Nonlinear optics and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Chen, C. H.
1990-08-01
The author was invited by the Institute of Atomic and Molecular Sciences, Academia Sinica, in Taiwan to give six lectures on nonlinear optics. The participants included graduate students, postdoctoral fellows, research staff, and professors from several research organizations and universities. Extensive discussion followed each lecture. Since both the Photophysics Group at Oak Ridge National Laboratory (ORNL) and Institute of Atomic and Molecular Sciences in Taiwan have been actively participating in nonlinear optics research, the discussions are very beneficial to ORNL programs. The author also visited several laboratories at IAMS to exchange research ideas on nonlinear optics.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
ERIC Educational Resources Information Center
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Orbital HP-Clouds for Solving Schr?dinger Equation inQuantum Mechanics
Chen, J; Hu, W; Puso, M
2006-10-19
Solving Schroedinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions, in addition to the highly coupled nature between wave functions. This work introduces orbital and polynomial enrichment functions to the partition of unity for solution of Schroedinger equation under the framework of HP-Clouds. An intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed. Due to the employment of higher order basis functions, a higher order stabilized conforming nodal integration is developed. The proposed methods are implemented using the density functional theory for solution of Schroedinger equation. Analysis of several single and multi-electron/nucleus structures demonstrates the effectiveness of the proposed method.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
[Nonlinear magnetohydrodynamics
Not Available
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday`s law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm`s law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile.
NASA Astrophysics Data System (ADS)
Lauterborn, Werner; Kurz, Thomas; Akhatov, Iskander
At high sound intensities or long propagation distances at
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.
Tomlin, R.
1990-01-27
A nonlinear oscillator design was imported from Cornell modified, and built for the purpose of simulating the chaotic states of a forced pendulum. Similar circuits have been investigated in the recent nonlinear explosion.
NASA Astrophysics Data System (ADS)
Hausmann, B. J. M.; Bulu, I.; Venkataraman, V.; Deotare, P.; Lončar, M.
2014-05-01
Despite progress towards integrated diamond photonics, studies of optical nonlinearities in diamond have been limited to Raman scattering in bulk samples. Diamond nonlinear photonics, however, could enable efficient, in situ frequency conversion of single photons emitted by diamond's colour centres, as well as stable and high-power frequency microcombs operating at new wavelengths. Both of these applications depend crucially on efficient four-wave mixing processes enabled by diamond's third-order nonlinearity. Here, we have realized a diamond nonlinear photonics platform by demonstrating optical parametric oscillation via four-wave mixing using single-crystal ultrahigh-quality-factor (1 × 106) diamond ring resonators operating at telecom wavelengths. Threshold powers as low as 20 mW are measured, and up to 20 new wavelengths are generated from a single-frequency pump laser. We also report the first measurement of the nonlinear refractive index due to the third-order nonlinearity in diamond at telecom wavelengths.
Nonlinear rotordynamics analysis
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.
Stationary nonlinear Airy beams
Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.
2011-08-15
We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.
Organic nonlinear optical materials
NASA Technical Reports Server (NTRS)
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinear optics at interfaces
Chen, C.K.
1980-12-01
Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory.
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.
Nonlinearly realized extended supergravity
Izawa, K.-I.; Nakai, Y.; Takahashi, Ryo
2010-10-01
We provide a nonlinear realization of supergravity with an arbitrary number of supersymmetries by means of coset construction. The number of gravitino degrees of freedom counts the number of supersymmetries, which will possibly be probed in future experiments. We also consider Goldstino embedding in the construction to discuss the relation to nonlinear realizations with rigid supersymmetries.
Friction and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
2016-07-01
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
NASA Astrophysics Data System (ADS)
McLaughlin, David W.
1994-01-01
The principal investigator, together with two post-doctoral fellows, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals, propagation through random nonlinear media, cross polarization instabilities and optical shocks for propagation along nonlinear optical fibers, and the dynamics of bistable optical switches coupled through both diffusion and diffraction. In the first project the extremely strong nonlinear response of a CW laser beam in a nematic liquid crystal medium produced striking undulation and filamentation of the CW beam which was observed experimentally and explained theoretically. In the second project the interaction of randomness with nonlinearity was investigated, as well as an effective randomness due to the simultaneous presence of many nonlinear instabilities. In the polarization problems theoretical hyperbolic structure (instabilities and homoclinic orbits) in the coupled nonlinear Schroedinger (NLS) equations was identified and used to explain cross polarization instabilities in both the focusing and defocusing cases, as well as to describe optical shocking phenomena. For the coupled bistable optical switches, a numerical code was carefully developed in two spatial and one temporal dimensions. The code was used to study the decay of temporal transients to 'on-off' steady states in a geometry which includes forward and backward longitudinal propagation, together with one dimensional transverse coupling of both electromagnetic diffraction and carrier diffusion.
NASA Technical Reports Server (NTRS)
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Whitney, Paul
1987-01-01
A technique for identifying nonlinear systems was introduced, beginning with a single input-single output system. Assuming the system is initially at rest, the first kernel (first convolution integral in the continuous case or first convolution sum in the discrete case) was calculated. A controllable and observable linear realization was then obtained in a particular canonical form. The actual nonlinear system was probed with an appropriate input (or inputs) and the output (or outputs) determined. For the linear system, the input was computed that produces the same output. In the difference between the inputs to the nonlinear and linear systems, basic information was found about the nonlinear system. There is an interesting class of nonlinear systems for which this type of identification scheme should prove to be accurate.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis. PMID:27250151
Nonlinear ordinary difference equations
NASA Technical Reports Server (NTRS)
Caughey, T. K.
1979-01-01
Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.
Martin, G; McGarel, S
2001-01-01
A mill is a mechanical device that grinds mined or processed material into small particles. The process is known to display significant deadtime, and, more notably, severe nonlinear behavior. Over the past 25 years attempts at continuous mill control have met varying degrees of failure, mainly due to model mismatch caused by changes in the mill process gains. This paper describes an on-line control application on a closed-circuit cement mill that uses nonlinear model predictive control technology. The nonlinear gains for the control model are calculated on-line from a neural network model of the process.
Multipole nonlinearity of metamaterials
Petschulat, J.; Chipouline, A.; Tuennermann, A.; Pertsch, T.; Menzel, C.; Rockstuhl, C.; Lederer, F.
2009-12-15
We report on the linear and nonlinear optical response of metamaterials evoked by first- and second-order multipoles. The analytical ground on which our approach is based permits for new insights into the functionality of metamaterials. For the sake of clarity we focus here on a key geometry, namely, the split-ring resonator, although the introduced formalism can be applied to arbitrary structures. We derive the equations that describe linear and nonlinear light propagation where special emphasis is put on second-harmonic generation. This contribution basically aims at stretching versatile and existing concepts to describe light propagation in nonlinear media toward the realm of metamaterials.
Nonlinear optomechanical pressure
NASA Astrophysics Data System (ADS)
Conti, Claudio; Boyd, Robert
2014-03-01
A transparent material exhibits ultrafast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, such as optical manipulation, biophysics, cavity optomechanics, quantum optics, and optical tractors, and is relevant in fundamental problems such as the Abraham-Minkoswky dilemma or the Casimir effect. Here, we show that an ultrafast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order-of-magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.
NASA Technical Reports Server (NTRS)
1984-01-01
Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.
Library for Nonlinear Optimization
2001-10-09
OPT++ is a C++ object-oriented library for nonlinear optimization. This incorporates an improved implementation of an existing capability and two new algorithmic capabilities based on existing journal articles and freely available software.
Nonlinear Dynamics in Cardiology
Krogh-Madsen, Trine; Christini, David J.
2013-01-01
The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counter-intuitively, result from a gradual change in a system parameter –this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work have suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity. PMID:22524390
Nonlinear Refractive Properties
NASA Technical Reports Server (NTRS)
Vikram, Chandra S.; Witherow, William K.
2001-01-01
Using nonlinear refractive properties of a salt-water solution at two wavelengths, numerical analysis has been performed to extract temperature and concentration from interferometric fringe data. The theoretical study, using a commercially available equation solving software, starts with critical fringe counting needs and the role of nonlinear refractive properties in such measurements. Finally, methodology of the analysis, codes, fringe counting accuracy needs, etc. is described in detail.
Nonlinear systems in medicine.
Higgins, John P.
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107
NASA Astrophysics Data System (ADS)
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear optomechanics with graphene
NASA Astrophysics Data System (ADS)
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Engineered nonlinear lattices.
Clausen, C B; Christiansen, P L; Torner, L; Gaididei, Y B
1999-11-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term a quasilattice, which interpolates between a lattice system and a continuous system. PMID:11970457
Nonlinear aerodynamic wing design
NASA Technical Reports Server (NTRS)
Bonner, Ellwood
1985-01-01
The applicability of new nonlinear theoretical techniques is demonstrated for supersonic wing design. The new technology was utilized to define outboard panels for an existing advanced tactical fighter model. Mach 1.6 maneuver point design and multi-operating point compromise surfaces were developed and tested. High aerodynamic efficiency was achieved at the design conditions. A corollary result was that only modest supersonic penalties were incurred to meet multiple aerodynamic requirements. The nonlinear potential analysis of a practical configuration arrangement correlated well with experimental data.
Nonlinear trajectory navigation
NASA Astrophysics Data System (ADS)
Park, Sang H.
Trajectory navigation entails the solution of many different problems that arise due to uncertain knowledge of the spacecraft state, including orbit prediction, correction maneuver design, and trajectory estimation. In practice, these problems are usually solved based on an assumption that linear dynamical models sufficiently approximate the local trajectory dynamics and their associated statistics. However, astrodynamics problems are nonlinear in general and linear spacecraft dynamics models can fail to characterize the true trajectory dynamics when the system is subject to a highly unstable environment or when mapped over a long time period. This limits the performance of traditional navigation techniques and can make it difficult to perform precision analysis or robust navigation. This dissertation presents an alternate method for spacecraft trajectory navigation based on a nonlinear local trajectory model and their statistics in an analytic framework. For a given reference trajectory, we first solve for the higher order Taylor series terms that describe the localized nonlinear motion and develop an analytic expression for the relative solution flow. We then discuss the nonlinear dynamical mapping of a spacecraft's probability density function by solving the Fokker-Planck equation for a deterministic system. From this result we derive an analytic method for orbit uncertainty propagation which can replicate Monte-Carlo simulations with the benefit of added flexibility in initial orbit statistics. Using this approach, we introduce the concept of the statistically correct trajectory where we directly incorporate statistical information about an orbit state into the trajectory design process. As an extension of this concept, we define a nonlinear statistical targeting method where we solve for a correction maneuver which intercepts the desired target on average. Then we apply our results to a Bayesian filtering problem to obtain a general filtering algorithm for
NASA Astrophysics Data System (ADS)
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Intramolecular and nonlinear dynamics
Davis, M.J.
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Generalized Nonlinear Yule Models
NASA Astrophysics Data System (ADS)
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Callen, J. D.
2002-11-04
The primary efforts this year have focused on exploring the nonlinear evolution of localized interchange instabilities, some extensions of neoclassical tearing mode theory, and developing a model for the dynamic electrical conductivity in a bumpy cylinder magnetic field. In addition, we have vigorously participated in the computationally-focused NIMROD and CEMM projects.
Universal nonlinear entanglement witnesses
Kotowski, Marcin; Kotowski, Michal
2010-06-15
We give a universal recipe for constructing nonlinear entanglement witnesses able to detect nonclassical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The constructed witnesses are expressed in terms of expectation values of observables. As such, they are, at least in principle, measurable in experiments.
Nonlinear growing neutrino cosmology
NASA Astrophysics Data System (ADS)
Ayaita, Youness; Baldi, Marco; Führer, Florian; Puchwein, Ewald; Wetterich, Christof
2016-03-01
The energy scale of dark energy, ˜2 ×10-3 eV , is a long way off compared to all known fundamental scales—except for the neutrino masses. If dark energy is dynamical and couples to neutrinos, this is no longer a coincidence. The time at which dark energy starts to behave as an effective cosmological constant can be linked to the time at which the cosmic neutrinos become nonrelativistic. This naturally places the onset of the Universe's accelerated expansion in recent cosmic history, addressing the why-now problem of dark energy. We show that these mechanisms indeed work in the growing neutrino quintessence model—even if the fully nonlinear structure formation and backreaction are taken into account, which were previously suspected of spoiling the cosmological evolution. The attractive force between neutrinos arising from their coupling to dark energy grows as large as 106 times the gravitational strength. This induces very rapid dynamics of neutrino fluctuations which are nonlinear at redshift z ≈2 . Nevertheless, a nonlinear stabilization phenomenon ensures only mildly nonlinear oscillating neutrino overdensities with a large-scale gravitational potential substantially smaller than that of cold dark matter perturbations. Depending on model parameters, the signals of large-scale neutrino lumps may render the cosmic neutrino background observable.
Teaching the Nonlinear Pendulum.
ERIC Educational Resources Information Center
Zheng, T. F.; And Others
1994-01-01
Emphasizes two aspects for a calculus-based physics course: applying calculus and numerical integral methods to determine the theoretical period of a pendulum with nonlinear motion, and achieving theoretical and experimental results by using "MathCad" software and a microcomputer-based laboratory (MBL) system. (MVL)
Nonlinear Theory and Breakdown
NASA Technical Reports Server (NTRS)
Smith, Frank
2007-01-01
The main points of recent theoretical and computational studies on boundary-layer transition and turbulence are to be highlighted. The work is based on high Reynolds numbers and attention is drawn to nonlinear interactions, breakdowns and scales. The research focuses in particular on truly nonlinear theories, i.e. those for which the mean-flow profile is completely altered from its original state. There appear to be three such theories dealing with unsteady nonlinear pressure-displacement interactions (I), with vortex/wave interactions (II), and with Euler-scale flows (III). Specific recent findings noted for these three, and in quantitative agreement with experiments, are the following. Nonlinear finite-time break-ups occur in I, leading to sublayer eruption and vortex formation; here the theory agrees with experiments (Nishioka) regarding the first spike. II gives rise to finite-distance blowup of displacement thickness, then interaction and break-up as above; this theory agrees with experiments (Klebanoff, Nishioka) on the formation of three-dimensional streets. III leads to the prediction of turbulent boundary-layer micro-scale, displacement-and stress-sublayer-thicknesses.
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.
Cubication of Conservative Nonlinear Oscillators
ERIC Educational Resources Information Center
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Nonlinear metamaterials for holography.
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency-the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Nonlinear metamaterials for holography
NASA Astrophysics Data System (ADS)
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-08-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency--the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed.
Nonlinear Photonics 2014: introduction.
Akhmediev, N; Kartashov, Yaroslav
2015-01-12
International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Nonlinear differential equations
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinear terahertz superconducting plasmonics
Wu, Jingbo; Liang, Lanju; Jin, Biaobing E-mail: tonouchi@ile.osaka-u.ac.jp Kang, Lin; Xu, Weiwei; Chen, Jian; Wu, Peiheng E-mail: tonouchi@ile.osaka-u.ac.jp; Zhang, Caihong; Kawayama, Iwao; Murakami, Hironaru; Tonouchi, Masayoshi E-mail: tonouchi@ile.osaka-u.ac.jp; Wang, Huabing
2014-10-20
Nonlinear terahertz (THz) transmission through subwavelength hole array in superconducting niobium nitride (NbN) film is experimentally investigated using intense THz pulses. The good agreement between the measurement and numerical simulations indicates that the field strength dependent transmission mainly arises from the nonlinear properties of the superconducting film. Under weak THz pulses, the transmission peak can be tuned over a frequency range of 145 GHz which is attributed to the high kinetic inductance of 50 nm-thick NbN film. Utilizing the THz pump-THz probe spectroscopy, we study the dynamic process of transmission spectra and demonstrate that the transition time of such superconducting plasmonic device is within 5 ps.
Nonlinear chiral transport phenomena
NASA Astrophysics Data System (ADS)
Chen, Jiunn-Wei; Ishii, Takeaki; Pu, Shi; Yamamoto, Naoki
2016-06-01
We study the nonlinear responses of relativistic chiral matter to the external fields such as the electric field E , gradients of temperature and chemical potential, ∇T and ∇μ . Using the kinetic theory with Berry curvature corrections under the relaxation time approximation, we compute the transport coefficients of possible new electric currents that are forbidden in usual chirally symmetric matter but are allowed in chirally asymmetric matter by parity. In particular, we find a new type of electric current proportional to ∇μ ×E due to the interplay between the effects of the Berry curvature and collisions. We also derive an analog of the "Wiedemann-Franz" law specific for anomalous nonlinear transport in relativistic chiral matter.
Optothermal nonlinearity of silica aerogel
NASA Astrophysics Data System (ADS)
Braidotti, Maria Chiara; Gentilini, Silvia; Fleming, Adam; Samuels, Michiel C.; Di Falco, Andrea; Conti, Claudio
2016-07-01
We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass (≃10-12 m2/W), with negligible optical nonlinear absorption. The nonlinear coefficient can be increased to values in the range of 10-10 m2/W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.
Leitão, J C; Miotto, J M; Gerlach, M; Altmann, E G
2016-07-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼x (β) ,β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. In this paper, we investigate the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)-(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed. PMID:27493764
2016-01-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼xβ,β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. In this paper, we investigate the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)–(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed. PMID:27493764
Ultrafast Thermal Nonlinearity
Khurgin, Jacob B.; Sun, Greg; Chen, Wei Ting; Tsai, Wei-Yi; Tsai, Din Ping
2015-01-01
Third order nonlinear optical phenomena explored in the last half century have been predicted to find wide range of applications in many walks of life, such as all-optical switching, routing, and others, yet this promise has not been fulfilled primarily because the strength of nonlinear effects is too low when they are to occur on the picosecond scale required in today’s signal processing applications. The strongest of the third-order nonlinearities, engendered by thermal effects, is considered to be too slow for the above applications. In this work we show that when optical fields are concentrated into the volumes on the scale of few tens of nanometers, the speed of the thermo-optical effects approaches picosecond scale. Such a sub-diffraction limit concentration of field can be accomplished with the use of plasmonic effects in metal nanoparticles impregnating the thermo-optic dielectric (e.g. amorphous Si) and leads to phase shifts sufficient for all optical switching on ultrafast scale. PMID:26644322
Duck, F
2010-01-01
The propagation of acoustic waves is a fundamentally non-linear process, and only waves with infinitesimally small amplitudes may be described by linear expressions. In practice, all ultrasound propagation is associated with a progressive distortion in the acoustic waveform and the generation of frequency harmonics. At the frequencies and amplitudes used for medical diagnostic scanning, the waveform distortion can result in the formation of acoustic shocks, excess deposition of energy, and acoustic saturation. These effects occur most strongly when ultrasound propagates within liquids with comparatively low acoustic attenuation, such as water, amniotic fluid, or urine. Attenuation by soft tissues limits but does not extinguish these non-linear effects. Harmonics may be used to create tissue harmonic images. These offer improvements over conventional B-mode images in spatial resolution and, more significantly, in the suppression of acoustic clutter and side-lobe artefacts. The quantity B/A has promise as a parameter for tissue characterization, but methods for imaging B/A have shown only limited success. Standard methods for the prediction of tissue in-situ exposure from acoustic measurements in water, whether for regulatory purposes, for safety assessment, or for planning therapeutic regimes, may be in error because of unaccounted non-linear losses. Biological effects mechanisms are altered by finite-amplitude effects. PMID:20349813
Nonlinearity without superluminality
NASA Astrophysics Data System (ADS)
Kent, Adrian
2005-07-01
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schrödinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.
Nonlinearity without superluminality
Kent, Adrian
2005-07-15
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schroedinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.
Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics. PMID:25401574
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.
Identification of nonlinear boundary effects using nonlinear normal modes
NASA Astrophysics Data System (ADS)
Ahmadian, Hamid; Zamani, Arash
2009-08-01
Local nonlinear effects due to micro-slip/slap introduced in boundaries of structures have dominant influence on their lower modal model. This paper studies these effects by experimentally observing the behavior of a clamped-free beam structure with local nonlinearities due to micro-slip at the clamped end. The structure is excited near one of its resonance frequencies and recorded responses are employed to identify the nonlinear effects at the boundary. The nonlinear response of structure is defined using an amplitude-dependent nonlinear normal mode identified from measured responses. A new method for reconstructing nonlinear normal mode is represented in this paper by relating the nonlinear normal mode to the clamped end displacement-dependent stiffness parameters using an eigensensitivity analysis. Solution of obtained equations results equivalent stiffness models at different vibration amplitudes and the corresponding nonlinear normal mode is identified. The approach results nonlinear modes with efficient capabilities in predicting dynamical behavior of the structure at different loading conditions. To evaluate the efficiency of the identified model, the structure is excited at higher excitation load levels than those employed in identification procedures and the observed responses are compared with the predictions of the model at the corresponding input force levels. The predictions are in good agreement with the observed behavior indicating success of identification procedure in capturing the physical merits involve in the boundary local nonlinearities.
