of Seattle, Washington. A hybrid, low-frequency, high-frequency method is used to calculate broadband (0-20 Hz) ground-motion time histories for a M 6.5 earthquake on the Seattle fault. Low frequencies (1 Hz) are calculated by a stochastic method that uses a fractal subevent size distribution to give an ω-2 displacement spectrum. Time histories are calculated for a grid of stations and then corrected for the local site response using a classification scheme based on the surficial geology. Average shear-wave velocity profiles are developed for six surficial geologic units: artificial fill, modified land, Esperance sand, Lawton clay, till, and Tertiary sandstone. These profiles together with other soil parameters are used to compare linear, equivalent-linear, and nonlinear predictions of ground motion in the frequency band 0-15 Hz. Linear site-response corrections are found to yield unreasonably large ground motions. Equivalent-linear and nonlinear calculations give peak values similar to the 1994 Northridge, California, earthquake and those predicted by regression relationships. Ground-motion variance is estimated for (1) randomization of the velocity profiles, (2) variation in source parameters, and (3) choice of nonlinear model. Within the limits of the models tested, the results are found to be most sensitive to the nonlinear model and soil parameters, notably the over consolidation ratio.

Cochlear compression: perceptual measures and implications for normal and impaired hearing.

PubMed

Oxenham, Andrew J; Bacon, Sid P

2003-10-01

This article provides a review of recent developments in our understanding of how cochlear nonlinearity affects sound perception and how a loss of the nonlinearity associated with cochlear hearing impairment changes the way sounds are perceived. The response of the healthy mammalian basilar membrane (BM) to sound is sharply tuned, highly nonlinear, and compressive. Damage to the outer hair cells (OHCs) results in changes to all three attributes: in the case of total OHC loss, the response of the BM becomes broadly tuned and linear. Many of the differences in auditory perception and performance between normal-hearing and hearing-impaired listeners can be explained in terms of these changes in BM response. Effects that can be accounted for in this way include poorer audiometric thresholds, loudness recruitment, reduced frequency selectivity, and changes in apparent temporal processing. All these effects can influence the ability of hearing-impaired listeners to perceive speech, especially in complex acoustic backgrounds. A number of behavioral methods have been proposed to estimate cochlear nonlinearity in individual listeners. By separating the effects of cochlear nonlinearity from other aspects of hearing impairment, such methods may contribute towards identifying the different physiological mechanisms responsible for hearing loss in individual patients. This in turn may lead to more accurate diagnoses and more effective hearing-aid fitting for individual patients. A remaining challenge is to devise a behavioral measure that is sufficiently accurate and efficient to be used in a clinical setting.

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

DTIC Science & Technology

2016-01-27

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

A Photonic Basis for Deriving Nonlinear Optical Response

ERIC Educational Resources Information Center

Andrews, David L.; Bradshaw, David S.

2009-01-01

Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as…

Modeling and Simulation of Linear and Nonlinear MEMS Scale Electromagnetic Energy Harvesters for Random Vibration Environments

PubMed Central

Sassani, Farrokh

2014-01-01

The simulation results for electromagnetic energy harvesters (EMEHs) under broad band stationary Gaussian random excitations indicate the importance of both a high transformation factor and a high mechanical quality factor to achieve favourable mean power, mean square load voltage, and output spectral density. The optimum load is different for random vibrations and for sinusoidal vibration. Reducing the total damping ratio under band-limited random excitation yields a higher mean square load voltage. Reduced bandwidth resulting from decreased mechanical damping can be compensated by increasing the electrical damping (transformation factor) leading to a higher mean square load voltage and power. Nonlinear EMEHs with a Duffing spring and with linear plus cubic damping are modeled using the method of statistical linearization. These nonlinear EMEHs exhibit approximately linear behaviour under low levels of broadband stationary Gaussian random vibration; however, at higher levels of such excitation the central (resonant) frequency of the spectral density of the output voltage shifts due to the increased nonlinear stiffness and the bandwidth broadens slightly. Nonlinear EMEHs exhibit lower maximum output voltage and central frequency of the spectral density with nonlinear damping compared to linear damping. Stronger nonlinear damping yields broader bandwidths at stable resonant frequency. PMID:24605063

Bright and singular soliton solutions of the conformable time-fractional Klein-Gordon equations with different nonlinearities

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Ansari, Reza

2018-07-01

Finding the exact solutions of nonlinear fractional differential equations has gained considerable attention, during the past two decades. In this paper, the conformable time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities are studied. Several exact soliton solutions, including the bright (non-topological) and singular soliton solutions are formally extracted by making use of the ansatz method. Results demonstrate that the method can efficiently handle the time-fractional Klein-Gordon equations with different nonlinearities.