Frequency domain nonlinear optics
NASA Astrophysics Data System (ADS)
Legare, Francois
2016-05-01
The universal dilemma of gain narrowing occurring in fs amplifiers prevents ultra-high power lasers from delivering few-cycle pulses. This problem is overcome by a new amplification concept: Frequency domain Optical Parametric Amplification - FOPA. It enables simultaneous up-scaling of peak power and amplified spectral bandwidth and can be performed at any wavelength range of conventional amplification schemes, however, with the capability to amplify single cycles of light. The key idea for amplification of octave-spanning spectra without loss of spectral bandwidth is to amplify the broad spectrum ``slice by slice'' in the frequency domain, i.e. in the Fourier plane of a 4f-setup. The striking advantages of this scheme, are its capability to amplify (more than) one octave of bandwidth without shorting the corresponding pulse duration. This is because ultrabroadband phase matching is not defined by the properties of the nonlinear crystal employed but the number of crystals employed. In the same manner, to increase the output energy one simply has to increase the spectral extension in the Fourier plane and to add one more crystal. Thus, increasing pulse energy and shortening its duration accompany each other. A proof of principle experiment was carried out at ALLS on the sub-two cycle IR beam line and yielded record breaking performance in the field of few-cycle IR lasers. 100 μJ two-cycle pulses from a hollow core fibre compression setup were amplified to 1.43mJ without distorting spatial or temporal properties. Pulse duration at the input of FOPA and after FOPA remains the same. Recently, we have started upgrading this system to be pumped by 250 mJ to reach 40 mJ two-cycle IR few-cycle pulses and latest results will be presented at the conference. Furthermore, the extension of the concept of FOPA to other nonlinear optical processes will be discussed. Frequency domain nonlinear optics.
Nonlinear magnetohydrodynamics from gravity
NASA Astrophysics Data System (ADS)
Hansen, James; Kraus, Per
2009-04-01
We apply the recently established connection between nonlinear fluid dynamics and AdS gravity to the case of the dyonic black brane in AdS4. This yields the equations of fluid dynamics for a 2+1 dimensional charged fluid in a background magnetic field. We construct the gravity solution to second order in the derivative expansion. From this we find the fluid dynamical stress tensor and charge current to second and third order in derivatives respectively, along with values for the associated transport coefficients.
Optical correlator tracking nonlinearity
NASA Astrophysics Data System (ADS)
Gregory, Don A.; Kirsch, James C.; Johnson, John L.
1987-01-01
A limitation observed in the tracking ability of optical correlators is reported. It is shown by calculations that an inherent nonlinearity exists in many optical correlator configurations, with the problem manifesting itself in a mismatch of the input scene with the position of the correlation signal. Results indicate that some care must be given to the selection of components and their configuration in constructing an optical correlator which exhibits true translational invariance. An input test scene is shown along with the correlation spot and cross hairs from a contrast detector; the offset is apparent.
Nonlinear methods for communications
NASA Astrophysics Data System (ADS)
1992-08-01
An innovative communication system has been developed. This system has the potential for improved secure communication for covert operations. By modulating data on the chaotic signal used to synchronize two nonlinear systems, they have created a Low Probability of Intercept (LPI) communications system. The researchers derived the equations which govern the system, made models of the system, and performed numerical simulations to test these models. The theoretical and numerical studies of this system have been validated by experiment. A recent design improvement has led to a system that synchronizes at 0 db Signal-to-Noise. This development holds the promise of a Low Probability of Detection (LPD) system.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
Nonlinear refraction in vitreous humor.
Rockwell, B A; Roach, W P; Rogers, M E; Mayo, M W; Toth, C A; Cain, C P; Noojin, G D
1993-11-01
We extend the application of the z-scan technique to determine the nonlinear refractive index (n(2)) for human and rabbit vitreous humor, water, and physiological saline. In these measurements there were nonlinear contributions to the measured signal from the aqueous samples and the quartz cell that held the sample. Measurements were made with 60-ps pulses at 532 nm. To our knowledge, this is the first measurement of the nonlinear refractive properties of biological material. PMID:19829406
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
T. MILONNI; G. CSANAK; ET AL
1999-07-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). The project objectives were to explore theoretically various aspects of nonlinear atom optics effects in cold-atom waves and traps. During the project a major development occurred the observation, by as many as a dozen experimental groups, of Bose-Einstein condensation (BEC) in cold-atom traps. This stimulated us to focus our attention on those aspects of nonlinear atom optics relating to BEC, in addition to continuing our work on a nonequilibrium formalism for dealing with the interaction of an electromagnetic field with multi-level atomic systems, allowing for macroscopic coherence effects such as BEC. Studies of several problems in BEC physics have been completed or are near completion, including the suggested use of external electric fields to modify the nature of the interatomic interaction in cold-atom traps; properties of two-phase condensates; and molecular loss processes associated with BEC experiments involving a so-called Feshbach resonance.
Improved nonlinear prediction method
NASA Astrophysics Data System (ADS)
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Nonlinear Attitude Filtering Methods
NASA Technical Reports Server (NTRS)
Markley, F. Landis; Crassidis, John L.; Cheng, Yang
2005-01-01
This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST, the super-iterated extended Kalman filter, the interlaced extended Kalman filter, and the second-order Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A two-step approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, including particle filters and a Bayesian filter based on a non-Gaussian, finite-parameter probability density function on SO(3). Finally, the predictive filter, nonlinear observers and adaptive approaches are shown. The strengths and weaknesses of the various approaches are discussed.
Problems in nonlinear resistive MHD
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Nonlinear ptychographic coherent diffractive imaging.
Odstrcil, M; Baksh, P; Gawith, C; Vrcelj, R; Frey, J G; Brocklesby, W S
2016-09-01
Ptychographic Coherent diffractive imaging (PCDI) is a significant advance in imaging allowing the measurement of the full electric field at a sample without use of any imaging optics. So far it has been confined solely to imaging of linear optical responses. In this paper we show that because of the coherence-preserving nature of nonlinear optical interactions, PCDI can be generalised to nonlinear optical imaging. We demonstrate second harmonic generation PCDI, directly revealing phase information about the nonlinear coefficients, and showing the general applicability of PCDI to nonlinear interactions. PMID:27607631
TOPICAL REVIEW: Nonlinear photonic crystals: III. Cubic nonlinearity
NASA Astrophysics Data System (ADS)
Babin, Anatoli; Figotin, Alexander
2003-10-01
Weakly nonlinear interactions between wavepackets in a lossless periodic dielectric medium are studied based on the classical Maxwell equations with a cubic nonlinearity. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the spatial range of a probing wavepacket is much smaller than the dimension of the medium sample, and it is not too small compared with the dimension of the primitive cell. These nonlinear processes are naturally described in terms of the cubic interaction phase function based on the dispersion relations of the underlying linear periodic medium. It turns out that only a few quadruplets of modes have significant nonlinear interactions. They are singled out by a system of selection rules including the group velocity, frequency and phase matching conditions. It turns out that the intrinsic symmetries of the cubic interaction phase stemming from assumed inversion symmetry of the dispersion relations play a significant role in the cubic nonlinear interactions. We also study canonical forms of the cubic interaction phase leading to a complete quantitative classification of all possible significant cubic interactions. The classification is ultimately based on a universal system of indices reflecting the intensity of nonlinear interactions.
Dislocation nonlinearity and nonlinear wave processes in polycrystals with dislocations
NASA Astrophysics Data System (ADS)
Nazarov, V. E.
2016-09-01
Based on the modification of the linear part of the Granato-Lücke dislocation theory of absorption, the equation of state of polycrystalline solids with dissipative and reactive nonlinearity has been derived. The nonlinear effects of the interaction and self-action of longitudinal elastic waves in such media have been theoretically studied.
Multimodal Nonlinear Optical Microscopy
Yue, Shuhua; Slipchenko, Mikhail N.; Cheng, Ji-Xin
2013-01-01
Because each nonlinear optical (NLO) imaging modality is sensitive to specific molecules or structures, multimodal NLO imaging capitalizes the potential of NLO microscopy for studies of complex biological tissues. The coupling of multiphoton fluorescence, second harmonic generation, and coherent anti-Stokes Raman scattering (CARS) has allowed investigation of a broad range of biological questions concerning lipid metabolism, cancer development, cardiovascular disease, and skin biology. Moreover, recent research shows the great potential of using CARS microscope as a platform to develop more advanced NLO modalities such as electronic-resonance-enhanced four-wave mixing, stimulated Raman scattering, and pump-probe microscopy. This article reviews the various approaches developed for realization of multimodal NLO imaging as well as developments of new NLO modalities on a CARS microscope. Applications to various aspects of biological and biomedical research are discussed. PMID:24353747
Nonlinear integrable ion traps
Nagaitsev, S.; Danilov, V.; /SNS Project, Oak Ridge
2011-10-01
Quadrupole ion traps can be transformed into nonlinear traps with integrable motion by adding special electrostatic potentials. This can be done with both stationary potentials (electrostatic plus a uniform magnetic field) and with time-dependent electric potentials. These potentials are chosen such that the single particle Hamilton-Jacobi equations of motion are separable in some coordinate systems. The electrostatic potentials have several free adjustable parameters allowing for a quadrupole trap to be transformed into, for example, a double-well or a toroidal-well system. The particle motion remains regular, non-chaotic, integrable in quadratures, and stable for a wide range of parameters. We present two examples of how to realize such a system in case of a time-independent (the Penning trap) as well as a time-dependent (the Paul trap) configuration.
Spherically symmetric nonlinear structures
NASA Astrophysics Data System (ADS)
Calzetta, Esteban A.; Kandus, Alejandra
1997-02-01
We present an analytical method to extract observational predictions about the nonlinear evolution of perturbations in a Tolman universe. We assume no a priori profile for them. We solve perturbatively a Hamilton-Jacobi equation for a timelike geodesic and obtain the null one as a limiting case in two situations: for an observer located in the center of symmetry and for a noncentered one. In the first case we find expressions to evaluate the density contrast and the number count and luminosity distance versus redshift relationships up to second order in the perturbations. In the second situation we calculate the CMBR anisotropies at large angular scales produced by the density contrast and by the asymmetry of the observer's location, up to first order in the perturbations. We develop our argument in such a way that the formulas are valid for any shape of the primordial spectrum.
Nonlinearities in vegetation functioning
NASA Astrophysics Data System (ADS)
Ceballos-Núñez, Verónika; Müller, Markus; Metzler, Holger; Sierra, Carlos
2016-04-01
Given the current drastic changes in climate and atmospheric CO2 concentrations, and the role of vegetation in the global carbon cycle, there is increasing attention to the carbon allocation component in biosphere terrestrial models. Improving the representation of C allocation in models could be the key to having better predictions of the fate of C once it enters the vegetation and is partitioned to C pools of different residence times. C allocation has often been modeled using systems of ordinary differential equations, and it has been hypothesized that most models can be generalized with a specific form of a linear dynamical system. However, several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems with model structure. Although efforts have been made to compare different models, the outcome of these qualitative assessments has been a conceptual categorization of them. In this contribution, we introduce a new effort to identify the main properties of groups of models by studying their mathematical structure. For this purpose, we performed a literature research of the relevant models of carbon allocation in vegetation and developed a database with their representation in symbolic mathematics. We used the Python package SymPy for symbolic mathematics as a common language and manipulated the models to calculate their Jacobian matrix at fixed points and their eigenvalues, among other mathematical analyses. Our preliminary results show a tendency of inverse proportionality between model complexity and size of time/space scale; complex interactions between the variables controlling carbon allocation in vegetation tend to operate at shorter time/space scales, and vice-versa. Most importantly, we found that although the linear structure is common, other structures with non-linearities have been also proposed. We, therefore, propose a new General Model that can accommodate these
Adaptive nonlinear flight control
NASA Astrophysics Data System (ADS)
Rysdyk, Rolf Theoduor
1998-08-01
Research under supervision of Dr. Calise and Dr. Prasad at the Georgia Institute of Technology, School of Aerospace Engineering. has demonstrated the applicability of an adaptive controller architecture. The architecture successfully combines model inversion control with adaptive neural network (NN) compensation to cancel the inversion error. The tiltrotor aircraft provides a specifically interesting control design challenge. The tiltrotor aircraft is capable of converting from stable responsive fixed wing flight to unstable sluggish hover in helicopter configuration. It is desirable to provide the pilot with consistency in handling qualities through a conversion from fixed wing flight to hover. The linear model inversion architecture was adapted by providing frequency separation in the command filter and the error-dynamics, while not exiting the actuator modes. This design of the architecture provides for a model following setup with guaranteed performance. This in turn allowed for convenient implementation of guaranteed handling qualities. A rigorous proof of boundedness is presented making use of compact sets and the LaSalle-Yoshizawa theorem. The analysis allows for the addition of the e-modification which guarantees boundedness of the NN weights in the absence of persistent excitation. The controller is demonstrated on the Generic Tiltrotor Simulator of Bell-Textron and NASA Ames R.C. The model inversion implementation is robustified with respect to unmodeled input dynamics, by adding dynamic nonlinear damping. A proof of boundedness of signals in the system is included. The effectiveness of the robustification is also demonstrated on the XV-15 tiltrotor. The SHL Perceptron NN provides a more powerful application, based on the universal approximation property of this type of NN. The SHL NN based architecture is also robustified with the dynamic nonlinear damping. A proof of boundedness extends the SHL NN augmentation with robustness to unmodeled actuator
Linearization of Conservative Nonlinear Oscillators
ERIC Educational Resources Information Center
Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.
2009-01-01
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…
Nonlinear diffusion and superconducting hysteresis
Mayergoyz, I.D.
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Passive linearization of nonlinear resonances
NASA Astrophysics Data System (ADS)
Habib, G.; Grappasonni, C.; Kerschen, G.
2016-07-01
The objective of this paper is to demonstrate that the addition of properly tuned nonlinearities to a nonlinear system can increase the range over which a specific resonance responds linearly. Specifically, we seek to enforce two important properties of linear systems, namely, the force-displacement proportionality and the invariance of resonance frequencies. Numerical simulations and experiments are used to validate the theoretical findings.
Solving Nonlinear Coupled Differential Equations
NASA Technical Reports Server (NTRS)
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
Nonlinear Oscillators in Space Physics
NASA Technical Reports Server (NTRS)
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
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 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.
NASA Astrophysics Data System (ADS)
Sutin, A. M.; Johnson, P. A.
2005-04-01
This paper presents the second part of the review of Nonlinear Elastic Wave Spectroscopy (NEWS) in NDE, and describe two different methods of nonlinear NDE that provide not only damage detection but location as well. Nonlinear Wave Modulation Spectroscopy is based on the application of an ultrasonic probe signal modulated by a low frequency vibration. Damage location can be obtained by application of Impulse Modulation Techniques that exploit the modulation of a short pulse reflected from a damage feature (e.g. crack) by low frequency vibration. Nonlinear Time Reversed Acoustic methods provide the means to focus acoustic energy to any point in a solid. In combination, we are applying the focusing properties of TRA and the nonlinear properties of cracks to locate them.
BRST Structure of Nonlinear Superalgebras
NASA Astrophysics Data System (ADS)
Asorey, M.; Lavrov, P. M.; Radchenko, O. V.; Sugamoto, A.
In this paper we analyze the structure of the BRST charge of nonlinear superalgebras. We consider quadratic nonlinear superalgebras where a commutator (in terms of (super-)Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
Intrinsic Negative Mass from Nonlinearity
NASA Astrophysics Data System (ADS)
Di Mei, F.; Caramazza, P.; Pierangeli, D.; Di Domenico, G.; Ilan, H.; Agranat, A. J.; Di Porto, P.; DelRe, E.
2016-04-01
We propose and provide experimental evidence of a mechanism able to support negative intrinsic effective mass. The idea is to use a shape-sensitive nonlinearity to change the sign of the mass in the leading linear propagation equation. Intrinsic negative-mass dynamics is reported for light beams in a ferroelectric crystal substrate, where the diffusive photorefractive nonlinearity leads to a negative-mass Schrödinger equation. The signature of inverted dynamics is the observation of beams repelled from strongly guiding integrated waveguides irrespective of wavelength and intensity and suggests shape-sensitive nonlinearity as a basic mechanism leading to intrinsic negative mass.
Dissipative nonlinear dynamics in holography
NASA Astrophysics Data System (ADS)
Basu, Pallab; Ghosh, Archisman
2014-02-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of O, the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems.
NASA Technical Reports Server (NTRS)
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
NASA Technical Reports Server (NTRS)
Meyer, George; Null, Cynthia H. (Technical Monitor)
1996-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordination, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
Nonlinear Frequency Compression
Scollie, Susan; Glista, Danielle; Seelisch, Andreas
2013-01-01
Frequency lowering technologies offer an alternative amplification solution for severe to profound high frequency hearing losses. While frequency lowering technologies may improve audibility of high frequency sounds, the very nature of this processing can affect the perceived sound quality. This article reports the results from two studies that investigated the impact of a nonlinear frequency compression (NFC) algorithm on perceived sound quality. In the first study, the cutoff frequency and compression ratio parameters of the NFC algorithm were varied, and their effect on the speech quality was measured subjectively with 12 normal hearing adults, 12 normal hearing children, 13 hearing impaired adults, and 9 hearing impaired children. In the second study, 12 normal hearing and 8 hearing impaired adult listeners rated the quality of speech in quiet, speech in noise, and music after processing with a different set of NFC parameters. Results showed that the cutoff frequency parameter had more impact on sound quality ratings than the compression ratio, and that the hearing impaired adults were more tolerant to increased frequency compression than normal hearing adults. No statistically significant differences were found in the sound quality ratings of speech-in-noise and music stimuli processed through various NFC settings by hearing impaired listeners. These findings suggest that there may be an acceptable range of NFC settings for hearing impaired individuals where sound quality is not adversely affected. These results may assist an Audiologist in clinical NFC hearing aid fittings for achieving a balance between high frequency audibility and sound quality. PMID:23539261
Nonlinear vibrational microscopy
Holtom, Gary R.; Xie, Xiaoliang Sunney; Zumbusch, Andreas
2000-01-01
The present invention is a method and apparatus for microscopic vibrational imaging using coherent Anti-Stokes Raman Scattering or Sum Frequency Generation. Microscopic imaging with a vibrational spectroscopic contrast is achieved by generating signals in a nonlinear optical process and spatially resolved detection of the signals. The spatial resolution is attained by minimizing the spot size of the optical interrogation beams on the sample. Minimizing the spot size relies upon a. directing at least two substantially co-axial laser beams (interrogation beams) through a microscope objective providing a focal spot on the sample; b. collecting a signal beam together with a residual beam from the at least two co-axial laser beams after passing through the sample; c. removing the residual beam; and d. detecting the signal beam thereby creating said pixel. The method has significantly higher spatial resolution then IR microscopy and higher sensitivity than spontaneous Raman microscopy with much lower average excitation powers. CARS and SFG microscopy does not rely on the presence of fluorophores, but retains the resolution and three-dimensional sectioning capability of confocal and two-photon fluorescence microscopy. Complementary to these techniques, CARS and SFG microscopy provides a contrast mechanism based on vibrational spectroscopy. This vibrational contrast mechanism, combined with an unprecedented high sensitivity at a tolerable laser power level, provides a new approach for microscopic investigations of chemical and biological samples.
Ohnuma, S.
1984-03-01
Two approximations are made, one essential and the other not so essential but convenient to keep the analytical treatment manageable: (1) Only one nonlinear resonance is considered at a time so that the treatment is best suited when the tune is close to one resonance only. To improve this approximation, one must go to the next order which involves a canonical transformation of dynamical variables. Analytical treatment of more than one resonance is not possible for general cases. (2) In the formalism using the action-angle variables, the Hamiltonian can have terms which are independent of the angle variables. These terms are called phase-independent terms or shear terms. The tune is then a function of the oscillation amplitudes. In the lowest-order treatment, the (4N)-pole components but not the (4N + 2)-pole components contribute to this dependence. In deriving the resonance width analytically, one ignores these terms in the Hamiltonian for the sake of simplicity. If these are retained, one needs at least three extra parameters and the analytical treatment becomes rather unwieldy.
Nonlinear algebra and Bogoliubov's recursion
NASA Astrophysics Data System (ADS)
Morozov, A. Yu.; Serbyn, M. N.
2008-02-01
We give many examples of applying Bogoliubov’s forest formula to iterative solutions of various nonlinear equations. The same formula describes an extremely wide class of objects, from an ordinary quadratic equation to renormalization in quantum field theory.
Reconstruction of nonlinear wave propagation
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.
Nonlinear viscoelastic characterization of polycarbonate
NASA Technical Reports Server (NTRS)
Caplan, E. S.; Brinson, H. F.
1982-01-01
Uniaxial tensile creep and recovery data from polycarbonate at six temperatures and six stress levels are analyzed for nonlinear viscoelastic constitutive modeling. A theory to account for combined effects of two or more accelerating factors is presented.
Nonlinear interaction between single photons.