Nonlinear Pedagogy and Its Role in Encouraging Twenty-First Century Competencies through Physical Education: A Singapore Experience

ERIC Educational Resources Information Center

Lee, Miriam Chang Yi; Chow, Jia Yi; Button, Chris; Tan, Clara Wee Keat

2017-01-01

Nonlinear Pedagogy is an exploratory approach to teaching and learning Physical Education that can be potentially effective to help children acquire relevant twenty-first century competencies. Underpinned by Ecological Dynamics, the focus of Nonlinear Pedagogy is on the learner and includes the provision of less prescriptive instructions and…

Vibrational dynamics of vocal folds using nonlinear normal modes.

PubMed

Pinheiro, Alan P; Kerschen, Gaëtan

2013-08-01

Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues. The results show very interesting and complex nonlinear phenomena including frequency-energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

Chaos and simple determinism in reversed field pinch plasmas: Nonlinear analysis of numerical simulation and experimental data

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

Watts, Christopher A.

In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulatemore » the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.« less

Turbulence of electrostatic electron cyclotron harmonic waves observed by Ogo 5.

NASA Technical Reports Server (NTRS)

Oya, H.

1972-01-01

Analysis of VLF emissions that have been observed near 3/2, 5/2, and 7/2 f sub H by Ogo 5 in the magnetosphere (f sub H is the electron cyclotron frequency) in the light of the mechanism used for the diffuse plasma resonance f sub Dn observed by Alouette 2 and Isis 1. The VLF emission is considered to be generated by nonlinear coupling mechanisms in certain portions of the observation as the f sub Dn is enhanced by its association with nonlinear wave-particle interaction of the electrostatic electron cyclotron harmonic wave, including the instability due to the nonlinear inverse Landau damping mechanism in the turbulence. The difference between the two observations is in the excitation mechanism of the turbulence; the turbulence in the plasma trough detected by Ogo 5 is due to natural origins, whereas the ionospheric topside sounder makes the plasma wave turbulence artificially by submitting strong stimulation pulses. Electron density values in the plasma trough are deduced by applying the f sub Dn-f sub N/f sub H relationship obtained from the Alouette 2 experiment as well as by applying the condition for the wave-particle nonlinear interactions. The electron density values reveal good agreement with the ion density values observed simultaneously by the highly sensitive ion mass spectrometer.

Self-Powered Temperature-Mapping Sensors Based on Thermo-Magneto-Electric Generator.

PubMed

Chun, Jinsung; Kishore, Ravi Anant; Kumar, Prashant; Kang, Min-Gyu; Kang, Han Byul; Sanghadasa, Mohan; Priya, Shashank

2018-04-04

We demonstrate a thermo-magneto-electric generator (TMEG) based on second-order phase transition of soft magnetic materials that provides a promising pathway for scavenging low-grade heat. It takes advantage of the cyclic magnetic forces of attraction and repulsion arising through ferromagnetic-to-paramagnetic phase transition to create mechanical vibrations that are converted into electricity through piezoelectric benders. To enhance the mechanical vibration frequency and thereby the output power of the TMEG, we utilize the nonlinear behavior of piezoelectric cantilevers and enhanced thermal transport through silver (Ag) nanoparticles (NPs) applied on the surface of a soft magnet. This results in large enhancement of the oscillation frequency reaching up to 9 Hz (300% higher compared with that of the prior literature). Optimization of the piezoelectric beam and Ag NP distribution resulted in the realization of nonlinear TMEGs that can generate a high output power of 80 μW across the load resistance of 0.91 MΩ, which is 2200% higher compared with that of the linear TMEG. Using a nonlinear TMEG, we fabricated and evaluated self-powered temperature-mapping sensors for monitoring the thermal variations across the surface. Combined, our results demonstrate that nonlinear TMEGs can provide additional functionality including temperature monitoring, thermal mapping, and powering sensor nodes.

A Mass Tracking Formulation for Bubbles in Incompressible Flow

DTIC Science & Technology

2012-10-14

incompressible flow to fully nonlinear compressible flow including the effects of shocks and rarefactions , and then subsequently making a number of...using the ideas from [19] to couple together incompressible flow with fully nonlinear compressible flow including shocks and rarefactions . The results...compressible flow including the effects of shocks and rarefactions , and then subsequently making a number of simplifying assumptions on the air flow

SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

DOEpatents

Collier, D.M.; Meeks, L.A.; Palmer, J.P.