Guerreiro, T; Martin, A; Sanguinetti, B; Pelc, J S; Langrock, C; Fejer, M M; Gisin, N; Zbinden, H; Sangouard, N; Thew, R T
2014-10-24
Harnessing nonlinearities strong enough to allow single photons to interact with one another is not only a fascinating challenge but also central to numerous advanced applications in quantum information science. Here we report the nonlinear interaction between two single photons. Each photon is generated in independent parametric down-conversion sources. They are subsequently combined in a nonlinear waveguide where they are converted into a single photon of higher energy by the process of sum-frequency generation. Our approach results in the direct generation of photon triplets. More generally, it highlights the potential for quantum nonlinear optics with integrated devices and, as the photons are at telecom wavelengths, it opens the way towards novel applications in quantum communication such as device-independent quantum key distribution.
Interaction Terms in Nonlinear Models
Karaca-Mandic, Pinar; Norton, Edward C; Dowd, Bryan
2012-01-01
Objectives To explain the use of interaction terms in nonlinear models. Study Design We discuss the motivation for including interaction terms in multivariate analyses. We then explain how the straightforward interpretation of interaction terms in linear models changes in nonlinear models, using graphs and equations. We extend the basic results from logit and probit to difference-in-differences models, models with higher powers of explanatory variables, other nonlinear models (including log transformation and ordered models), and panel data models. Empirical Application We show how to calculate and interpret interaction effects using a publicly available Stata data set with a binary outcome. Stata 11 has added several features which make those calculations easier. LIMDEP code also is provided. Conclusions It is important to understand why interaction terms are included in nonlinear models in order to be clear about their substantive interpretation. PMID:22091735
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.
Studies of Nonlinear Problems. I
DOE R&D Accomplishments Database
Fermi, E.; Pasta, J.; Ulam, S.
1955-05-01
A one-dimensional dynamical system of 64 particles with forces between neighbors containing nonlinear terms has been studied on the Los Alamos computer MANIAC I. The nonlinear terms considered are quadratic, cubic, and broken linear types. The results are analyzed into Fourier components and plotted as a function of time. The results show very little, if any, tendency toward equipartition of energy among the degrees of freedom.
Nonlinear scattering in gold nanospheres
NASA Astrophysics Data System (ADS)
Shen, Po-Ting; Lin, Cheng-Wei; Liu, Hsiang-Lin; Chu, Shi-Wei
2016-03-01
Nonlinearity enhanced by noble metallic nanoparticles provide novel light manipulation capabilities and innovative applications. Recently, we discovered a new nonlinear phenomenon on the scattering of metallic nanoparticles by continuous-wave (CW) lasers at the intensity around MW/cm2 and applied to super-resolution microscopy that allowed spatial resolution of plasmonic nanostructures down to λ/8. However, its mechanism is still unknown. In this work, we elaborate the mechanism behind the nonlinear scattering of gold nanospheres. There are four possible candidates: intraband transition, interband transition, hot electron, and hot lattice. Each of them has a corresponding nonlinear refractive index (n2), which is related to temporal dependence of its light-matter interaction. We first measure the intensity dependence of nonlinear scattering to extract the effective n2 value. We find out it has the closest n2 value to hot lattice, which causes either the shift or weakening of the surface plasmon resonance (SPR). To further verify the mechanism, the nanospheres are heated up with both a hot plate and a CW laser, and the variation of single-particle SPR scattering spectra are measured. In both cases, more than 50% reduction of scattering is observed, when temperature rises a few tens of degrees or when illumination intensity reaches the order of 1MW/cm2. Thus, we conclude the spectra variation by the two different heating source, as well as the nonlinear scattering are all due to hot lattice, and subsequent permittivity change with temperature. The innovative concept of hot lattice plasmonics not only opens up a new dimension for nonlinear plasmonics, but also predicts the potential of similar nonlinearity in other materials as long as their permittivity changes with temperature.
Mobius Strip underlying Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Lopaz, Edaurdo; Satija, Indubala
2004-03-01
Geometrical and topolgocial aspects of phase space orbits of driven nonlinear oscillators are shown to share many features with the circuits on the mobius strips. Most important characteristic shared by nonlinear oscillators and the mobius strip is the first order geometrical phase transition characterized in terms of local variable torsion and the global variable the geometrical phase . These geometrical transitions are geometrical resonances and lead to geometrical localization that underlie not only limit cycles but also the strange attractors.
Dynamics of Cochlear Nonlinearity.
Cooper, Nigel P; van der Heijden, Marcel
2016-01-01
Dynamic aspects of cochlear mechanical compression were studied by recording basilar membrane (BM) vibrations evoked by tone pairs ("beat stimuli") in the 11-19 kHz region of the gerbil cochlea. The frequencies of the stimulus components were varied to produce a range of "beat rates" at or near the characteristic frequency (CF) of the BM site under study, and the amplitudes of the components were balanced to produce near perfect periodic cancellations, visible as sharp notches in the envelope of the BM response. We found a compressive relation between instantaneous stimulus intensity and BM response magnitude that was strongest at low beat rates (e.g., 10-100 Hz). At higher beat rates, the amount of compression reduced progressively (i.e. the responses became linearized), and the rising and falling flanks of the response envelope showed increasing amounts of hysteresis; the rising flank becoming steeper than the falling flank. This hysteresis indicates that cochlear mechanical compression is not instantaneous, and is suggestive of a gain control mechanism having finite attack and release times. In gain control terms, the linearization that occurs at higher beat rates occurs because the instantaneous gain becomes smoothened, or low-pass filtered, with respect to the magnitude fluctuations in the stimulus. In terms of peripheral processing, the linearization corresponds to an enhanced coding, or decompression, of rapid amplitude modulations. These findings are relevant both to those who wish to understand the underlying mechanisms and those who need a realistic model of nonlinear processing by the auditory periphery. PMID:27080667
NASA Technical Reports Server (NTRS)
Leslie, Thomas M.
1993-01-01
A focused approach to development and evaluation of organic polymer films for use in optoelectronics is presented. The issues and challenges that are addressed include: (1) material synthesis, purification, and the tailoring of the material properties; (2) deposition of uniform thin films by a variety of methods; (3) characterization of material physical properties (thermal, electrical, optical, and electro-optical); and (4) device fabrication and testing. Photonic materials, devices, and systems were identified as critical technology areas by the Department of Commerce and the Department of Defense. This approach offers strong integration of basic material issues through engineering applications by the development of materials that can be exploited as the active unit in a variety of polymeric thin film devices. Improved materials were developed with unprecedented purity and stability. The absorptive properties can be tailored and controlled to provide significant improvement in propagation losses and nonlinear performance. Furthermore, the materials were incorporated into polymers that are highly compatible with fabrication and patterning processes for integrated optical devices and circuits. By simultaneously addressing the issues of materials development and characterization, keeping device design and fabrication in mind, many obstacles were overcome for implementation of these polymeric materials and devices into systems. We intend to considerably improve the upper use temperature, poling stability, and compatibility with silicon based devices. The principal device application that was targeted is a linear electro-optic modulation etalon. Organic polymers need to be properly designed and coupled with existing integrated circuit technology to create new photonic devices for optical communication, image processing, other laser applications such as harmonic generation, and eventually optical computing. The progression from microscopic sample to a suitable film
BOOK REVIEW: Nonlinear Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Shafranov, V.
1998-08-01
Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium
[Nonlinear magnetohydrodynamics]. Final report
Montgomery, D.C.
1998-11-01
This is a final report on the research activities carried out under the above grant at Dartmouth. During the period considered, the grant was identified as being for nonlinear magnetohydrodynamics, considered as the most tractable theoretical framework in which the plasma problems associated with magnetic confinement of fusion plasmas could be studied. During the first part of the grant`s lifetime, the author was associated with Los Alamos National Laboratory as a consultant and the work was motivated by the reversed-field pinch. Later, when that program was killed at Los Alamos, the problems became ones that could be motivated by their relation to tokamaks. Throughout the work, the interest was always on questions that were as fundamental as possible, compatible with those motivations. The intent was always to contribute to plasma physics as a science, as well as to the understanding of mission-oriented confined fusion plasmas. Twelve Ph.D. theses were supervised during this period and a comparable number of postdoctoral research associates were temporarily supported. Many of these have gone on to distinguished careers, though few have done so in the context of the controlled fusion program. Their work was a combination of theory and numerical computation, in gradually less and less idealized settings, moving from rectangular periodic boundary conditions in two dimensions, through periodic straight cylinders and eventually, before the grant was withdrawn, to toroids, with a gradually more prominent role for electrical and mechanical boundary conditions. The author never had access to a situation where he could initiate experiments and relate directly to the laboratory data he wanted. Computers were the laboratory. Most of the work was reported in referred publications in the open literature, copies of which were transmitted one by one to DOE at the time they appeared. The Appendix to this report is a bibliography of published work which was carried out under the
Nonlinear analysis of pupillary dynamics.
Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo
2016-02-01
Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (p<0.001). Our results suggest that (a) pupil size at constant light condition is characterized by nonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. PMID:26351899
Nonlinear problems in flight dynamics
NASA Technical Reports Server (NTRS)
Chapman, G. T.; Tobak, M.
1984-01-01
A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.
Nonlinear variations in axisymmetric accretion
NASA Astrophysics Data System (ADS)
Bose, Soumyajit; Sengupta, Anindya; Ray, Arnab K.
2014-05-01
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of the perturbation bears a form that is similar to the metric equation of an analogue acoustic black hole. We bring out the time dependence of the perturbation in the form of a Liénard system by requiring the perturbation to be a standing wave under the second order of nonlinearity. We perform a dynamical systems analysis of the Liénard system to reveal a saddle point in real time, whose implication is that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. We also model the perturbation as a high-frequency traveling wave and carry out a Wentzel-Kramers-Brillouin analysis, treating nonlinearity iteratively as a very feeble effect. Under this approach, both the amplitude and the energy flux of the perturbation exhibit growth, with the acoustic horizon segregating the regions of stability and instability.
Nonlinear acoustics - History and outlook
NASA Astrophysics Data System (ADS)
Rott, N.
1980-08-01
A historical review of the development of nonlinear acoustics before the epoch beginning with Riemann is presented followed by a review of the more recent developments of the last 20 years, including a cinematical view of nonlinear acoustic waves. The review emphasizes the works of Poisson and his equations and solutions of particle and wave velocity as well as Stoke's theory of sound. Attention is given to the developments of the last two decades through an examination of Lagrange and Chester problems, such as the transition of Euler coordinates into Lagrange coordinates and equations. The nonlinear theory of resonance is discussed by describing a closed tube resonance problem where periodic excitation through a piston characterizes wave movements.
Nonlinear Single Spin Spectrum Analyzer
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2014-03-01
Qubits have been used as linear spectrum analyzers of their environments, through the use of decoherence spectroscopy. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013). Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: NIST, Boulder, CO.
Nonlinear photoacoustic spectroscopy of hemoglobin
Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P.; Xia, Jun; Wang, Lihong V.
2015-05-18
As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography.
Neoclassical Transport Including Collisional Nonlinearity
Candy, J.; Belli, E. A.
2011-06-10
In the standard {delta}f theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction {delta}f is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlueter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.
Generation of Nonlinear Vortex Precursors.
Chen, Yue-Yue; Feng, Xun-Li; Liu, Chengpu
2016-07-01
We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex harmonics are generated in the transmitted field due to carrier effects associated with ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provides a straightforward way to measure precursors. By virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical information and communication fields where controllable loss, large information-carrying capacity, and high speed communication are required.
Higher dimensional nonlinear massive gravity
NASA Astrophysics Data System (ADS)
Do, Tuan Q.
2016-05-01
Inspired by a recent ghost-free nonlinear massive gravity in four-dimensional spacetime, we study its higher dimensional scenarios. As a result, we are able to show the constantlike behavior of massive graviton terms for some well-known metrics such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini (anti-) de Sitter metrics in a specific five-dimensional nonlinear massive gravity under an assumption that its fiducial metrics are compatible with physical ones. In addition, some simple cosmological solutions of the five-dimensional massive gravity are figured out consistently.
Prediction of nonlinear soil effects
Hartzell, S.; Bonilla, L.F.; Williams, R.A.
2004-01-01
Mathematical models of soil nonlinearity in common use and recently developed nonlinear codes compared to investigate the range of their predictions. We consider equivalent linear formulations with and without frequency-dependent moduli and damping ratios and nonlinear formulations for total and effective stress. Average velocity profiles to 150 m depth with midrange National Earthquake Hazards Reduction Program site classifications (B, BC, C, D, and E) in the top 30 m are used to compare the response of a wide range of site conditions from rock to soft soil. Nonlinear soil models are compared using the amplification spectrum, calculated as the ratio of surface ground motion to the input motion at the base of the velocity profile. Peak input motions from 0.1g to 0.9g are considered. For site class B, no significant differences exist between the models considered in this article. For site classes BC and C, differences are small at low input motions (0.1g to 0.2g), but become significant at higher input levels. For site classes D and E the overdamping of frequencies above about 4 Hz by the equivalent linear solution with frequency-independent parameters is apparent for the entire range of input motions considered. The equivalent linear formulation with frequency-dependent moduli and damping ratios under damps relative to the nonlinear models considered for site class C with larger input motions and most input levels for site classes D and E. At larger input motions the underdamping for site classes D and E is not as severe as the overdamping with the frequency-independent formulation, but there are still significant differences in the time domain. A nonlinear formulation is recommended for site classes D and E and for site classes BC and C with input motions greater than a few tenths of the acceleration of gravity. The type of nonlinear formulation to use is driven by considerations of the importance of water content and the availability of laboratory soils data. Our
Generation of Nonlinear Vortex Precursors.
Chen, Yue-Yue; Feng, Xun-Li; Liu, Chengpu
2016-07-01
We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex harmonics are generated in the transmitted field due to carrier effects associated with ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provides a straightforward way to measure precursors. By virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical information and communication fields where controllable loss, large information-carrying capacity, and high speed communication are required. PMID:27447507
Time series with tailored nonlinearities
NASA Astrophysics Data System (ADS)
Räth, C.; Laut, I.
2015-10-01
It is demonstrated how to generate time series with tailored nonlinearities by inducing well-defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncorrelated Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for, e.g., turbulence and financial data can thus be explained in terms of phase correlations.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Du, Jiajia
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results. PMID:24592160
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
NASA Astrophysics Data System (ADS)
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
Back in 1967, Clifford Gardner, John Greene, Martin Kruskal and Robert Miura published a seminal paper in Physical Review Letters which was to become a cornerstone in the theory of integrable systems. In 2006, the authors of this paper received the AMS Steele Prize. In this award the AMS pointed out that `In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.' From this discovery the modern theory of integrability bloomed, leading scientists to a deep understanding of many nonlinear phenomena which is by no means reachable by perturbation methods or other previous tools from linear theories. Nonlinear phenomena appear everywhere in nature, their description and understanding is therefore of great interest both from the theoretical and applicative point of view. If a nonlinear phenomenon can be represented by an integrable system then we have at our disposal a variety of tools to achieve a better mathematical description of the phenomenon. This special issue is largely dedicated to investigations of nonlinear phenomena which are related to the concept of integrability, either involving integrable systems themselves or because they use techniques from the theory of integrability. The idea of this special issue originated during the 18th edition of the Nonlinear Evolution Equations and Dynamical Systems (NEEDS) workshop, held at Isola Rossa, Sardinia, Italy, 16-23 May 2009 (http://needs-conferences.net/2009/). The issue benefits from the occasion offered by the meeting, in particular by its mini-workshops programme, and contains invited review papers and contributed papers. It is worth pointing out that there was an open call for papers and all contributions were peer reviewed
Duffing's Equation and Nonlinear Resonance
ERIC Educational Resources Information Center
Fay, Temple H.
2003-01-01
The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…
Nonlinear analysis of drought dynamics
NASA Astrophysics Data System (ADS)
Ma, M.
2015-12-01
Drought is an extreme natural hazard and becomes a severe problem in the world. It arises as a result of interactions between climate input and human activity, displaying the nonlinearity and complexity. Nonlinear time series analyses open a way to study the underlying dynamic characteristics of drought, and then provide the forward knowledge to understanding the physical mechanism of drought event. The rationale behind this idea is that information about the representation of nonlinear properties could be used as an additional quality indicator. To that end, the correlation dimension method, a powerful nonlinear time series analysis method based on the chaos theory, has been suggested to assess the intrinsic dimensionality or degree of freedom of time series according to Takens (1981). It can provide an assessment of the dominant processes that is required to map the observed dynamics. In this study, daily discharge and hourly groundwater level data of 63 catchments in Germany and China were investigated with correlation dimension method. The results indicated that the correlation dimension values of studied discharge exhibited none clear spatial patterns, but showed significant correlations with the spatial heterogeneity within the catchments. In contrast, the correlation dimension values of groundwater level displayed spatial patterns due to the different aquifer conditions (confined or unconfined). High correlation dimension values indicate partly confined conditions. In addition, Hurst analysis was involved to qualify the persistence of drought. It seems that drought mechanisms can be learnt from the data themselves in an inverse manner.
Nonlinear bubble dynamics of cavitation.
An, Yu
2012-01-01
For cavitation clouds generated in a standing sound wave driven by an ultrasonic horn, the nonlinear acoustic wave equation governing cavitation dynamics is numerically solved together with the bubble motion equation under an approximation. This conceptual calculation can qualitatively reproduce the observed characteristics of cavitation.
Gauge fields, nonlinear realizations, supersymmetry
NASA Astrophysics Data System (ADS)
Ivanov, E. A.
2016-07-01
This is a brief survey of the all-years research activity in the Sector "Supersymmetry" (the former Markov Group) at the Bogoliubov Laboratory of Theoretical Physics. The focus is on the issues related to gauge fields, spontaneously broken symmetries in the nonlinear realizations approach, and diverse aspects of supersymmetry.
Nonlinear connectivity by Granger causality.
Marinazzo, Daniele; Liao, Wei; Chen, Huafu; Stramaglia, Sebastiano
2011-09-15
The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. The state of the art to understand the communication between brain systems are dynamic causal modeling (DCM) and Granger causality. While DCM models nonlinear couplings, Granger causality, which constitutes a major tool to reveal effective connectivity, and is widely used to analyze EEG/MEG data as well as fMRI signals, is usually applied in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a few approaches have been proposed. We review them and focus on a recently proposed flexible approach has been recently proposed, consisting in the kernel version of Granger causality. We show the application of the proposed approach on EEG signals and fMRI data.
Nonlinear eigenvalue problems in smectics
Marchenko, V. I. Podolyak, E. R.
2010-01-15
The asymptotic forms of strains in a smectic around the linear distributions of multipole force are determined. The law of a decrease in strains is specified by the indices, which are eigenvalues of nonlinear equations describing the angular dependence of the strains.
Multilevel algorithms for nonlinear optimization
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia; Dennis, J. E., Jr.
1994-01-01
Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.
Solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.
Cooper, Fred; Khare, Avinash; Mihaila, Bogdan; Saxena, Avadh
2010-09-01
We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction g{2}/k+1(ΨΨ){k+1} , as well as a vector-vector self interaction g{2}/k+1(Ψγ{μ}ΨΨγ{μ}Ψ){1/2(k+1)} . We find the exact analytic form for solitary waves for arbitrary k and find that they are a generalization of the exact solutions for the nonlinear Schrödinger equation (NLSE) and reduce to these solutions in a well defined nonrelativistic limit. We perform the nonrelativistic reduction and find the 1/2m correction to the NLSE, valid when |ω-m|<2m , where ω is the frequency of the solitary wave in the rest frame. We discuss the stability and blowup of solitary waves assuming the modified NLSE is valid and find that they should be stable for k<2 . PMID:21230200
Nonlinear electron oscillations in a warm plasma
Sarkar, Anwesa; Maity, Chandan; Chakrabarti, Nikhil
2013-12-15
A class of nonstationary solutions for the nonlinear electron oscillations of a warm plasma are presented using a Lagrangian fluid description. The solution illustrates the nonlinear steepening of an initial Gaussian electron density disturbance and also shows collapse behavior in time. The obtained solution may indicate a class of nonlinear transient structures in an unmagnetized warm plasma.
Unsymmetrical squaraines for nonlinear optical materials
NASA Technical Reports Server (NTRS)
Marder, Seth R. (Inventor); Chen, Chin-Ti (Inventor); Cheng, Lap-Tak (Inventor)
1996-01-01
Compositions for use in non-linear optical devices. The compositions have first molecular electronic hyperpolarizability (.beta.) either positive or negative in sign and therefore display second order non-linear optical properties when incorporated into non-linear optical devices.
From linear mechanics to nonlinear mechanics
NASA Technical Reports Server (NTRS)
Loeb, Julian
1955-01-01
Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.
Nonlinear Principal Components Analysis: Introduction and Application
ERIC Educational Resources Information Center
Linting, Marielle; Meulman, Jacqueline J.; Groenen, Patrick J. F.; van der Koojj, Anita J.
2007-01-01
The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal…
NASA Technical Reports Server (NTRS)
Young, G.
1982-01-01
A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.