1960-05-10

A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

Toward patient-specific articular contact mechanics

PubMed Central

Ateshian, Gerard A.; Henak, Corinne R.; Weiss, Jeffrey A.

2015-01-01

The mechanics of contacting cartilage layers is fundamentally important to understanding the development, homeostasis and pathology of diarthrodial joints. Because of the highly nonlinear nature of both the materials and the contact problem itself, numerical methods such as the finite element method are typically incorporated to obtain solutions. Over the course of five decades, we have moved from an initial qualitative understanding of articular cartilage material behavior to the ability to perform complex, three-dimensional contact analysis, including multiphasic material representations. This history includes the development of analytical and computational contact analysis methods that now provide the ability to perform highly nonlinear analyses. Numerical implementations of contact analysis based on the finite element method are rapidly advancing and will soon enable patient-specific analysis of joint contact mechanics using models based on medical image data. In addition to contact stress on the articular surfaces, these techniques can predict variations in strain and strain through the cartilage layers, providing the basis to predict damage and failure. This opens up exciting areas for future research and application to patient-specific diagnosis and treatment planning applied to a variety of pathologies that affect joint function and cartilage homeostasis. PMID:25698236

Risk Preferences, Probability Weighting, and Strategy Tradeoffs in Wildfire Management.

PubMed

Hand, Michael S; Wibbenmeyer, Matthew J; Calkin, David E; Thompson, Matthew P

2015-10-01

Wildfires present a complex applied risk management environment, but relatively little attention has been paid to behavioral and cognitive responses to risk among public agency wildfire managers. This study investigates responses to risk, including probability weighting and risk aversion, in a wildfire management context using a survey-based experiment administered to federal wildfire managers. Respondents were presented with a multiattribute lottery-choice experiment where each lottery is defined by three outcome attributes: expenditures for fire suppression, damage to private property, and exposure of firefighters to the risk of aviation-related fatalities. Respondents choose one of two strategies, each of which includes "good" (low cost/low damage) and "bad" (high cost/high damage) outcomes that occur with varying probabilities. The choice task also incorporates an information framing experiment to test whether information about fatality risk to firefighters alters managers' responses to risk. Results suggest that managers exhibit risk aversion and nonlinear probability weighting, which can result in choices that do not minimize expected expenditures, property damage, or firefighter exposure. Information framing tends to result in choices that reduce the risk of aviation fatalities, but exacerbates nonlinear probability weighting. © 2015 Society for Risk Analysis.

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.

Survey of optimization techniques for nonlinear spacecraft trajectory searches

NASA Technical Reports Server (NTRS)

Wang, Tseng-Chan; Stanford, Richard H.; Sunseri, Richard F.; Breckheimer, Peter J.

1988-01-01

Mathematical analysis of the optimal search of a nonlinear spacecraft trajectory to arrive at a set of desired targets is presented. A high precision integrated trajectory program and several optimization software libraries are used to search for a converged nonlinear spacecraft trajectory. Several examples for the Galileo Jupiter Orbiter and the Ocean Topography Experiment (TOPEX) are presented that illustrate a variety of the optimization methods used in nonlinear spacecraft trajectory searches.

Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru

2017-11-01

This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2  +  1)D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2  +  1)D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.

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.

Analytical and Computational Modeling of Mechanical Waves in Microscale Granular Crystals: Nonlinearity and Rotational Dynamics

NASA Astrophysics Data System (ADS)

Wallen, Samuel P.