Topics in complex nonlinear systems
NASA Astrophysics Data System (ADS)
Ying, Linghang
In the dissertation, I include two topics of my research in nonlinear dynamic systems. In the first topic, we use numerical optimization techniques to investigate the behavior of the success rates for two- and three-qubit entangling gates, first for perfect fidelity, and then extended to imperfect gates. We find that as the perfect fidelity condition is relaxed, the maximum attainable success rates increase in a predictable fashion depending on the size of the system, and we compare that rate of increase for several gates. Finally, we propose an experiment to test our imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing. In the second topic, we quantitatively study nonlinear effects on the evolution of surface gravity waves on the ocean, to explore systematically the effects of various input parameters on the probability of rogue wave formation. The fourth-order current-modified nonlinear Schrodinger equation (CNLS4) is employed to describe the wave evolution. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single "freak index" parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Then, we obtain quantitative predictions for the wave height distribution as a
Noise in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2009-08-01
List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.
Condition assessment of nonlinear processes
Hively, Lee M.; Gailey, Paul C.; Protopopescu, Vladimir A.
2002-01-01
There is presented a reliable technique for measuring condition change in nonlinear data such as brain waves. The nonlinear data is filtered and discretized into windowed data sets. The system dynamics within each data set is represented by a sequence of connected phase-space points, and for each data set a distribution function is derived. New metrics are introduced that evaluate the distance between distribution functions. The metrics are properly renormalized to provide robust and sensitive relative measures of condition change. As an example, these measures can be used on EEG data, to provide timely discrimination between normal, preseizure, seizure, and post-seizure states in epileptic patients. Apparatus utilizing hardware or software to perform the method and provide an indicative output is also disclosed.
Max-Planck-Institut fur Quantenoptik; Goulielmakis, E.; Schultze, M.; Hofstetter, M.; Yakovlev, V. S.; Gagnon, J.; Uiberacker, M.; Aquila, A. L.; gullikson, E. M.; attwood, D. T.; Kienberger, R.; Krausz, F.; Kleineberg, U.
2008-11-05
Nonlinear optics plays a central role in the advancement of optical science and laser-based technologies. We report on the confinement of the nonlinear interaction of light with matter to a single wave cycle and demonstrate its utility for time-resolved and strong-field science. The electric field of 3.3-femtosecond, 0.72-micron laser pulses with a controlled and measured waveform ionizes atoms near the crests of the central wave cycle, with ionization being virtually switched off outside this interval. Isolated sub-100-attosecond pulses of extreme ultraviolet light (photon energy {approx} 80 electron volts), containing {approx} 0.5 nanojoule of energy, emerge from the interaction with a conversion efficiency of {approx} 10{sup -6}. These tools enable the study of the precision control of electron motion with light fields and electron-electron interactions with a resolution approaching the atomic unit of time ({approx} 24 attoseconds).
Some nonlinear space decomposition algorithms
Tai, Xue-Cheng; Espedal, M.
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
Solitons and nonlinear wave equations
Dodd, Roger K.; Eilbeck, J. Chris; Gibbon, John D.; Morris, Hedley C.
1982-01-01
A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.
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.
Nonlinear dynamics in cardiac conduction
NASA Technical Reports Server (NTRS)
Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.
1988-01-01
Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.
A nonlinear SIR with stability
NASA Astrophysics Data System (ADS)
Trisilowati, Darti, I.; Fitri, S.
2014-02-01
The aim of this work is to develop a mathematical model of a nonlinear susceptible-infectious-removed (SIR) epidemic model with vaccination. We analyze the stability of the model by linearizing the model around the equilibrium point. Then, diphtheria data from East Java province is fitted to the model. From these estimated parameters, we investigate which parameters that play important role in the epidemic model. Some numerical simulations are given to illustrate the analytical results and the behavior of the model.
Townes' contribution to nonlinear optics
NASA Astrophysics Data System (ADS)
Garmire, Elsa
2015-03-01
In honour of the Fiftieth Anniversary of the Nobel Prize in Physics, this talk introduced the contributions of Nicholas Basov and Alexei Prokhorov, who shared the prize with Charles Townes. The talk then detailed the quantum electronics research of Townes, particularly at MIT, which was related to nonlinear optics. The years from 1961 to 1968 were particularly exciting, as the ruby laser enabled a wide variety of new physics to be discovered and explored.
Linear superposition in nonlinear equations.
Khare, Avinash; Sukhatme, Uday
2002-06-17
Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions. PMID:12059300
Nonlinear transient simulation of transformers
Pierrat, L.; Tran-Quoc, T. |; Montmeat, A.
1995-12-31
In this paper, a nonlinear model of transformer which takes into account both the saturation and the hysteresis is proposed. In order to simulate transient phenomena in transformers, a system of equations is presented. The digital simulation of the energization and de-energization of a three-phase distribution transformer is studied. Ferroresonant phenomena in iron core transformers supplied through capacitive links are presented. Finally, the influence of MOV arresters on overvoltage reduction is investigated.
Nonlinear positron acoustic solitary waves
Tribeche, Mouloud; Aoutou, Kamel; Younsi, Smain; Amour, Rabia
2009-07-15
The problem of nonlinear positron acoustic solitary waves involving the dynamics of mobile cold positrons is addressed. A theoretical work is presented to show their existence and possible realization in a simple four-component plasma model. The results should be useful for the understanding of the localized structures that may occur in space and laboratory plasmas as new sources of cold positrons are now well developed.
Nonlinear input-output systems
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Luksic, Mladen; Su, Renjeng
1987-01-01
Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.
Nonlinear microscopy of collagen fibers
NASA Astrophysics Data System (ADS)
Strupler, M.; Pena, A.-M.; Hernest, M.; Tharaux, P.-L.; Fabre, A.; Marchal-Somme, J.; Crestani, B.; Débarre, D.; Martin, J.-L.; Beaurepaire, E.; Schanne-Klein, M.-C.
2007-02-01
We used intrinsic Second Harmonic Generation (SHG) by fibrillar collagen to visualize the three-dimensional architecture of collagen fibrosis at the micrometer scale using laser scanning nonlinear microscopy. We showed that SHG signals are highly specific to fibrillar collagen and provide a sensitive probe of the micrometer-scale structural organization of collagen in tissues. Moreover, recording simultaneously other nonlinear optical signals in a multimodal setup, we visualized the tissue morphology using Two-Photon Excited Fluorescence (2PEF) signals from endogenous chromophores such as NADH or elastin. We then compared different methods to determine accurate indexes of collagen fibrosis using nonlinear microscopy, given that most collagen fibrils are smaller than the microscope resolution and that second harmonic generation is a coherent process. In order to define a robust method to process our three-dimensional images, we either calculated the fraction of the images occupied by a significant SHG signal, or averaged SHG signal intensities. We showed that these scores provide an estimation of the extension of renal and pulmonary fibrosis in murine models, and that they clearly sort out the fibrotic mice.
Nonlinear Single Spin Spectrum Analayzer
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2014-05-01
Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.
Focus issue introduction: nonlinear photonics.
Akhmediev, Nail; Rottwitt, Karsten
2012-11-19
It is now 23 years since the first Topical Meeting "Nonlinear Guided Wave Phenomena" (Houston, TX, February 2-4, 1989) has been organised by George Stegeman and Allan Boardman with support of the Optical Society of America. These series of the OSA conferences known as NLGW, continued under the name "Nonlinear Photonics" starting from 2007. The latest one, in Colorado Springs in June 17-21, 2012 has been a great success despite the fierce fires advancing around the city at the time of the conference. This Focus issue is a collection of several papers presented at the conference with extended content submitted to Optics Express. Although this collection is small in comparison to the total number of papers presented at the conference, it gives a flavor of the topics considered at the meeting. It is also worthy to mention here that the next meeting "Nonlinear Photonics" is planned to be held in Barcelona - one of the main European centers on this subject.
NASA Astrophysics Data System (ADS)
Rincon, F.; Schekochihin, A. A.; Cowley, S. C.
2015-02-01
Slow dynamical changes in magnetic-field strength and invariance of the particles' magnetic moments generate ubiquitous pressure anisotropies in weakly collisional, magnetized astrophysical plasmas. This renders them unstable to fast, small-scale mirror and firehose instabilities, which are capable of exerting feedback on the macroscale dynamics of the system. By way of a new asymptotic theory of the early non-linear evolution of the mirror instability in a plasma subject to slow shearing or compression, we show that the instability does not saturate quasi-linearly at a steady, low-amplitude level. Instead, the trapping of particles in small-scale mirrors leads to non-linear secular growth of magnetic perturbations, δB/B ∝ t2/3. Our theory explains recent collisionless simulation results, provides a prediction of the mirror evolution in weakly collisional plasmas and establishes a foundation for a theory of non-linear mirror dynamics with trapping, valid up to δB/B = O(1).
Challenges in nonlinear gravitational clustering
NASA Astrophysics Data System (ADS)
Padmanabhan, Thanu
2006-04-01
This article addresses some issues related to the statistical description of gravitating systems in an expanding backgrounds. In particular, I describe (a) how the nonlinear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale and (b) what are the asymptotic characteristics of gravitational clustering that are independent of the initial conditions. The analysis uses a new approach based on an integro-differential equation for the evolution of the gravitational potential in the Fourier space. I show how this equation allows one to understand several aspects of nonlinear gravitational clustering and provides insight in to the transfer of power from one scale to another through nonlinear mode coupling. Numerical simulations as well as analytic work shows that power transfer leads to a universal power spectrum at late times, somewhat reminiscent of the existence of Kolmogorov spectrum in fluid turbulence. To cite this article: T. Padmanabhan, C. R. Physique 7 (2006).
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.
spin pumping occurred under nonlinear spin precession
NASA Astrophysics Data System (ADS)
Zhou, Hengan; Fan, Xiaolong; Ma, Li; Zhou, Shiming; Xue, Desheng
Spin pumping occurs when a pure-spin current is injected into a normal metal thin layer by an adjacent ferromagnetic metal layer undergoing ferromagnetic resonance, which can be understood as the inverse effect of spin torque, and gives access to the physics of magnetization dynamics and damping. An interesting question is that whether spin pumping occurring under nonlinear spin dynamics would differ from linear case. It is known that nonlinear spin dynamics differ distinctly from linear response, a variety of amplitude dependent nonlinear effect would present. It has been found that for spin precession angle above a few degrees, nonlinear damping term would present and dominated the dynamic energy/spin-moment dissipation. Since spin pumping are closely related to the damping process, it is interesting to ask whether the nonlinear damping term could be involved in spin pumping process. We studied the spin pumping effect occurring under nonlinear spin precession. A device which is a Pt/YIG microstrip coupled with coplanar waveguide was used. High power excitation resulted in spin precession entering in a nonlinear regime. Foldover resonance lineshape and nonlinear damping have been observed. Based on those nonlinear effects, we determined the values of the precession cone angles, and the maximum cone angle can reach a values as high as 21.5 degrees. We found that even in nonlinear regime, spin pumping is still linear, which means the nonlinear damping and foldover would not affect spin pumping process.
Global methods for nonlinear complementarity problems
More, J.J.
1994-04-01
Global methods for nonlinear complementarity problems formulate the problem as a system of nonsmooth nonlinear equations approach, or use continuation to trace a path defined by a smooth system of nonlinear equations. We formulate the nonlinear complementarity problem as a bound-constrained nonlinear least squares problem. Algorithms based on this formulation are applicable to general nonlinear complementarity problems, can be started from any nonnegative starting point, and each iteration only requires the solution of systems of linear equations. Convergence to a solution of the nonlinear complementarity problem is guaranteed under reasonable regularity assumptions. The converge rate is Q-linear, Q-superlinear, or Q-quadratic, depending on the tolerances used to solve the subproblems.
Earth solids and dynamic nonlinear elasticity
Johnson, P.A. |; Abeele, K.E.A. Van Den
1997-05-01
The authors` intention is to describe several manifestations of nonlinear behavior in rock. Nonlinear response may manifest itself in a variety of manners, including a nonlinear stress-strain relation, nonlinear attenuation, harmonic generation, resonant peak shift and slow dynamics, all of which are related. The authors have ample evidence that the responsible mechanism for nonlinear response [to first order] is the presence of compliant features and the influence of fluid. They define compliant features as those features that are the weakest in the rock, e.g., grain-to-grain contacts, low aspect ratio cracks, joints, etc. In addition, there may be other mechanisms responsible as yet unidentified. In the following, the authors emphasize the robust nature of observations by illustrating several experimental examples. They do not review the related theoretical framework. Finally, they do not present nonlinear parameters derived from these experiments as the purpose in this paper is to illustrate rather than quantify nonlinear response.
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.
Nonlinear buffer layers relevant for reduced nonlinear effects in HTS microwave devices
NASA Astrophysics Data System (ADS)
Seron, D.
2008-02-01
Microwave devices made of a High-Temperature Superconductor (HTS) exhibit a nonlinear response as the microwave power increases. The HTS nonlinearities generate a nonlinear inductance Ld(irf) and a nonlinear resistance Rd(irf) in a device. Ld(irf) and Rd(irf) are responsible for an increase of the device loss, a small frequency dispersion as well as the generation of spurious signals like Intermodulation Distortion (IMD). Nevertheless, the HTS nonlinearities in a microwave device can be reduced using a nonlinear dielectric like a ParaElectric Material (PEM). This assumption has recently been demonstrated theoretically. In a microwave device made of a HTS and a PEM, the nonlinear contribution to the capacitance Cd(vrf) from the PEM acts oppositely to the nonlinear contribution to Ld(irf). This may cancel the effect of the HTS inductive nonlinearities. The PEM also produces a nonlinear conductance Gd(vrf) in a device. All these nonlinear terms contribute to the IMD output power and the nonlinear quality factor (Q0) of a resonant passive microwave device. In this paper, the dependence of the different nonlinear contributions on frequency and applied dc bias voltage (Vdc) is investigated. The relevance to employ PEM in order to reduce the nonlinearities in HTS microwave devices is discussed.
Probing hysteretic elasticity in weakly nonlinear materials
Johnson, Paul A; Haupert, Sylvain; Renaud, Guillaume; Riviere, Jacques; Talmant, Maryline; Laugier, Pascal
2010-12-07
Our work is aimed at assessing the elastic and dissipative hysteretic nonlinear parameters' repeatability (precision) using several classes of materials with weak, intermediate and high nonlinear properties. In this contribution, we describe an optimized Nonlinear Resonant Ultrasound Spectroscopy (NRUS) measuring and data processing protocol applied to small samples. The protocol is used to eliminate the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic elastic nonlinearity. As an example, in our experiments, we identified external temperature fluctuation as a primary source of material resonance frequency and elastic modulus variation. A variation of 0.1 C produced a frequency variation of 0.01 %, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to eliminate environmental effects, the variation in f{sub 0} (the elastically linear resonance frequency proportional to modulus) is fit with the appropriate function, and that function is used to correct the NRUS calculation of nonlinear parameters. With our correction procedure, we measured relative resonant frequency shifts of 10{sup -5} , which are below 10{sup -4}, often considered the limit to NRUS sensitivity under common experimental conditions. Our results show that the procedure is an alternative to the stringent control of temperature often applied. Applying the approach, we report nonlinear parameters for several materials, some with very small nonclassical nonlinearity. The approach has broad application to NRUS and other Nonlinear Elastic Wave Spectroscopy approaches.
Nonlinear microscopy for material characterization
NASA Astrophysics Data System (ADS)
Weber, Reed Alan
Making use of femtosecond laser sources, nonlinear microscopy provides access to previously unstudied aspects of materials. By probing third order nonlinear optical signals determined by the nonlinear susceptibility chi (3), which is present in all materials, we gain insight not available by conventional linear or electron microscopy. Third-harmonic (TH) microscopy is applied to supplement laser-induced damage studies of dielectric oxide thin film optical coatings. We present high contrast (S/N> 100 : 1) TH imaging of ≈17 nm nanoindentations, individual 10 nm gold nanoparticles, nascent scandia and hafnia films, and laser induced material modification both above and below damage threshold conditions in hafnia thin-films. These results imply that TH imaging is potentially sensitive to laser-induced strain as well as to nanoscale defects or contamination in oxide films. Compared to other sensitive imaging techniques such as Nomarski and dark field, TH imaging exhibits dramatically increased sensitivity to typical material modifications undergone during the formation of optical damage as evidenced by a dynamic range ≈106 : 1. Four-wave mixing (FWM) microscopy is employed to investigate delay dependent FWM signals and their implied characteristic resonant response times in multiple solvents. Mathematical modeling of resonant coherent anti-Stokes Raman scattering (CARS), coherent Stokes Raman scattering (CSRS) and stimulated parametric emission (SPE) processes supplement the FWM studies and suggest a resonant CARS process that accounts for ≈95% of the total visible FWM signal which probes a characteristic material response time ≈100 fs. This signal enhancement likely indicates the net effects of probing several Raman active C-H stretch bands near 2950 cm-1. This FWM technique may be applied to characterize the dominant resonant response of the sample under study. Furthermore this technique presents the newfound capability to provide estimates of characteristic
Nonlinear Processes in Vibroseismic Monitoring
Khairetdinov, M. S.; Voskoboynikova, G. M.
2008-06-24
In this paper, on the basis of numerical calculations and results of processing of the data of field experiments, quantitative estimates of the spectral broadening of the initial sounding seismic oscillations are presented. The estimates were obtained as a result of vibroseismic sounding of fractured dilatancy media typical for seismically and volcanically dangerous zones. The authors' idea about the applicability of the parameters of wave field nonlinearity in the form of possible prognostic characteristics of the earthquake-volcano source development process is justified.
Beams on nonlinear elastic foundation
Lukkassen, Dag; Meidell, Annette
2014-12-10
In order to determination vertical deflections and rail bending moments the Winkler model (1867) is often used. This linear model neglects several conditions. For example, by using experimental results, it has been observed that there is a substantial increase in the maximum rail deflection and rail bending moment when considering the nonlinearity of the track support system. A deeper mathematical analysis of the models is necessary in order to obtain better methods for more accurate numerical solutions in the determination of deflections and rail bending moments. This paper is intended to be a small step in this direction.
Nonlinear dynamics of cell orientation
NASA Astrophysics Data System (ADS)
Safran, S. A.; de, Rumi
2009-12-01
The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, τc , for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, τc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.
Galerkin Method for Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
Noack, Bernd R.; Schlegel, Michael; Morzynski, Marek; Tadmor, Gilead
A Galerkin method is presented for control-oriented reduced-order models (ROM). This method generalizes linear approaches elaborated by M. Morzyński et al. for the nonlinear Navier-Stokes equation. These ROM are used as plants for control design in the chapters by G. Tadmor et al., S. Siegel, and R. King in this volume. Focus is placed on empirical ROM which compress flow data in the proper orthogonal decomposition (POD). The chapter shall provide a complete description for construction of straight-forward ROM as well as the physical understanding and teste
A model of nonlinear electrodynamics
Kruglov, S.I.
2015-02-15
A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.
Dimensional interpolation for nonlinear filters
NASA Astrophysics Data System (ADS)
Daum, Fred
2005-09-01
Dimensional interpolation has been used successfully by physicists and chemists to solve the Schroedinger equation for atoms and complex molecules. The same basic idea can be used to solve the Fokker-Planck equation for nonlinear filters. In particular, it is well known (by physicists) that two Schroedinger equations are equivalent to two Fokker-Planck equations. Moreover, we can avoid the Schroedinger equation altogether and use dimensional interpolation directly on the Fokker-Planck equation. Dimensional interpolation sounds like a crazy idea, but it works. We will attempt to make this paper accessible to normal engineers who do not have quantum mechanics for breakfast.
Split quaternion nonlinear adaptive filtering.
Ujang, Bukhari Che; Took, Clive Cheong; Mandic, Danilo P
2010-04-01
A split quaternion learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of three- and four-dimensional signals is proposed. The derivation takes into account the non-commutativity of the quaternion product, an aspect neglected in the derivation of the existing learning algorithms. It is shown that the additional information taken into account by a rigorous treatment of quaternion algebra provides improved performance on hypercomplex processes. A rigorous analysis of the convergence of the proposed algorithms is also provided. Simulations on both benchmark and real-world signals support the approach.
Nonlinear structural crack growth monitoring
Welch, Donald E.; Hively, Lee M.; Holdaway, Ray F.
2002-01-01
A method and apparatus are provided for the detection, through nonlinear manipulation of data, of an indicator of imminent failure due to crack growth in structural elements. The method is a process of determining energy consumption due to crack growth and correlating the energy consumption with physical phenomena indicative of a failure event. The apparatus includes sensors for sensing physical data factors, processors or the like for computing a relationship between the physical data factors and phenomena indicative of the failure event, and apparatus for providing notification of the characteristics and extent of such phenomena.
Nonlinear Mode-Coupling in Nanomechanical Systems
Matheny, M. H.; Villanueva, L. G.; Karabalin, R. B.; Sader, J. E.; Roukes, M. L.
2013-01-01
Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced nanomechanical devices; it has important implications for applications ranging from quantitative sensing to fundamental research. However, achieving accurate experimental characterization of nonlinearities in nanomechanical systems (NEMS) is problematic. Currently employed detection and actuation schemes themselves tend to be highly nonlinear, and this unrelated nonlinear response has been inadvertently convolved into many previous measurements. In this Letter we describe an experimental protocol and a highly linear transduction scheme, specifically designed for NEMS, that enables accurate, in situ characterization of device nonlinearities. By comparing predictions from Euler–Bernoulli theory for the intra- and intermodal nonlinearities of a doubly clamped beam, we assess the validity of our approach and find excellent agreement. PMID:23496001
Nonlinear magnetohydrodynamics of edge localized mode precursors
Guo, Z. B.; Wang, Lu; Wang, X. G.
2015-02-15
A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.
NASA Astrophysics Data System (ADS)
Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.
2014-05-01
The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects
Aspects of coherent states of nonlinear algebras
NASA Astrophysics Data System (ADS)
Shreecharan, T.; Chaitanya, K. V. S. Shiv
2010-12-01
Various aspects of coherent states of nonlinear su(2) and su(1, 1) algebras are studied. It is shown that the nonlinear su(1, 1) Barut-Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived.
Deterministic implementation of weak quantum cubic nonlinearity
Marek, Petr; Filip, Radim; Furusawa, Akira
2011-11-15
We propose a deterministic implementation of weak cubic nonlinearity, which is a basic building block of a full-scale continuous-variable quantum computation. Our proposal relies on preparation of a specific ancillary state and transferring its nonlinear properties onto the desired target by means of deterministic Gaussian operations and feed forward. We show that, despite the imperfections arising from the deterministic nature of the operation, the weak quantum nonlinearity can be implemented and verified with the current level of technology.
Investigation of a Nonlinear Control System
NASA Technical Reports Server (NTRS)
Flugge-Lotz, I; Taylor, C F; Lindberg, H E
1958-01-01
A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.
Spurious Solutions Of Nonlinear Differential Equations
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.; Griffiths, D. F.
1992-01-01
Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.
Nonlinear long-range plasmonic waveguides
Degiron, Aloyse; Smith, David R.
2010-09-15
We report on plasmonic waveguides made of a thin metal stripe surrounded on one or both sides by a Kerr nonlinear medium. Using an iterative numerical method, we investigate the stationary long-range plasmons that exist for self-focusing and self-defocusing Kerr-type nonlinearities. The solutions are similar to the well-known case of infinitely wide nonlinear waveguides - they are strongly power-dependent and can experience symmetry-breaking bifurcations under appropriate conditions.
Vibrational Control of a Nonlinear Elastic Panel
NASA Technical Reports Server (NTRS)
Chow, P. L.; Maestrello, L.
1998-01-01
The paper is concerned with the stabilization of the nonlinear panel oscillation by an active control. The control is actuated by a combination of additive and parametric vibrational forces. A general method of vibrational control is presented for stabilizing panel vibration satisfying a nonlinear beam equation. To obtain analytical results, a perturbation technique is used in the case of weak nonlinearity. Possible application to other types of problems is briefly discussed.
Nonlinear secret image sharing scheme.
Shin, Sang-Ho; Lee, Gil-Je; Yoo, Kee-Young
2014-01-01
Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2 m⌉ bit-per-pixel (bpp), respectively.
Nonlinear spectroscopy of trapped ions
NASA Astrophysics Data System (ADS)
Schlawin, Frank; Gessner, Manuel; Mukamel, Shaul; Buchleitner, Andreas
2014-08-01
Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and it has become a highly successful method for experiments in chemical physics. Current quantum optical experiments approach system sizes and levels of complexity that require the development of efficient techniques to assess spectral and dynamical features with scalable experimental overhead. However, established methods from optical spectroscopy of macroscopic ensembles cannot be applied straightforwardly to few-atom systems. Based on the ideas proposed in M. Gessner et al., (arXiv:1312.3365), we develop a diagrammatic approach to construct nonlinear measurement protocols for controlled quantum systems, and we discuss experimental implementations with trapped ion technology in detail. These methods, in combination with distinct features of ultracold-matter systems, allow us to monitor and analyze excitation dynamics in both the electronic and vibrational degrees of freedom. They are independent of system size, and they can therefore reliably probe systems in which, e.g., quantum state tomography becomes prohibitively expensive. We propose signals that can probe steady-state currents, detect the influence of anharmonicities on phonon transport, and identify signatures of chaotic dynamics near a quantum phase transition in an Ising-type spin chain.
Nonlinear secret image sharing scheme.
Shin, Sang-Ho; Lee, Gil-Je; Yoo, Kee-Young
2014-01-01
Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2 m⌉ bit-per-pixel (bpp), respectively. PMID:25140334
Nonlinear electrodynamics and CMB polarization
Cuesta, Herman J. Mosquera; Lambiase, G. E-mail: lambiase@sa.infn.it
2011-03-01
Recently WMAP and BOOMERanG experiments have set stringent constraints on the polarization angle of photons propagating in an expanding universe: Δα = (−2.4±1.9)°. The polarization of the Cosmic Microwave Background radiation (CMB) is reviewed in the context of nonlinear electrodynamics (NLED). We compute the polarization angle of photons propagating in a cosmological background with planar symmetry. For this purpose, we use the Pagels-Tomboulis (PT) Lagrangian density describing NLED, which has the form L ∼ (X/Λ{sup 4}){sup δ−1} X, where X = ¼F{sub αβ}F{sup αβ}, and δ the parameter featuring the non-Maxwellian character of the PT nonlinear description of the electromagnetic interaction. After looking at the polarization components in the plane orthogonal to the (x)-direction of propagation of the CMB photons, the polarization angle is defined in terms of the eccentricity of the universe, a geometrical property whose evolution on cosmic time (from the last scattering surface to the present) is constrained by the strength of magnetic fields over extragalactic distances.
Nonlinear Secret Image Sharing Scheme
Shin, Sang-Ho; Yoo, Kee-Young
2014-01-01
Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2m⌉ bit-per-pixel (bpp), respectively. PMID:25140334
Multilayer perceptron for nonlinear programming.
Reifman, J.; Feldman, E. E.; Reactor Analysis
2002-08-01
A new method for solving nonlinear programming problems within the framework of a multilayer neural network perceptron is proposed. The method employs the Penalty Function method to transform a constrained optimization problem into a sequence of unconstrained optimization problems and then solves the sequence of unconstrained optimizations of the transformed problem by training a series of multilayer perceptrons. The neural network formulation is represented in such a way that the multilayer perceptron prediction error to be minimized mimics the objective function of the unconstrained problem, and therefore, the minimization of the objective function for each unconstrained optimization is attained by training a single perceptron. The multilayer perceptron allows for the transformation of problems with two-sided bounding constraints on the decision variables x, e.g., a{<=}x{sub n}{<=}b, into equivalent optimization problems in which these constraints do not explicitly appear. Hence, when these are the only constraints in the problem, the transformed problem is constraint free (i.e., the transformed objective function contains no penalty terms) and is solved by training a multilayer perceptron only once. In addition, we present a new Penalty Function method for solving nonlinear programming problems that is parameter free and guarantees that feasible solutions are obtained when the optimal solution is on the boundary of the feasible region. Simulation results, including an example from operations research, illustrate the proposed methods.
A chinchilla nonlinear cochlear filterbank
NASA Astrophysics Data System (ADS)
Lopez-Najera, Alberto; Lopez-Poveda, Enrique A.; Meddis, Ray
2002-05-01
A dual-resonance nonlinear (DRNL) filter [Meddis et al., J. Acoust. Soc. Am. 106, 2852-2861 (2001)] was fitted to model chinchilla cochlear responses to tonal stimuli at individual sites along the basilar membrane (BM) with best frequencies (BF) of 0.8, 5.5, 7.25, 9.75, 10.0, 12.0, and 14.0 kHz. At each BF, parameters were obtained for the DRNL filter to reproduce input/output and tuning curves. The match between the model and the experimental data is almost perfect for frequencies near BF. Quantitatively, the model response gets worse (but is still reasonable) for frequencies well below and well above BF. These discrepancies are discussed in terms of the middle-ear function, which proves critical. The model responses to clicks, AM, multicomponent, and Schroder-phase stimuli were also compared against experimental data. Results show that the architecture of the DRNL filter seems suitable to reproduce this wide range of phenomena. Strategies are discussed for developing a chinchilla nonlinear cochlear filterbank from current parameters. [Work supported by the Consejería de Sanidad of the Junta de Comunidades of Castilla, La Mancha.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Inertial Mass from Spin Nonlinearity
NASA Astrophysics Data System (ADS)
Cohen, Marcus
The inertial mass of a Fermion shows up as chiral cross-coupling in its Dirac system. No scalar term can invariantly couple left and right chirality fields; the Dirac matrices must be spin tensors of mixed chirality. We show how such tensor couplings could arise from nonlinear mixing of four spinor fields, two representing the local electron fields and two inertial spinor fields sourced in the distant masses. We thus give a model that implements Mach's principle. Following Mendel Sachs,1 we let the inertial spinors factor the moving spacetime tetrads qα(x) and bar {q}α (x) that appear in the Dirac operator. The inertial spinors do more than set the spacetime "stage;" they are players in the chiral dynamics. Specifically, we show how the massive Dirac system arises as the envelope modulation equations coupling left and right chirality electron fields on a Friedmann universe via nonlinear "spin gratings" with the inertial spinor fields. These gratings implement Penrose's "mass-scatterings," which keep the null zig-zags of the bispinor wave function confined to a timelike world tube. Local perturbations to the inertial spinor fields appear in the Dirac system as Abelian and non-Abelian vector potentials.
Scalar discrete nonlinear multipoint boundary value problems
NASA Astrophysics Data System (ADS)
Rodriguez, Jesus; Taylor, Padraic
2007-06-01
In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].
Detecting nonlinear oscillations in broadband signals
NASA Astrophysics Data System (ADS)
Vejmelka, Martin; Paluš, Milan
2009-03-01
A framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modeled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, it can be further analyzed using nonlinear approaches such as phase synchronization analysis. For linear processes standard approaches, such as the coherence analysis, are more appropriate. The method is illustrated in a numerical example and applied to analyze experimentally obtained human electroencephalogram time series from a sleeping subject.
Nonlinear magnetohydrodynamics of electron-positron plasmas
NASA Astrophysics Data System (ADS)
Shukla, P. K.; Dasgupta, B.; Sakanaka, P. H.
2000-05-01
A set of nonlinear magnetohydrodynamic (MHD) equations for magnetized, nonrelativistic electron-positron plasmas is derived by employing a two fluid model that is supplemented by Ampère's and Faraday's laws. The nonlinear equations show how the baroclinic driver (the Biermann battery) generates the electron positron flows and how these flows give rise to plasma currents which act as a source for the magnetic fields. The newly derived nonlinear equations form a basis for investigating waves, instabilities, as well as coherent nonlinear structures, in addition to studying exact equilibria of electron-positron jets in a magnetoplasma.
Detonator comprising a nonlinear transmission line
Elizondo-Decanini, Juan M
2014-12-30
Detonators are described herein. In a general embodiment, the detonator includes a nonlinear transmission line that has a variable capacitance. Capacitance of the nonlinear transmission line is a function of voltage on the nonlinear transmission line. The nonlinear transmission line receives a voltage pulse from a voltage source and compresses the voltage pulse to generate a trigger signal. Compressing the voltage pulse includes increasing amplitude of the voltage pulse and decreasing length of the voltage pulse in time. An igniter receives the trigger signal and detonates an explosive responsive to receipt of the trigger signal.
Single-ion nonlinear mechanical oscillator
Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.
2010-12-15
We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
Single-ion nonlinear mechanical oscillator
NASA Astrophysics Data System (ADS)
Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.
2010-12-01
We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
Kurtosis Approach for Nonlinear Blind Source Separation
NASA Technical Reports Server (NTRS)
Duong, Vu A.; Stubbemd, Allen R.
2005-01-01
In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.
Kurtosis Approach Nonlinear Blind Source Separation
NASA Technical Reports Server (NTRS)
Duong, Vu A.; Stubbemd, Allen R.
2005-01-01
In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.
Nonlinear wave dynamics in honeycomb lattices
Bahat-Treidel, Omri; Segev, Mordechai
2011-08-15
We study the nonlinear dynamics of wave packets in honeycomb lattices and show that, in quasi-one-dimensional configurations, the waves propagating in the lattice can be separated into left-moving and right-moving waves, and any wave packet composed of only left (or only right) movers does not change its intensity structure in spite of the nonlinear evolution of its phase. We show that the propagation of a general wave packet can be described, within a good approximation, as a superposition of left- and right-moving self-similar (nonlinear) wave packets. Finally, we find that Klein tunneling is not suppressed by nonlinearity.
Nonlinearly stacked low noise turbofan stator
NASA Technical Reports Server (NTRS)
Schuster, William B. (Inventor); Kontos, Karen B. (Inventor); Weir, Donald S. (Inventor); Nolcheff, Nick A. (Inventor); Gunaraj, John A. (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.
Nonlinear optics quantum computing with circuit QED.
Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M
2013-02-01
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.
Dark energy simulacrum in nonlinear electrodynamics
Labun, Lance; Rafelski, Johann
2010-03-15
Quasiconstant external fields in nonlinear electromagnetism generate a global contribution proportional to g{sup {mu}{nu}}in the energy-momentum tensor, thus a simulacrum of dark energy. To provide a thorough understanding of the origin and strength of its effects, we undertake a complete theoretical and numerical study of the energy-momentum tensor T{sup {mu}{nu}}for nonlinear electromagnetism. The Euler-Heisenberg nonlinearity due to quantum fluctuations of spinor and scalar matter fields is considered and contrasted with the properties of classical nonlinear Born-Infeld electromagnetism. We address modifications of charged particle kinematics by strong background fields.
Nonlinear response theory in chemical kinetics.
Kryvohuz, Maksym; Mukamel, Shaul
2014-01-21
A theory of nonlinear response of chemical kinetics, in which multiple perturbations are used to probe the time evolution of nonlinear chemical systems, is developed. Expressions for nonlinear chemical response functions and susceptibilities, which can serve as multidimensional measures of the kinetic pathways and rates, are derived. A new class of multidimensional measures that combine multiple perturbations and measurements is also introduced. Nonlinear fluctuation-dissipation relations for steady-state chemical systems, which replace operations of concentration measurement and perturbations, are proposed. Several applications to the analysis of complex reaction mechanisms are provided.
Nonlinear mode conversion in monodomain magnetic squares
NASA Astrophysics Data System (ADS)
Kostylev, Mikhail; Demidov, Vladislav E.; Hansen, Ulf-Hendrik; Demokritov, Sergej O.
2007-12-01
Modifications of the spatial distributions of dynamic magnetization corresponding to spin-wave eigenmodes of magnetic squares subjected to a strong microwave excitation field have been studied experimentally and theoretically. We show that an increase of the excitation power leads to nonlinear generation of long-wavelength spatial harmonics caused by the nonlinear cross coupling between the eigenmodes. The analysis of the experimental data shows that this process is mainly governed by the action of the nonlinear spin-wave damping. This conclusion is further supported by numerical calculations based on the complex Ginzburg-Landau equation, phenomenologically taking into account the nonlinear damping.
Nonlinear optical protection against frequency agile lasers
McDowell, V.P.
1988-08-04
An eye-protection or equipment-filter device for protection from laser energy is disclosed. The device may be in the form of a telescope, binoculars, goggles, constructed as part of equipment such as image intensifiers or range designators. Optical elements focus the waist of the beam within a nonlinear frequency-doubling crystal or nonlinear optical element or fiber. The nonlinear elements produce a harmonic outside the visible spectrum in the case of crystals, or absorb the laser energy in the case of nonlinear fibers. Embodiments include protectors for the human eye as well as filters for sensitive machinery such as TV cameras, FLIR systems or other imaging equipment.
NASA Astrophysics Data System (ADS)
Vörös, Jozef
2016-07-01
The paper deals with the parameter identification of cascade nonlinear dynamic systems with noninvertible piecewise linear input nonlinearities and backlash output nonlinearities. Application of the key term separation principle provides special expressions for the corresponding nonlinear model description that are linear in parameters. A least squares based iterative technique allows estimation of all the model parameters based on measured input/output data. Simulation studies illustrate the feasibility of proposed identification method.
Theory and design of nonlinear metamaterials
NASA Astrophysics Data System (ADS)
Rose, Alec Daniel
If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers
Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1999-01-01
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model.
Altmann, Yoann; Dobigeon, Nicolas; Tourneret, Jean-Yves
2013-04-01
This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér-Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies.
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
NASA Astrophysics Data System (ADS)
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
Back in 1967, Clifford Gardner, John Greene, Martin Kruskal and Robert Miura published a seminal paper in Physical Review Letters which was to become a cornerstone in the theory of integrable systems. In 2006, the authors of this paper received the AMS Steele Prize. In this award the AMS pointed out that `In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.' From this discovery the modern theory of integrability bloomed, leading scientists to a deep understanding of many nonlinear phenomena which is by no means reachable by perturbation methods or other previous tools from linear theories. Nonlinear phenomena appear everywhere in nature, their description and understanding is therefore of great interest both from the theoretical and applicative point of view. If a nonlinear phenomenon can be represented by an integrable system then we have at our disposal a variety of tools to achieve a better mathematical description of the phenomenon. This special issue is largely dedicated to investigations of nonlinear phenomena which are related to the concept of integrability, either involving integrable systems themselves or because they use techniques from the theory of integrability. The idea of this special issue originated during the 18th edition of the Nonlinear Evolution Equations and Dynamical Systems (NEEDS) workshop, held at Isola Rossa, Sardinia, Italy, 16-23 May 2009 (http://needs-conferences.net/2009/). The issue benefits from the occasion offered by the meeting, in particular by its mini-workshops programme, and contains invited review papers and contributed papers. It is worth pointing out that there was an open call for papers and all contributions were peer reviewed
Nonlinear features for product inspection
NASA Astrophysics Data System (ADS)
Talukder, Ashit; Casasent, David P.
1999-03-01
Classification of real-time X-ray images of randomly oriented touching pistachio nuts is discussed. The ultimate objective is the development of a system for automated non-invasive detection of defective product items on a conveyor belt. We discuss the extraction of new features that allow better discrimination between damaged and clean items (pistachio nuts). This feature extraction and classification stage is the new aspect of this paper; our new maximum representation and discriminating feature (MRDF) extraction method computes nonlinear features that are used as inputs to a new modified k nearest neighbor classifier. In this work, the MRDF is applied to standard features (rather than iconic data). The MRDF is robust to various probability distributions of the input class and is shown to provide good classification and new ROC (receiver operating characteristic) data.
Shaping the nonlinear near field.
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states. PMID:26762487
Nonlinear optical photovoltaics (presentation video)
NASA Astrophysics Data System (ADS)
Nunzi, Jean-Michel; Mirzaee, Somayeh M.
2014-10-01
Nonlinear absorption was investigated in a poly (3-hexylthiophene) (P3HT) PCBM fullerene blend, one of the most popular organic solar cell's materials. We observed three-photon absorption in the bulk hetero junction photodiode configuration. The output photocurrent of the photodiode was interpreted in terms of the three-photon absorption properties of the P3HT:PCBM blend at 1550 nm. Can the concept be extrapolated to high efficiency solar cells? We propose an optical antenna technology revisited with plasmonics and organic rectifiers that should permit the development of an ultra-high efficiency PV technology that is compatible with large-area fabrication (self assembling) and low-cost (plastic) technologies.
Nonlinear image filtering within IDP++
Lehman, S.K.; Wieting, M.G.; Brase, J.M.
1995-02-09
IDP++, image and data processing in C++, is a set of a signal processing libraries written in C++. It is a multi-dimension (up to four dimensions), multi-data type (implemented through templates) signal processing extension to C++. IDP++ takes advantage of the object-oriented compiler technology to provide ``information hiding.`` Users need only know C, not C++. Signals or data sets are treated like any other variable with a defined set of operators and functions. We here some examples of the nonlinear filter library within IDP++. Specifically, the results of MIN, MAX median, {alpha}-trimmed mean, and edge-trimmed mean filters as applied to a real aperture radar (RR) and synthetic aperture radar (SAR) data set.
Nonlinear control of magnetic bearings
NASA Technical Reports Server (NTRS)
Pradeep, A. K.; Gurumoorthy, R.
1994-01-01
In this paper we present a variety of nonlinear controllers for the magnetic bearing that ensure both stability and robustness. We utilize techniques of discontinuous control to design novel control laws for the magnetic bearing. We present in particular sliding mode controllers, time optimal controllers, winding algorithm based controllers, nested switching controllers, fractional controllers, and synchronous switching controllers for the magnetic bearing. We show existence of solutions to systems governed by discontinuous control laws, and prove stability and robustness of the chosen control laws in a rigorous setting. We design sliding mode observers for the magnetic bearing and prove the convergence of the state estimates to their true values. We present simulation results of the performance of the magnetic bearing subject to the aforementioned control laws, and conclude with comments on design.
Nonlinear control with neural networks
Malik, S.A.