Granular media are one of the most common, yet least understood forms of matter on earth. The difficulties in understanding the physics of granular media stem from the fact that they are typically heterogeneous and highly disordered, and the grains interact via nonlinear contact forces. Historically, one approach to reducing these complexities and gaining new insight has been the study of granular crystals, which are ordered arrays of similarly-shaped particles (typically spheres) in Hertzian contact. Using this setting, past works explored the rich nonlinear dynamics stemming from contact forces, and proposed avenues where such granular crystals could form designer, dynamically responsive materials, which yield beneficial functionality in dynamic regimes. In recent years, the combination of self-assembly fabrication methods and laser ultrasonic experimental characterization have enabled the study of granular crystals at microscale. While our intuition may suggest that these microscale granular crystals are simply scaled-down versions of their macroscale counterparts, in fact, the relevant physics change drastically; for example, short-range adhesive forces between particles, which are negligible at macroscale, are several orders of magnitude stronger than gravity at microscale. In this thesis, we present recent advances in analytical and computational modeling of microscale granular crystals, in particular concerning the interplay of nonlinearity, shear interactions, and particle rotations, which have previously been either absent, or included separately at macroscale. Drawing inspiration from past works on phononic crystals and nonlinear lattices, we explore problems involving locally-resonant metamaterials, nonlinear localized modes, amplitude-dependent energy partition, and other rich dynamical phenomena. This work enhances our understanding of microscale granular media, which may find applicability in fields such as ultrasonic wave tailoring, signal processing, shock and vibration mitigation, and powder processing.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Relationships between nonlinear normal modes and response to random inputs

NASA Astrophysics Data System (ADS)

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2017-02-01

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.

Multidisciplinary Analysis and Optimal Design: As Easy as it Sounds?

NASA Technical Reports Server (NTRS)

Moore, Greg; Chainyk, Mike; Schiermeier, John

2004-01-01

The viewgraph presentation examines optimal design for precision, large aperture structures. Discussion focuses on aspects of design optimization, code architecture and current capabilities, and planned activities and collaborative area suggestions. The discussion of design optimization examines design sensitivity analysis; practical considerations; and new analytical environments including finite element-based capability for high-fidelity multidisciplinary analysis, design sensitivity, and optimization. The discussion of code architecture and current capabilities includes basic thermal and structural elements, nonlinear heat transfer solutions and process, and optical modes generation.

Improvement of SPM nonlinear limit by chirped duobinary PolSK transmission

NASA Astrophysics Data System (ADS)

Yang, Lixiu; Fan, Jiayu; Wang, Lutang; Huang, Zhaoming

2005-02-01

In today's terrestrial long-haul optical fiber communication systems, high channel powers are required to obtain a large transmission distance with reasonable optical amplifier spacing. In such systems, however, the presence of nonlinear effects such as the self-phase modulation (SPM) and the fiber dispersion as well as their combined effects, called SPM-induced nonlinear limitation or SPM limit, will seriously degrade the system performances in respect of the effective transmission distance and ultimately become a limiting factor in high-speed, long-haul optical fiber transmission.In this paper, a new transmission format: chirped duobinary PolSK transmission, has been proposed to generate a pre-chirped duobianry signal with fixed polarity (either positive or negative), which is modulated by a PolSK modulator. This format is based on a transmitter setup consisting of a duobinary PolSK Modulation transmitter followed by an additional phase modulator. The chirped duobinary PolSK transmission reduces the signal degradation and spectral broadening in the nonlinear regime significantly. Thus it shifts this SPM nonlinear limit to enable more relaxed dispersion compensation at high optical power compared to the conventional duobinary schemes.The simulation results show chirped duobinary PolSK transmission enlarges the dispersion limited transmission distance, increases the dispersion tolerance and overcome the SPM nonlinear limit.

The Vestibular System Implements a Linear–Nonlinear Transformation In Order to Encode Self-Motion

PubMed Central

Massot, Corentin; Schneider, Adam D.; Chacron, Maurice J.; Cullen, Kathleen E.

2012-01-01

Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular) sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (∼50%) attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways. PMID:22911113

Theoretical investigation of intensity-dependent optical nonlinearity in graphene-aided D-microfiber

NASA Astrophysics Data System (ADS)

Shah, Manoj Kumar; Lu, Rongguo; Zhang, Yali; Ye, Shengwei; Zhang, Shangjian; Liu, Yong

2018-01-01

We theoretically investigate the intensity-dependent optical nonlinearity in graphene-aided D-microfiber, by tuning the chemical potential of graphene and varying radial distance and radii of the D-microfiber. Utilizing an interplay between graphene and the enhanced evanescent field of a guided mode in the waveguide of interest, the net utility of nonlinear coefficient is harnessed up to a very high value of 106 W-1m-1. Importantly, which is ∼ two orders of magnitude larger than in PMMA-graphene-PMMA waveguide. The highly dispersive nature of the waveguide, D ∼ 103 ps/nm-km, and large nonlinear figure-of-merit, FOMNL ∼ 1.29, have raised the possibilities of utilizing slow light structures to operate devices at few watts power level with microscale length. These studies have opened one window towards the next-generation all fiber-optic graphene nonlinear optical devices.