1996-12-31
Research results are presented to show the successful industrial application of neural networks in closed loop. Two distillation columns are used to demonstrate the effectiveness of nonlinear controllers. The two columns chosen for this purpose are very dissimilar in operating characteristics, and dynamic behavior. One of the columns is a crude column, and the second, a depropaniser, is a smaller column in a vapor recovery unit. In earlier work, neural networks had been presented as general function estimators, for prediction of stream compositions and the suitability of the various network architectures for this task had been investigated. This report reviews the successful application of neural networks, as feedback controllers, to large industrial distillation columns. 21 refs.
Nonlinear stability of supersonic jets
NASA Technical Reports Server (NTRS)
Tiwari, S. N. (Principal Investigator); Bhat, T. R. S. (Principal Investigator)
1996-01-01
The stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations are presented. In this analysis the large scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.
Nonlinear Stability of Supersonic Jets
NASA Technical Reports Server (NTRS)
Bhat, T. R. S.; Seiner, J. M.; Tiwari, S. N.
1995-01-01
This paper presents stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations. In this analysis the large-scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.
Nonlinear Diffusion and Transient Osmosis
NASA Astrophysics Data System (ADS)
Akira, Igarashi; Lamberto, Rondoni; Antonio, Botrugno; Marco, Pizzi
2011-08-01
We investigate both analytically and numerically the concentration dynamics of a solution in two containers connected by a narrow and short channel, in which diffusion obeys a porous medium equation. We also consider the variation of the pressure in the containers due to the flow of matter in the channel. In particular, we identify a phenomenon, which depends on the transport of matter across nano-porous membranes, which we call “transient osmosis". We find that nonlinear diffusion of the porous medium equation type allows numerous different osmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion. Experimental results suggest one possible candidate for transiently osmotic processes.
Shaping the nonlinear near field
NASA Astrophysics Data System (ADS)
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states.
Nonlinear image filtering within IDP++
NASA Astrophysics Data System (ADS)
Lehman, Sean K.; Wieting, Mel G.; Brase, James M.
1995-03-01
IDP++, image and data processing in C++, is a set of signal processing libraries written in C++. It is a multi-dimension (up to four dimensions), multi-data type (implemented through templates) signal processing extension to C++. IDP++ takes advantage of the object-oriented compiler technology to provide `information hiding.' Users need only know C, not C++. Signals or data sets are treated like any other variable with a defined set of operators and functions. We present here some examples of the nonlinear filter library within IDP++. Specifically, the results of min, max, median, (alpha) -trimmed mean, and edge-trimmed mean filters as applied to a real aperture radar (RAR) and synthetic aperture radar (SAR) data set.
Shaping the nonlinear near field
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states. PMID:26762487
NASA Astrophysics Data System (ADS)
Pai, P. Frank
2011-10-01
Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.
Nonlinear control of magnetic signatures
NASA Astrophysics Data System (ADS)
Niemoczynski, Bogdan
Magnetic properties of ferrite structures are known to cause fluctuations in Earth's magnetic field around the object. These fluctuations are known as the object's magnetic signature and are unique based on the object's geometry and material. It is a common practice to neutralize magnetic signatures periodically after certain time intervals, however there is a growing interest to develop real time degaussing systems for various applications. Development of real time degaussing system is a challenging problem because of magnetic hysteresis and difficulties in measurement or estimation of near-field flux data. The goal of this research is to develop a real time feedback control system that can be used to minimize magnetic signatures for ferrite structures. Experimental work on controlling the magnetic signature of a cylindrical steel shell structure with a magnetic disturbance provided evidence that the control process substantially increased the interior magnetic flux. This means near field estimation using interior sensor data is likely to be inaccurate. Follow up numerical work for rectangular and cylindrical cross sections investigated variations in shell wall flux density under a variety of ambient excitation and applied disturbances. Results showed magnetic disturbances could corrupt interior sensor data and magnetic shielding due to the shell walls makes the interior very sensitive to noise. The magnetic flux inside the shell wall showed little variation due to inner disturbances and its high base value makes it less susceptible to noise. This research proceeds to describe a nonlinear controller to use the shell wall data as an input. A nonlinear plant model of magnetics is developed using a constant tau to represent domain rotation lag and a gain function k to describe the magnetic hysteresis curve for the shell wall. The model is justified by producing hysteresis curves for multiple materials, matching experimental data using a particle swarm algorithm, and
NLINEAR - NONLINEAR CURVE FITTING PROGRAM
NASA Technical Reports Server (NTRS)
Everhart, J. L.
1994-01-01
A common method for fitting data is a least-squares fit. In the least-squares method, a user-specified fitting function is utilized in such a way as to minimize the sum of the squares of distances between the data points and the fitting curve. The Nonlinear Curve Fitting Program, NLINEAR, is an interactive curve fitting routine based on a description of the quadratic expansion of the chi-squared statistic. NLINEAR utilizes a nonlinear optimization algorithm that calculates the best statistically weighted values of the parameters of the fitting function and the chi-square that is to be minimized. The inputs to the program are the mathematical form of the fitting function and the initial values of the parameters to be estimated. This approach provides the user with statistical information such as goodness of fit and estimated values of parameters that produce the highest degree of correlation between the experimental data and the mathematical model. In the mathematical formulation of the algorithm, the Taylor expansion of chi-square is first introduced, and justification for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations are derived, which are solved by matrix algebra. To achieve convergence, the algorithm requires meaningful initial estimates for the parameters of the fitting function. NLINEAR is written in Fortran 77 for execution on a CDC Cyber 750 under NOS 2.3. It has a central memory requirement of 5K 60 bit words. Optionally, graphical output of the fitting function can be plotted. Tektronix PLOT-10 routines are required for graphics. NLINEAR was developed in 1987.
Nonlinear optical studies of surfaces
Shen, Y.R.
1994-07-01
The possibly of using nonlinear optical processes for surface studies has attracted increasing attention in recent years. Optical second harmonic generation (SHG) and sum frequency generation (SFG), in particular, have been well accepted as viable surface probes. They have many advantages over the conventional techniques. By nature, they are highly surface-specific and has a submonolayer sensitivity. As coherent optical processes, they are capable of in-situ probing of surfaces in hostile environment as well as applicable to all interfaces accessible by light. With ultrafast pump laser pulses, they can be employed to study surface dynamic processes with a subpicosecond time resolution. These advantages have opened the door to many exciting research opportunities in surface science and technology. This paper gives a brief overview of this fast-growing new area of research. Optical SHG from a surface was first studied theoretically and experimentally in the sixties. Even the submonolayer surface sensitivity of the process was noticed fairly early. The success was, however, limited because of difficulties in controlling the experimental conditions. It was not until the early 1980`s that the potential of the process for surface analysis was duly recognized. The first surface study by SHG was actually motivated by the then active search for an understanding of the intriguing surface enhanced Raman scattering (SERS). It had been suspected that the enhancement in SERS mainly came from the local-field enhancement due to local plasmon resonances and pointing rod effect on rough metal surfaces. In our view, Raman scattering is a two-photon process and is therefore a nonlinear optical effect.
Nonlinear Statistical Modeling of Speech
NASA Astrophysics Data System (ADS)
Srinivasan, S.; Ma, T.; May, D.; Lazarou, G.; Picone, J.
2009-12-01
Contemporary approaches to speech and speaker recognition decompose the problem into four components: feature extraction, acoustic modeling, language modeling and search. Statistical signal processing is an integral part of each of these components, and Bayes Rule is used to merge these components into a single optimal choice. Acoustic models typically use hidden Markov models based on Gaussian mixture models for state output probabilities. This popular approach suffers from an inherent assumption of linearity in speech signal dynamics. Language models often employ a variety of maximum entropy techniques, but can employ many of the same statistical techniques used for acoustic models. In this paper, we focus on introducing nonlinear statistical models to the feature extraction and acoustic modeling problems as a first step towards speech and speaker recognition systems based on notions of chaos and strange attractors. Our goal in this work is to improve the generalization and robustness properties of a speech recognition system. Three nonlinear invariants are proposed for feature extraction: Lyapunov exponents, correlation fractal dimension, and correlation entropy. We demonstrate an 11% relative improvement on speech recorded under noise-free conditions, but show a comparable degradation occurs for mismatched training conditions on noisy speech. We conjecture that the degradation is due to difficulties in estimating invariants reliably from noisy data. To circumvent these problems, we introduce two dynamic models to the acoustic modeling problem: (1) a linear dynamic model (LDM) that uses a state space-like formulation to explicitly model the evolution of hidden states using an autoregressive process, and (2) a data-dependent mixture of autoregressive (MixAR) models. Results show that LDM and MixAR models can achieve comparable performance with HMM systems while using significantly fewer parameters. Currently we are developing Bayesian parameter estimation and
Nonlinear dynamics of cardiovascular ageing
Shiogai, Y.; Stefanovska, A.; McClintock, P.V.E.
2010-01-01
The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time–frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in
Nonlinear Chemical Dynamics and Synchronization
NASA Astrophysics Data System (ADS)
Li, Ning
Alan Turing's work on morphogenesis, more than half a century ago, continues to motivate and inspire theoretical and experimental biologists even today. That said, there are very few experimental systems for which Turing's theory is applicable. In this thesis we present an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions in which droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants are dispersed in oil. The BZ reaction has become the prototype of nonlinear dynamics in chemistry and a preferred system for exploring the behavior of coupled nonlinear oscillators. Our system consists of a surfactant stabilized monodisperse emulsion of drops of aqueous BZ solution dispersed in a continuous phase of oil. In contrast to biology, here the chemistry is understood, rate constants are measured and interdrop coupling is purely diffusive. We explore a large set of parameters through control of rate constants, drop size, spacing, and spatial arrangement of the drops in lines and rings in one-dimension (1D) and hexagonal arrays in two-dimensions (2D). The Turing model is regarded as a metaphor for morphogenesis in biology but not for prediction. Here, we develop a quantitative and falsifiable reaction-diffusion model that we experimentally test with synthetic cells. We quantitatively establish the extent to which the Turing model in 1D describes both stationary pattern formation and temporal synchronization of chemical oscillators via reaction-diffusion and in 2D demonstrate that chemical morphogenesis drives physical differentiation in synthetic cells.
Nonlinear simulation of tumor growth.
Cristini, Vittorio; Lowengrub, John; Nie, Qing
2003-03-01
We study solid tumor ( carcinoma) growth in the nonlinear regime using boundary-integral simulations. The tumor core is nonnecrotic and no inhibitor chemical species are present. A new formulation of the classical models [18,24,8,3] is developed and it is demonstrated that tumor evolution is described by a reduced set of two dimensionless parameters and is qualitatively unaffected by the number of spatial dimensions. One parameter describes the relative rate of mitosis to the relaxation mechanisms (cell mobility and cell-to-cell adhesion). The other describes the balance between apoptosis (programmed cell-death) and mitosis. Both parameters also include the effect of vascularization. Our analysis and nonlinear simulations reveal that the two new dimensionless groups uniquely subdivide tumor growth into three regimes associated with increasing degrees of vascularization: low (diffusion dominated, e.g., in vitro), moderate and high vascularization, that correspond to the regimes observed in vivo. We demonstrate that critical conditions exist for which the tumor evolves to nontrivial dormant states or grows self-similarly (i.e., shape invariant) in the first two regimes. This leads to the possibility of shape control and of controlling the release of tumor angiogenic factors by restricting the tumor volume-to-surface-area ratio. Away from these critical conditions, evolution may be unstable leading to invasive fingering into the external tissues and to topological transitions such as tumor breakup and reconnection. Interestingly we find that for highly vascularized tumors, while they grow unbounded, their shape always stays compact and invasive fingering does not occur. This is in agreement with recent experimental observations [30] of in vivo tumor growth, and suggests that the invasive growth of highly-vascularized tumors is associated to vascular and elastic anisotropies, which are not included in the model studied here.
On Least Squares Fitting Nonlinear Submodels.
ERIC Educational Resources Information Center
Bechtel, Gordon G.
Three simplifying conditions are given for obtaining least squares (LS) estimates for a nonlinear submodel of a linear model. If these are satisfied, and if the subset of nonlinear parameters may be LS fit to the corresponding LS estimates of the linear model, then one attains the desired LS estimates for the entire submodel. Two illustrative…
Optimal nonlinear guidance for a reentry vehicle
NASA Astrophysics Data System (ADS)
Harel, D.; Guelman, M.
Using the exact nonlinear equations of motion an optimal guidance law for a reentry vehicle to achieve at impact a zero miss and a predefined flight path angle is derived. The application of the optimal guidance law in feedback form is based on the on-line solution of a nonlinear algebraic equation. Numerical results are presented.
Nonlinear optical beam interactions in waveguide arrays.
Meier, Joachim; Stegeman, George I; Silberberg, Y; Morandotti, R; Aitchison, J S
2004-08-27
We report our investigation of Kerr nonlinear beam interactions in discrete systems. The influence of power and the relative phase between two Gaussian shaped beams was investigated in detail by performing numerical simulations of the discrete nonlinear Schrödinger equation and comparing the results with experiments done in AlGaAs waveguide arrays. Good agreement between theory and experiment was obtained.
Method for analyzing multilayer nonlinear optical waveguide.
Wu, Yaw-Dong; Chen, Mao-Hsiung
2005-10-01
We propose a novel method for analyzing a multilayer optical waveguide structure with all nonlinear guiding films. This method can also be used to analyze a multibranch optical waveguide structure with all nonlinear guiding branches. The results show that agreement between theory and numerics is excellent.
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.
NEW NONLINEAR ACOUSTIC TECHNIQUES FOR NDE
J. A. TENCATE
2000-09-01
Acoustic nonlinearity in a medium may occur as a result of a variety of mechanisms. Some of the more common nonlinear effects may come from: (1) one or several cracks, volumetrically distributed due to age or fatigue or single disbonds or delamination; (2) imperfect grain-to-grain contacts, e.g., materials like concretes that are cemented together and have less than perfect bonds; (3) hard parts in a soft matrix, e.g., extreme duty materials like tungsten/copper alloys; or (4) atomic-scale nonlinearities. Nonlinear effects that arise from the first two mechanisms are considerably larger than the last two; thus, we have focused considerable attention on these. The most pervasive nonlinear measure of damage today is a second harmonic measurement. We show that for many cases of interest to NDE, a second harmonic measurement may not be the best choice. We examine the manifestations of nonlinearity in (nonlinear) materials with cracks and/or imperfect bonds and illustrate their applicability to NDE. For example, nonlinear resonance frequency shifts measured at increasing drive levels correlate strongly with the amount of ASR (alkali-silica reaction) damage of concrete cores. Memory effects (slow dynamics) also seem to correlate with the amount of damage.
Nonlinear elastic properties of particulate composites
NASA Astrophysics Data System (ADS)
Chen, Yi-Chao; Jiang, Xiaohu
1993-07-01
A METHOD of computing effective elastic moduli of isotropic nonlinear composites is developed by using a perturbation scheme. It is demonstrated that only solutions from linear elasticity are needed in computing higher order moduli. As an application of the method, particulate composites of nonlinear elastic materials are analysed.
The nonlinear CWFA (Cherenkov Wakefield Accelerator)
Schoessow, P.
1989-01-01
The possible use of nonlinear media to enhance the performance of the Cherenkov Wakefield Accelerator (CWFA) is considered. Numerical experiments have been performed using a new wakefield code which demonstrate larger gradients and transformer ratios in the nonlinear CWFA than are obtained in the linear case. 7 refs., 3 figs.
Nonlinear Terahertz Absorption of Graphene Plasmons.
Jadidi, Mohammad M; König-Otto, Jacob C; Winnerl, Stephan; Sushkov, Andrei B; Drew, H Dennis; Murphy, Thomas E; Mittendorff, Martin
2016-04-13
Subwavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, subwavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a terahertz pump-terahertz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by 2 orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results. The model shows that the observed strong linearity is caused by an unexpected red shift of plasmon resonance together with a broadening and weakening of the resonance caused by the transient increase in electron temperature. The model further predicts that even greater resonant enhancement of the nonlinear response can be expected in high-mobility graphene, suggesting that nonlinear graphene plasmonic devices could be promising candidates for nonlinear optical processing. PMID:26978242
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1972-01-01
Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
Non-Linear Transformation of the Criterion.
ERIC Educational Resources Information Center
McNeil, Keith; And Others
The utility of a non-linear transformation of the criterion is established. The Pythagorean Theorem is used as the example to demonstrate the point. The functional relationships may be such (as in the Pythagorean Theorem) that an R-squared of 1.00 cannot be found without making a non-linear transformation of the criterion. The goal of…
A simple approach to nonlinear oscillators
NASA Astrophysics Data System (ADS)
Ren, Zhong-Fu; He, Ji-Huan
2009-10-01
A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.
Generating nonlinear FM chirp waveforms for radar.
Doerry, Armin Walter
2006-09-01
Nonlinear FM waveforms offer a radar matched filter output with inherently low range sidelobes. This yields a 1-2 dB advantage in Signal-to-Noise Ratio over the output of a Linear FM waveform with equivalent sidelobe filtering. This report presents design and implementation techniques for Nonlinear FM waveforms.
Inverting Monotonic Nonlinearities by Entropy Maximization
López-de-Ipiña Pena, Karmele; Caiafa, Cesar F.
2016-01-01
This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results. PMID:27780261
Nonlinear fiber gyroscope for quantum metrology
NASA Astrophysics Data System (ADS)
Luis, Alfredo; Morales, Irene; Rivas, Ángel
2016-07-01
We examine the performance of a nonlinear fiber gyroscope for improved signal detection beating the quantum limits of its linear counterparts. The performance is examined when the nonlinear gyroscope is illuminated by practical field states, such as coherent and quadrature squeezed states. This is compared with the case of more ideal probes such as photon-number states.
Interfacial Nonlinear Dynamics, Phenomena, and Devices
NASA Astrophysics Data System (ADS)
Zhou, Ping
The dynamics of an optical switch based on a dielectric -clad nonlinear film is presented. Two transition processes of the optical switching, from total internal reflection (TIR) to transmission (Tr) and from Tr to TIR, are investigated in theory as well as experiment. Nonlinear dynamic layered transfer matrix theory is developed to study the transition process from TIR to Tr at a nonlinear thin film due to the optically induced refractive index change. A simple theoretical model based on a dynamic nonlinear Fabry-Perot etalon is given for the analysis of the switching process from Tr to TIR. The quantitative analysis can be used for the design and optimization of an optical sensor protector and other devices. Experiments have been done on both the processes of TIR to Tr and Tr to TIR switching for visible as well as infrared wavelengths. A theory for the design of an optimal anti-reflection coating is proposed in order to aid the design and optimization of a nonlinear interfacial switch. Furthermore, a detailed study of the dynamic optical tunneling through the nonlinear interface indicates that the reflected wave would undergo an additional dynamic nonlinear phase shift which is a novel nonlinear interfacial phenomenon, first revealed by this study.
Quasicompactons in inverted nonlinear photonic crystals
Li Yongyao; Malomed, Boris A.; Wu Jianxiong; Pang Wei; Wang Sicong; Zhou Jianying
2011-10-15
We study large-amplitude one-dimensional solitary waves in photonic crystals featuring competition between linear and nonlinear lattices, with minima of the linear potential coinciding with maxima of the nonlinear pseudopotential, and vice versa (inverted nonlinear photonic crystals, INPCs), in the case of the saturable self-focusing nonlinearity. Such crystals were recently fabricated using a mixture of SU-8 and Rhodamine-B optical materials. By means of numerical methods and analytical approximations, we find that large-amplitude solitons are broad sharply localized stable pulses (quasicompactons, QCs). With the increase of the total power, P, the QC's centroid performs multiple switchings between minima and maxima of the linear potential. Unlike cubic INPCs, the large-amplitude solitons are mobile in the medium with the saturable nonlinearity. The threshold value of the kick necessary to set the soliton in motion is found as a function of P. Collisions between moving QCs are considered too.
Strongly Nonlinear Stress Waves in Dissipative Metamaterials
NASA Astrophysics Data System (ADS)
Xu, Yichao; Nesterenko, Vitali
2015-06-01
We present the measurements, numerical simulations, and theoretical analysis of stress wave propagation in a one-dimensional strongly nonlinear dissipative metamaterial composed of steel disks and Nitrile O-rings. A stress wave of bell shape is generated by impactor with different masses. A strongly nonlinear double power-law is used to describe the nonlinear viscoelastic force interaction between the disks due to the compression of rubber O-rings. Numerical modeling including a nonlinear dissipative term is developed to predict the wave shape and propagation speed. The shape of generated stress wave can be dramatically changed by the viscous dissipation, which may prevent the pulse from splitting into trains of solitary waves. This strongly nonlinear dissipative metamaterial has a potential for attenuation of dynamic loading and allows an enhanced tunability of signal speed.
Weakly nonlinear hydrodynamic instabilities in inertial fusion
Haan, S.W. )
1991-08-01
For many cases of interest to inertial fusion, growth of Rayleigh--Taylor and other hydrodynamic instabilities is such that the perturbations remain linear or weakly nonlinear. The transition to nonlinearity is studied via a second-order solution for multimode classical Rayleigh--Taylor growth. The second-order solution shows how classical Rayleigh--Taylor systems forget initial amplitude information in the weakly nonlinear phase. Stabilized growth relevant to inertial fusion is qualitatively different, and initial amplitudes are not dominated by nonlinear effects. In all systems with a full spectrum of modes, nonlinear effects begin when mode amplitudes reach about 1/{ital Lk}{sup 2}, for modes of wave number {ital k} and system size {ital L}.
Nonlinear dynamics enabled systems design and control
NASA Astrophysics Data System (ADS)
Lacarbonara, Walter
2012-08-01
There is a growing interest towards design of high-performance structures and devices by seeking ways to exploit advantageously different nonlinearities at different scales rather than constraining operations to avoid nonlinear phenomena. Tools of robust nonlinear modeling and analysis are shown to be turned into design tools for achieving high levels of vibration control authority and synthesis of engineered systems and materials. A brief overview of methods and results on active resonance cancellation and passive nonlinear hysteretic vibration absorbers is illustrated. Recent results on the diffused hysteresis exhibited at the nano-microscale in nanocomposites due to the powerful nonlinear stick-slip mechanism exhibited by carbon nanotubes dispersed in a hosting matrix are discussed. The optimization of the main microstructural parameters is shown to lead to unprecedented levels of damping capacity in next-generation nanostructured materials tailored for wide-band vibrational energy dissipation.
Electrically tunable nonlinear plasmonics in graphene nanoislands.
Cox, Joel D; Javier García de Abajo, F
2014-12-11
Nonlinear optical processes rely on the intrinsically weak interactions between photons enabled by their coupling with matter. Unfortunately, many applications in nonlinear optics are severely hindered by the small response of conventional materials. Metallic nanostructures partially alleviate this situation, as the large light enhancement associated with their localized plasmons amplifies their nonlinear response to record high levels. Graphene hosts long-lived, electrically tunable plasmons that also interact strongly with light. Here we show that the nonlinear polarizabilities of graphene nanoislands can be electrically tuned to surpass by several orders of magnitude those of metal nanoparticles of similar size. This extraordinary behaviour extends over the visible and near-infrared spectrum for islands consisting of hundreds of carbon atoms doped with moderate carrier densities. Our quantum-mechanical simulations of the plasmon-enhanced optical response of nanographene reveal this material as an ideal platform for the development of electrically tunable nonlinear optical nanodevices.
Nonlinear lower hybrid modeling in tokamak plasmas
Napoli, F.; Schettini, G.; Castaldo, C.; Cesario, R.
2014-02-12
We present here new results concerning the nonlinear mechanism underlying the observed spectral broadening produced by parametric instabilities occurring at the edge of tokamak plasmas in present day LHCD (lower hybrid current drive) experiments. Low frequency (LF) ion-sound evanescent modes (quasi-modes) are the main parametric decay channel which drives a nonlinear mode coupling of lower hybrid (LH) waves. The spectrum of the LF fluctuations is calculated here considering the beating of the launched LH wave at the radiofrequency (RF) operating line frequency (pump wave) with the noisy background of the RF power generator. This spectrum is calculated in the frame of the kinetic theory, following a perturbative approach. Numerical solutions of the nonlinear LH wave equation show the evolution of the nonlinear mode coupling in condition of a finite depletion of the pump power. The role of the presence of heavy ions in a Deuterium plasma in mitigating the nonlinear effects is analyzed.
Modeling of active and passive nonlinear metamaterials
NASA Astrophysics Data System (ADS)
Colestock, Patrick L.; Reiten, Matthew T.; O'Hara, John F.
2012-11-01
We develop general results for nonlinear metamaterials based on simple circuit models that reflect the elementary nonlinear behavior of the medium. In particular, we consider both active and passive nonlinearities which can lead to gain, harmonic generation and a variety of nonlinear waves depending on circuit parameters and signal amplitude. We show that the medium can exhibit a phase transition to a synchronized state and derive conditions for the transformation based on a widely used multiple time scale approach that leads to the well-known Complex Ginzburg-Landau equation. Further, we examine the variety of nonlinear waves that can exist in such systems, and we present numerical results for both active and passive metamaterial cases.
Networks of nonlinear superconducting transmission line resonators
NASA Astrophysics Data System (ADS)
Leib, M.; Deppe, F.; Marx, A.; Gross, R.; Hartmann, M. J.
2012-07-01
We investigate a network of coupled superconducting transmission line resonators, each of them made nonlinear with a capacitively shunted Josephson junction coupling to the odd flux modes of the resonator. The resulting eigenmode spectrum shows anticrossings between the plasma mode of the shunted junction and the odd resonator modes. Notably, we find that the combined device can inherit the complete nonlinearity of the junction, allowing for a description as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID instead of a single junction, the nonlinearity can be tuned between 10 kHz and 4 MHz while maintaining resonance frequencies of a few gigahertz for realistic device parameters. An array of such nonlinear resonators can be considered a scalable superconducting quantum simulator for a Bose-Hubbard Hamiltonian. The device would be capable of accessing the strongly correlated regime and be particularly well suited for investigating quantum many-body dynamics of interacting particles under the influence of drive and dissipation.
Nonlinear dynamics aspects of modern storage rings
Helleman, R.H.G.; Kheifets, S.A.
1986-01-01
It is argued that the nonlinearity of storage rings becomes an essential problem as the design parameters of each new machine are pushed further and further. Yet the familiar methods of classical mechanics do not allow determination of single particle orbits over reasonable lengths of time. It is also argued that the single particle dynamics of a storage ring is possibly one of the cleanest and simplest nonlinear dynamical systems available with very few degrees of freedom. Hence, reasons are found for accelerator physicists to be interested in nonlinear dynamics and for researchers in nonlinear dynamics to be interested in modern storage rings. The more familiar methods of treating nonlinear systems routinely used in acclerator theory are discussed, pointing out some of their limitations and pitfalls. 39 refs., 1 fig. (LEW)
Compact waves in microscopic nonlinear diffusion.
Hurtado, P I; Krapivsky, P L
2012-06-01
We analyze the spread of a localized peak of energy into vacuum for nonlinear diffusive processes. In contrast with standard diffusion, the nonlinearity results in a compact wave with a sharp front separating the perturbed region from vacuum. In d spatial dimensions, the front advances as t^{1/(2+da)} according to hydrodynamics, with a the nonlinearity exponent. We show that fluctuations in the front position grow as ∼t^{μ}η, where μ<1/2+da is an exponent that we measure and η is a random variable whose distribution we characterize. Fluctuating corrections to hydrodynamic profiles give rise to an excess penetration into vacuum, revealing scaling behaviors and robust features. We also examine the discharge of a nonlinear rarefaction wave into vacuum. Our results suggest the existence of universal scaling behaviors at the fluctuating level in nonlinear diffusion.
Nonlinear vibrations of viscoelastic rectangular plates
NASA Astrophysics Data System (ADS)
Amabili, Marco
2016-02-01
Nonlinear vibrations of viscoelastic thin rectangular plates subjected to normal harmonic excitation in the spectral neighborhood of the lowest resonances are investigated. The von Kármán nonlinear strain-displacement relationships are used and geometric imperfections are taken into account. The material is modeled as a Kelvin-Voigt viscoelastic solid by retaining all the nonlinear terms. The discretized nonlinear equations of motion are studied by using the arclength continuation and collocation method. Numerical results are obtained for the fundamental mode of a simply supported square plate with immovable edges by using models with 16 and 22 degrees of freedom and investigating solution convergence. Comparison to viscous damping and the effect of neglecting nonlinear viscoelastic damping terms are shown. The change of the frequency-response with the retardation time parameter is also investigated as well as the effect of geometric imperfections.
Nonlinear self-adjointness and conservation laws
NASA Astrophysics Data System (ADS)
Ibragimov, N. H.
2011-10-01
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation ut - Δu = 0 becomes strictly self-adjoint after multiplying by u-1. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems.
Nonlinear Modeling by Assembling Piecewise Linear Models
NASA Technical Reports Server (NTRS)
Yao, Weigang; Liou, Meng-Sing
2013-01-01
To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.
Nonlinear model for building-soil systems
McCallen, D.B.; Romstad, K.M.
1994-05-01
A finite-element based, numerical analysis methodology has been developed for the nonlinear analysis of building-soil systems. The methodology utilizes a reduced-order, nonlinear continuum model to represent the building, and the soil is represented with a simple nonlinear two-dimensional plane strain finite element. The foundation of the building is idealized as a rigid block and the interface between the soil and the foundation is modeled with an interface contract element. The objectives of the current paper are to provide the theoretical development of the system model, with particular emphasis on the modeling of the foundation-soil contact, and to demonstrate the special-purpose finite-element program that has been developed for nonlinear analysis of the building-soil system. Examples are included that compare the results obtained with the special-purpose program with the results of a general-purpose nonlinear finite-element program.
Nonlinear radial oscillations of neutron stars
Gabler, Michael; Sperhake, Ulrich; Andersson, Nils
2009-09-15
The effects of nonlinear oscillations in compact stars are attracting considerable current interest. In order to study such phenomena in the framework of fully nonlinear general relativity, highly accurate numerical studies are required. A numerical scheme specifically tailored for such a study is based on formulating the time evolution in terms of deviations from a stationary equilibrium configuration. Using this technique, we investigate over a wide range of amplitudes nonlinear effects in the evolution of radial oscillations of neutron stars. In particular, we discuss mode coupling due to nonlinear interaction, the occurrence of resonance phenomena, shock formation near the stellar surface as well as the capacity of nonlinearities to stabilize perturbatively unstable neutron star models.
Movement Enhances the Nonlinearity of Hippocampal Theta
Sheremet, Alex; Burke, Sara N.
2016-01-01
The nonlinear, metastable dynamics of the brain are essential for large-scale integration of smaller components and for the rapid organization of neurons in support of behavior. Therefore, understanding the nonlinearity of the brain is paramount for understanding the relationship between brain dynamics and behavior. Explicit quantitative descriptions of the properties and consequences of nonlinear neural networks, however, are rare. Because the local field potential (LFP) reflects the total activity across a population of neurons, nonlinearites of the nervous system should be quantifiable by examining oscillatory structure. We used high-order spectral analysis of LFP recorded from the dorsal and intermediate regions of the rat hippocampus to show that the nonlinear character of the hippocampal theta rhythm is directly related to movement speed of the animal. In the time domain, nonlinearity is expressed as the development of skewness and asymmetry in the theta shape. In the spectral domain, nonlinear dynamics manifest as the development of a chain of harmonics statistically phase coupled to the theta oscillation. This evolution was modulated across hippocampal regions, being stronger in the dorsal CA1 relative to more intermediate areas. The intensity and timing of the spiking activity of pyramidal cells and interneurons was strongly correlated to theta nonlinearity. Because theta is known to propagate from dorsal to ventral regions of the hippocampus, these data suggest that the nonlinear character of theta decreases as it travels and supports a hypothesis that activity dissipates along the longitudinal axis of the hippocampus. SIGNIFICANCE STATEMENT We describe the first explicit quantification regarding how behavior enhances the nonlinearity of the nervous system. Our findings demonstrate uniquely how theta changes with increasing speed due to the altered underlying neuronal dynamics and open new directions of research on the relationship between single
Sauer's non-linear voltage division.
Schwan, H P; McAdams, E T; Jossinet, J
2002-09-01
The non-linearity of the electrode-tissue interface impedance gives rise to harmonics and thus degrades the accuracy of impedance measurements. Also, electrodes are often driven into the non-linear range of their polarisation impedance. This is particularly true in clinical applications. Techniques to correct for electrode effects are usually based on linear electrode impedance data. However, these data can be very different from the non-linear values needed. Non-linear electrode data suggested a model based on simple assumptions. It is useful in predicting the frequency dependence of non-linear effects from linear properties. Sauer's treatment is a first attempt to provide a more general and rigorous basis for modelling the non-linear state. The paper reports Sauer's treatment of the non-linear case and points out its limitations. The paper considers Sauer's treatment of a series arrangement of two impedances. The tissue impedance is represented by a linear voltage-current characteristic. The interface impedance is represented by a Volterra expansion. The response of this network to periodic signals is calculated up to the second-order term of the series expansion. The resultant, time-dependent current is found to contain a DC term (rectification), as well as frequency-dependent terms. Sauer's treatment assumes a voltage clamp across the impedances and neglects higher-order terms in the series expansion. As a consequence, it fails adequately to represent some experimentally observed phenomena. It is therefore suggested that Sauer's expressions for the voltage divider should be combined with the non-linear treatments previously published by the co-authors. Although Sauer's work on the non-linear voltage divider was originally applied to the study of the non-linear behaviour of the electrode-electrolyte interface and biological tissues, it is stressed, however, that the work is applicable to a wide range of research areas.
Nonlinear waves in the solar atmosphere.
Ruderman, Michael S
2006-02-15
In this paper, we give a brief review of the contemporary theory of nonlinear waves in the solar atmosphere. The choice of topics reflects personal interests of the author. Historically the theory of nonlinear waves was first applied to the solar atmosphere to explain the chromospheric and coronal heating. It was assumed that the turbulent motion in the solar convective zone excites sound waves that propagate upwards. Due to nonlinearity these waves steepen and form shocks. The wave energy dissipates in these shocks thus heating the corona. We give a brief description of propagation and damping of nonlinear sound waves in the stratified solar atmosphere, and point out that, at present, the acoustic heating remains the most popular theory of heating the lower chromosphere. Then we extend the analysis to nonlinear slow magnetosonic waves in coronal plumes and loops, and discuss its implications for interpretation of observational results. The next topic of interest is the propagation of nonlinear waves in a magnetically structured atmosphere. Here, we restrict our analysis to slow sausage waves in magnetic tubes and discuss properties of solitary waves described by the Leibovich-Roberts equation. We conclude with the discussion of nonlinear theory of slow resonant layers, and its possible application to helioseismology. PMID:16414893
Nonlinear Krylov acceleration of reacting flow codes
Kumar, S.; Rawat, R.; Smith, P.; Pernice, M.
1996-12-31
We are working on computational simulations of three-dimensional reactive flows in applications encompassing a broad range of chemical engineering problems. Examples of such processes are coal (pulverized and fluidized bed) and gas combustion, petroleum processing (cracking), and metallurgical operations such as smelting. These simulations involve an interplay of various physical and chemical factors such as fluid dynamics with turbulence, convective and radiative heat transfer, multiphase effects such as fluid-particle and particle-particle interactions, and chemical reaction. The governing equations resulting from modeling these processes are highly nonlinear and strongly coupled, thereby rendering their solution by traditional iterative methods (such as nonlinear line Gauss-Seidel methods) very difficult and sometimes impossible. Hence we are exploring the use of nonlinear Krylov techniques (such as CMRES and Bi-CGSTAB) to accelerate and stabilize the existing solver. This strategy allows us to take advantage of the problem-definition capabilities of the existing solver. The overall approach amounts to using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method and its variants as nonlinear preconditioners for the nonlinear Krylov method. We have also adapted a backtracking approach for inexact Newton methods to damp the Newton step in the nonlinear Krylov method. This will be a report on work in progress. Preliminary results with nonlinear GMRES have been very encouraging: in many cases the number of line Gauss-Seidel sweeps has been reduced by about a factor of 5, and increased robustness of the underlying solver has also been observed.
NOVEL SIGNAL PROCESSING WITH NONLINEAR TRANSMISSION LINES
D. REAGOR; ET AL
2000-08-01
Nonlinear dielectrics offer uniquely strong and tunable nonlinearities that make them attractive for current devices (for example, frequency-agile microwave filters) and for future signal-processing technologies. The goal of this project is to understand pulse propagation on nonlinear coplanar waveguide prototype devices. We have performed time-domain and frequency-domain experimental studies of simple waveguide structures and pursued a theoretical understanding of the propagation of signals on these nonlinear waveguides. To realistically assess the potential applications, we used a time-domain measurement and analysis technique developed during this project to perform a broadband electrodynamics characterization in terms of nonlinear, dispersive, and dissipative effects. We completed a comprehensive study of coplanar waveguides made from high-temperature superconducting thin-film YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} electrodes on nonlinear dielectric single-crystal SrTiO{sub 3} substrates. By using parameters determined from small-signal (linear) transmission characteristics of the waveguides, we develop a model equation that successfully predicts and describes large-signal (nonlinear) behavior.
A nonlinear elasticity phantom containing spherical inclusions
Pavan, Theo Z.; Madsen, Ernest L.; Frank, Gary R.; Jiang, Jingfeng; Carneiro, Antonio Adilton O.; Hall, Timothy J.
2012-01-01
The strain image contrast of some in vivo breast lesions changes with increasing applied load. This change is attributed to differences in the nonlinear elastic properties of the constituent tissues suggesting some potential to help classify breast diseases by their nonlinear elastic properties. A phantom with inclusions and long-term stability is desired to serve as a test bed for nonlinear elasticity imaging method development, testing, etc. This study reports a phantom designed to investigate nonlinear elastic properties with ultrasound elastographic techniques. The phantom contains four spherical inclusions and was manufactured from a mixture of gelatin, agar and oil. The phantom background and each of the inclusions has distinct Young’s modulus and nonlinear mechanical behavior. This phantom was subjected to large deformations (up to 20%) while scanning with ultrasound, and changes in strain image contrast and contrast-to-noise ratio (CNR) between inclusion and background, as a function of applied deformation, were investigated. The changes in contrast over a large deformation range predicted by the finite element analysis (FEA) were consistent with those experimentally observed. Therefore, the paper reports a procedure for making phantoms with predictable nonlinear behavior, based on independent measurements of the constituent materials, and shows that the resulting strain images (e.g., strain contrast) agrees with that predicted with nonlinear FEA. PMID:22772074
Nonlinear waves in PT -symmetric systems
NASA Astrophysics Data System (ADS)
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-07-01
Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.
Geometrically nonlinear behavior of piezoelectric laminated plates
NASA Astrophysics Data System (ADS)
Rabinovitch, Oded
2005-08-01
The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.
Nonlinear identification of ionic polymer actuator systems
NASA Astrophysics Data System (ADS)
Kothera, Curt S.; Lacy, Seth L.; Erwin, R. Scott; Leo, Donald J.
2004-07-01
Ionic polymers are a class of electromechanically coupled materials that can be used as flexible transducers. When set up in the cantilever configuration, the actuators exhibit a large bending deflection when an electric field is applied across their thickness. Being a relatively new research topic, the governing physical and chemical mechanisms are not yet fully understood. Experimental results have demonstrated nonlinear dynamic behavior. The nonlinear dynamics can be seen in the response of current, displacement, and velocity of the actuator. This work presents results for the nonlinear identification of ionic polymer actuator systems driven at a specific frequency. Identification results using a 5th-degree Volterra expansion show that the nonlinear distortion can be accurately modeled. Using such a high power in the series expansion is necessary to capture the most dominant harmonics, as evidenced when examining the power spectral density of the response. An investigation of how nonlinearities enter into the response is also performed. By analyzing both the actuation current and tip velocity, results show that both the voltage to current and current to velocity stages influence the nonlinear response, but the voltage to current stage is more dominantly nonlinear.
Statistical energy analysis of nonlinear vibrating systems.
Spelman, G M; Langley, R S
2015-09-28
Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy being found in frequency bands other than those being driven by external forces. To analyse this phenomenon, a method is developed here in which the response of the structure in the frequency domain is divided into frequency bands, and the energy flow between the frequency bands is calculated. The frequency bands are assigned an energy variable to describe the mean response and the nonlinear coupling between bands is described in terms of weighted summations of the convolutions of linear modal transfer functions. This represents a nonlinear extension to an established linear theory known as statistical energy analysis (SEA). The nonlinear extension to SEA theory is presented for the case of a plate structure with quadratic and cubic nonlinearity. PMID:26303923
Nonlinear Susceptibility Magnitude Imaging of Magnetic Nanoparticles
Ficko, Bradley W.; Giacometti, Paolo; Diamond, Solomon G.
2014-01-01
This study demonstrates a method for improving the resolution of susceptibility magnitude imaging (SMI) using spatial information that arises from the nonlinear magnetization characteristics of magnetic nanoparticles (mNPs). In this proof-of-concept study of nonlinear SMI, a pair of drive coils and several permanent magnets generate applied magnetic fields and a coil is used as a magnetic field sensor. Sinusoidal alternating current (AC) in the drive coils results in linear mNP magnetization responses at primary frequencies, and nonlinear responses at harmonic frequencies and intermodulation frequencies. The spatial information content of the nonlinear responses is evaluated by reconstructing tomographic images with sequentially increasing voxel counts using the combined linear and nonlinear data. Using the linear data alone it is not possible to accurately reconstruct more than 2 voxels with a pair of drive coils and a single sensor. However, nonlinear SMI is found to accurately reconstruct 12 voxels (R2 = 0.99, CNR = 84.9) using the same physical configuration. Several time-multiplexing methods are then explored to determine if additional spatial information can be obtained by varying the amplitude, phase and frequency of the applied magnetic fields from the two drive coils. Asynchronous phase modulation, amplitude modulation, intermodulation phase modulation, and frequency modulation all resulted in accurate reconstruction of 6 voxels (R2 > 0.9) indicating that time multiplexing is a valid approach to further increase the resolution of nonlinear SMI. The spatial information content of nonlinear mNP responses and the potential for resolution enhancement with time multiplexing demonstrate the concept and advantages of nonlinear SMI. PMID:25505816
Topological approximation of the nonlinear Anderson model.
Milovanov, Alexander V; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t→+∞. The second moment of the associated probability distribution grows with time as a power law ∝ t^{α}, with the exponent α=1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the
Topological approximation of the nonlinear Anderson model
NASA Astrophysics Data System (ADS)
Milovanov, Alexander V.; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the
Nonlinear susceptibility magnitude imaging of magnetic nanoparticles
NASA Astrophysics Data System (ADS)
Ficko, Bradley W.; Giacometti, Paolo; Diamond, Solomon G.
2015-03-01
This study demonstrates a method for improving the resolution of susceptibility magnitude imaging (SMI) using spatial information that arises from the nonlinear magnetization characteristics of magnetic nanoparticles (mNPs). In this proof-of-concept study of nonlinear SMI, a pair of drive coils and several permanent magnets generate applied magnetic fields and a coil is used as a magnetic field sensor. Sinusoidal alternating current (AC) in the drive coils results in linear mNP magnetization responses at primary frequencies, and nonlinear responses at harmonic frequencies and intermodulation frequencies. The spatial information content of the nonlinear responses is evaluated by reconstructing tomographic images with sequentially increasing voxel counts using the combined linear and nonlinear data. Using the linear data alone it is not possible to accurately reconstruct more than 2 voxels with a pair of drive coils and a single sensor. However, nonlinear SMI is found to accurately reconstruct 12 voxels (R2=0.99, CNR=84.9) using the same physical configuration. Several time-multiplexing methods are then explored to determine if additional spatial information can be obtained by varying the amplitude, phase and frequency of the applied magnetic fields from the two drive coils. Asynchronous phase modulation, amplitude modulation, intermodulation phase modulation, and frequency modulation all resulted in accurate reconstruction of 6 voxels (R2>0.9) indicating that time multiplexing is a valid approach to further increase the resolution of nonlinear SMI. The spatial information content of nonlinear mNP responses and the potential for resolution enhancement with time multiplexing demonstrate the concept and advantages of nonlinear SMI.
Analysis of a non-linear structure by considering two non-linear formulations
NASA Astrophysics Data System (ADS)
Majed, R.; Raynaud, J. L.
2003-03-01
In recent years, modal synthesis methods have been extended for solving non-linear dynamic problems subjected to harmonic excitation. These methods are based on the notion of non-linear or linearized modes and exploited in the case of structures affected by localized non-linearity. Actually, the experimental tests executed on non-linear structures are time consuming, particularly when repeated experimental tests are needed. It is often preferable to consider new non-linear methods with a view to decrease significantly the number of attempts during prototype tests and improving the accuracy of the dynamic behaviour. This article describes two fundamental non-linear formulations based on two different strategies. The first formulation exploits the eigensolutions of the associated linear system and the dynamics characteristics of each localized non-linearity. The second formulation is based on the exploitation of the linearized eigensolutions obtained using an iterative process. This article contains a numerical and an experimental study which examines the non-linear behaviour of the structure affected by localized non-linearities. The study is intended to validate the numerical algorithm and to evaluate the problems arising from the introduction of non-linearities. The complex responses are evaluated using the iterative Newton-Raphson method and for a series of discrete frequencies. The theory has been applied to a bi-dimensional structure and consists of evaluating the harmonic responses obtained using the proposed formulations by comparing measured and calculated transfer functions.
Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar
2014-09-25
Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.
NASA Astrophysics Data System (ADS)
Stojanović, Vladimir
2015-11-01
Geometrically nonlinear vibrations of a Timoshenko beam resting on a nonlinear Winkler and Pasternak elastic foundation with variable discontinuity are investigated in this paper. A p-version finite element method is developed for geometric nonlinear vibrations of a shear deformable beam resting on a nonlinear foundation with discontinuity. The elastic foundation has cubic nonlinearity with the shearing layer. In the study the p-element which comes from the use of explored special displacement shape functions for damaged beams is used and applied to a model with nonlinear foundation. The novelty of the present study lies in the easy generalisation of the approach of natural frequencies, general mode shapes (transverse and rotations of cross sections), and maximal deflections in nonlinear steady state vibrations of the shear deformable beam for any size and location of discontinuity of the nonlinear elastic support. A new set of nonlinear partial differential equations is developed, and they are solved in the time domain using the Newmark method for obtaining the amplitudes and deformed shapes of a beam in the steady state forced vibration regime. The present work consists of the comparison of the results with various stiffnesses of nonlinear elastic supports of the Winkler and Pasternak type.
Testing for nonlinear dependence in financial markets.
Dore, Mohammed; Matilla-Garcia, Mariano; Marin, Manuel Ruiz
2011-07-01
This article addresses the question of improving the detection of nonlinear dependence by means of recently developed nonparametric tests. To this end a generalized version of BDS test and a new test based on symbolic dynamics are used on realizations from a well-known artificial market for which the dynamic equation governing the market is known. Comparisons with other tests for detecting nonlinearity are also provided. We show that the test based on symbolic dynamics outperforms other tests with the advantage that it depends only on one free parameter, namely the embedding dimension. This does not hold for other tests for nonlinearity.
Nonlinear Single-Spin Spectrum Analyzer
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2013-03-01
Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.
Polarization renormalization due to nonlinear optical generation
NASA Astrophysics Data System (ADS)
Wynne, J. J.
1984-02-01
A classical Maxwellian analysis of the reduction of multiphoton excitation associated with the coherent third-harmonic generation of electromagnetic waves propagating in nonlinear media is presented. The approach of Bloembergen and Pershan (1962) is followed, making no use of quantum-mechanical description and considering the total electric polarization (the sum of the medium's linear response and the nonlinear source polarization) at the generated frequency. It is demonstrated that this method successfully explains the experimental results of Aron and Johnson (1977), Miller et al. (1980), Glownia and Sander (1982), and Faisal et al. (1977) by analyzing the relationship of the total and nonlinear polarization components.
Optical nonlinearity of HBI in different solvents
NASA Astrophysics Data System (ADS)
Wu, Feng; Ma, Lina; Geng, Yaohui; Zhang, Siwen; Wang, Zhe; Cheng, Xiaoman
2014-04-01
2-(2'-Hydroxyphenyl) benzimidazole (HBI) is one kind of organic molecules featuring excited-state proton transfer (ESPT). The nonlinear optical properties of 2-(2'-hydroxyphenyl) benzimidazole (HBI) in different polar solvents were investigated by means of Z-scan technique under the excitation of the 1064 nm picoseconds laser pulse. The experimental results show that the nonlinear refractive indices decrease with the enhancement of the polarity of the solvent. The nonlinear refractive indices sensitive to the solvent polarity allow them to be widely used for the optoelectronic devices.
Experimental verification of transient nonlinear acoustical holography.
Jing, Yun; Cannata, Jonathan; Wang, Tianren
2013-05-01
This paper presents an experimental study on nonlinear transient acoustical holography. The validity and effectiveness of a recently proposed nonlinear transient acoustical holography algorithm is evaluated in the presence of noise. The acoustic field measured on a post-focal plane of a high-intensity focused transducer is backward projected to reconstruct the pressure distributions on the focal and a pre-focal plane, which are shown to be in good agreement with the measurement. In contrast, the conventional linear holography produces erroneous results in this case where the nonlinearity involved is strong. Forward acoustic field projection was also carried out to further verify the algorithm. PMID:23654362
Nonlinear dynamics and numerical uncertainties in CFD
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.
1996-01-01
The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.
Experimental verification of transient nonlinear acoustical holography.
Jing, Yun; Cannata, Jonathan; Wang, Tianren
2013-05-01
This paper presents an experimental study on nonlinear transient acoustical holography. The validity and effectiveness of a recently proposed nonlinear transient acoustical holography algorithm is evaluated in the presence of noise. The acoustic field measured on a post-focal plane of a high-intensity focused transducer is backward projected to reconstruct the pressure distributions on the focal and a pre-focal plane, which are shown to be in good agreement with the measurement. In contrast, the conventional linear holography produces erroneous results in this case where the nonlinearity involved is strong. Forward acoustic field projection was also carried out to further verify the algorithm.
Nonlinear dynamical system approaches towards neural prosthesis
Torikai, Hiroyuki; Hashimoto, Sho
2011-04-19
An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.
HTS nonlinearities in microwave disk resonators
NASA Astrophysics Data System (ADS)
Collado, Carlos; Mateu, Jordi; Shaw, Timothy J.; O'Callaghan, Juan M.
2002-08-01
This article describes a procedure for the calculation of the intermodulation behavior of the TM0 1 0 mode in high temperature superconducting (HTS) disk resonators from a description of the local HTS nonlinearities. Successful cross-checks are performed by comparing the theoretical results with experimental measurements and simulations based on the multiport harmonic balance algorithm for a specific model of HTS nonlinearity. The application of this procedure to the determination of nonlinear material parameters from disk resonator measurements is illustrated and compared to theoretical predictions.
Nonlinear viscoelastic characterization of thin polyethylene film
NASA Technical Reports Server (NTRS)
Wilbeck, J. S.
1981-01-01
In order to understand the state of stress and strain in a typical balloon fabricated from thin polyethylene film, experiment data in the literature reviewed. It was determined that the film behaves as a nonlinear viscoelasticity material and should be characterized accordingly. A simple uniaxial, nonlinear viscoelastic model was developed for predicting stress given a certain strain history. The simple model showed good qualitative agreement with results of constant rate, uniaxial accurately predicting stresses for cyclic strain histories typical of balloon flights. A program was outlined which will result in the development of a more complex nonlinear viscoelastic model.
Minimizing radiation damage in nonlinear optical crystals
Cooke, D.W.; Bennett, B.L.; Cockroft, N.J.
1998-09-08
Methods are disclosed for minimizing laser induced damage to nonlinear crystals, such as KTP crystals, involving various means for electrically grounding the crystals in order to diffuse electrical discharges within the crystals caused by the incident laser beam. In certain embodiments, electrically conductive material is deposited onto or into surfaces of the nonlinear crystals and the electrically conductive surfaces are connected to an electrical ground. To minimize electrical discharges on crystal surfaces that are not covered by the grounded electrically conductive material, a vacuum may be created around the nonlinear crystal. 5 figs.
Minimizing radiation damage in nonlinear optical crystals
Cooke, D. Wayne; Bennett, Bryan L.; Cockroft, Nigel J.
1998-01-01
Methods are disclosed for minimizing laser induced damage to nonlinear crystals, such as KTP crystals, involving various means for electrically grounding the crystals in order to diffuse electrical discharges within the crystals caused by the incident laser beam. In certain embodiments, electrically conductive material is deposited onto or into surfaces of the nonlinear crystals and the electrically conductive surfaces are connected to an electrical ground. To minimize electrical discharges on crystal surfaces that are not covered by the grounded electrically conductive material, a vacuum may be created around the nonlinear crystal.
GENERAL RELATIVISTIC EFFECTS ON NONLINEAR POWER SPECTRA
Jeong, Donghui; Gong, Jinn-Ouk; Noh, Hyerim; Hwang, Jai-chan E-mail: jgong@lorentz.leidenuniv.nl E-mail: jchan@knu.ac.kr
2011-01-20
The nonlinear nature of Einstein's equation introduces genuine relativistic higher order corrections to the usual Newtonian fluid equations describing the evolution of cosmological perturbations. We study the effect of such novel nonlinearities on the next-to-leading order matter and velocity power spectra for the case of a pressureless, irrotational fluid in a flat Friedmann background. We find that pure general relativistic corrections are negligibly small over all scales. Our result guarantees that, in the current paradigm of standard cosmology, one can safely use Newtonian cosmology even in nonlinear regimes.
Nonlinear gyrokinetic equations for tokamak microturbulence
Hahm, T.S.
1988-05-01
A nonlinear electrostatic gyrokinetic Vlasov equation, as well as Poisson equation, has been derived in a form suitable for particle simulation studies of tokamak microturbulence and associated anomalous transport. This work differs from the existing nonlinear gyrokinetic theories in toroidal geometry, since the present equations conserve energy while retaining the crucial linear and nonlinear polarization physics. In the derivation, the action-variational Lie perturbation method is utilized in order to preserve the Hamiltonian structure of the original Vlasov-Poisson system. Emphasis is placed on the dominant physics of the collective fluctuations in toroidal geometry, rather than on details of particle orbits. 13 refs.
Vibration control using nonlinear damped coupling
NASA Astrophysics Data System (ADS)
Ghandchi Tehrani, Maryam; Gattulli, Vincenzo
2016-09-01
In this paper, a dynamical system, which consists of two linear mechanical oscillators, coupled with a nonlinear damping device is considered. First, the dynamic equations are derived, then, an analytical method such as harmonic balance method, is applied to obtain the response to a harmonic base excitation. The response of the system depends on the excitation characteristics. A parametric study is carried out based on different base excitation amplitudes, frequencies, and different nonlinear damping values and the response of the system is fully described. For validation, time domain simulations are carried out to obtain the nonlinear response of the coupled system.
A canonical form for nonlinear systems
NASA Technical Reports Server (NTRS)
Su, R.; Hunt, L. R.
1986-01-01
The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.
Ring for test of nonlinear integrable optics
Valishev, A.; Nagaitsev, S.; Kashikhin, V.; Danilov, V.; /SNS Project, Oak Ridge
2011-03-01
Nonlinear optics is a promising idea potentially opening the path towards achieving super high beam intensities in circular accelerators. Creation of a tune spread reaching 50% of the betatron tune would provide strong Landau damping and make the beam immune to instabilities. Recent theoretical work has identified a possible way to implement stable nonlinear optics by incorporating nonlinear focusing elements into a specially designed machine lattice. In this report we propose the design of a test accelerator for a proof-of-principle experiment. We discuss possible studies at the machine, requirements on the optics stability and sensitivity to imperfections.
Nonlinear and nonequilibrium dynamics in geomaterials.
TenCate, James A; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A
2004-08-01
The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.
Fractional non-linear modelling of ultracapacitors
NASA Astrophysics Data System (ADS)
Bertrand, Nicolas; Sabatier, Jocelyn; Briat, Olivier; Vinassa, Jean-Michel
2010-05-01
In this paper, it is demonstrated that an ultracapacitor exhibits a non-linear behaviour in relation to the operating voltage. A set of fractional order linear systems resulting from a frequency analysis of the ultracapacitor at various operating points is first obtained. Then, a non-linear model is deduced from the linear systems set, so that its Taylor linearization around the considered operating points (for the frequency analysis), produces the linear system set. The resulting non-linear model is validated on a Hybrid Electric Vehicle (HEV) application.
Nonlinear Dynamical Analysis of Fibrillation
NASA Astrophysics Data System (ADS)
Kerin, John A.; Sporrer, Justin M.; Egolf, David A.
2013-03-01
The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.
Micromechanics of nonlinear plastic modes.
Lerner, Edan
2016-05-01
Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their associated stiffnesses under external deformations. The deformation dynamics of NPMs is compared to those of the analogous observables derived from atomistic linear elastic theory, namely, destabilizing eigenmodes of the dynamical matrix and their associated eigenvalues. The key result we present and explain is that the dynamics of NPMs and of destabilizing eigenmodes under external deformations follow different scaling laws with respect to the proximity to imminent instabilities. In particular, destabilizing modes vary with a singular rate, whereas NPMs exhibit no such singularity. As a result, NPMs converge much earlier than destabilizing eigenmodes to their common final form at plastic instabilities. This dynamical difference between NPMs and linear destabilizing eigenmodes underlines the usefulness of NPMs for predicting the locus and geometry of plastic instabilities, compared to their linear-elastic counterparts. PMID:27300970
Nonlinear Dynamics in Viscoelastic Jets
NASA Astrophysics Data System (ADS)
Majmudar, Trushant; Varagnat, Matthieu; McKinley, Gareth
2008-11-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain poorly understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in considerable detail, both theoretically and experimentally. Instability in viscous jets leads to regular periodic coiling of the jet, which exhibits a non-trivial frequency dependence with the height of the fall. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities. We observe complex nonlinear spatio-temporal dynamics of the jet, and uncover a transition from periodic to quasi-periodic to a multi-frequency, broad-spectrum dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo'' or the Kaye effect. We examine different dynamical regimes in terms of scaling variables, which depend on the geometry (dimensionless height), kinematics (dimensionless flow rate), and the fluid properties (elasto-gravity number) and present a regime map of the dynamics of the jet in terms of these dimensionless variables.
Nonlinear Dynamics in Viscoelastic Jets
NASA Astrophysics Data System (ADS)
Majmudar, Trushant; Varagnat, Matthieu; McKinley, Gareth
2009-03-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain poorly understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in considerable detail, both theoretically and experimentally. Instability in viscous jets leads to regular periodic coiling of the jet, which exhibits a non-trivial frequency dependence with the height of the fall. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities. We observe complex nonlinear spatio-temporal dynamics of the jet, and uncover a transition from periodic to quasi-periodic to a multi-frequency, broad-spectrum dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo'' or the Kaye effect. We examine different dynamical regimes in terms of scaling variables, which depend on the geometry (dimensionless height), kinematics (dimensionless flow rate), and the fluid properties (elasto-gravity number) and present a regime map of the dynamics of the jet in terms of these dimensionless variables.
Micromechanics of nonlinear plastic modes
NASA Astrophysics Data System (ADS)
Lerner, Edan
2016-05-01
Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their associated stiffnesses under external deformations. The deformation dynamics of NPMs is compared to those of the analogous observables derived from atomistic linear elastic theory, namely, destabilizing eigenmodes of the dynamical matrix and their associated eigenvalues. The key result we present and explain is that the dynamics of NPMs and of destabilizing eigenmodes under external deformations follow different scaling laws with respect to the proximity to imminent instabilities. In particular, destabilizing modes vary with a singular rate, whereas NPMs exhibit no such singularity. As a result, NPMs converge much earlier than destabilizing eigenmodes to their common final form at plastic instabilities. This dynamical difference between NPMs and linear destabilizing eigenmodes underlines the usefulness of NPMs for predicting the locus and geometry of plastic instabilities, compared to their linear-elastic counterparts.
Nonlinear waves in capillary electrophoresis
Ghosal, Sandip; Chen, Zhen
2011-01-01
Electrophoretic separation of a mixture of chemical species is a fundamental technique of great usefulness in biology, health care and forensics. In capillary electrophoresis the sample migrates in a microcapillary in the presence of a background electrolyte. When the ionic concentration of the sample is sufficiently high, the signal is known to exhibit features reminiscent of nonlinear waves including sharp concentration ‘shocks’. In this paper we consider a simplified model consisting of a single sample ion and a background electrolyte consisting of a single co-ion and a counterion in the absence of any processes that might change the ionization states of the constituents. If the ionic diffusivities are assumed to be the same for all constituents the concentration of sample ion is shown to obey a one dimensional advection diffusion equation with a concentration dependent advection velocity. If the analyte concentration is sufficiently low in a suitable non-dimensional sense, Burgers’ equation is recovered, and thus, the time dependent problem is exactly solvable with arbitrary initial conditions. In the case of small diffusivity either a leading edge or trailing edge shock is formed depending on the electrophoretic mobility of the sample ion relative to the background ions. Analytical formulas are presented for the shape, width and migration velocity of the sample peak and it is shown that axial dispersion at long times may be characterized by an effective diffusivity that is exactly calculated. These results are consistent with known observations from physical and numerical simulation experiments. PMID:20238181
Nonlinear elasticity of alginate gels
NASA Astrophysics Data System (ADS)
Hashemnejad, Seyed Meysam; Kundu, Santanu
Alginate is a naturally occurring anionic polysaccharide extracted from brown algae. Because of biocompatibility, low toxicity, and simple gelation process, alginate gels are used in biomedical and food applications. Here, we report the rheological behavior of ionically crosslinked alginate gels, which are obtained by in situ gelation of alginates with calcium salts, in between two parallel plates of a rheometer. Strain stiffening behavior was captured using large amplitude oscillatory shear (LAOS) experiments. In addition, negative normal stress was observed for these gels, which has not been reported earlier for any polysaccharide networks. The magnitude of negative normal stress increases with applied strain and can exceed that of the shear stress at large strain. Rheological results fitted with a constitutive model that considers both stretching and bending of chains indicate that nonlinearity is likely related to the stretching of the chains between the crosslink junctions. The results provide an improved understanding of the deformation mechanism of ionically crosslinked alginate gel and the results will be important in developing synthetic extracellular matrix (ECM) from these materials.
Topics in fluctuating nonlinear hydrodynamics
Milner, S.T.
1986-01-01
Models of fluctuating nonlinear hydrodynamics have enjoyed much success in explaining the effect of long-wavelength fluctuations in diverse hydrodynamic systems. This thesis explores two such problems; in both, the body of hydrodynamic assumptions powerfully constrains the predictions of a well-posed theory. The effects of layer fluctuations in smectic-A liquid crystals are first examined. The static theory (introduced by Grinstein and Pelcovits) is reviewed. Ward identities, resulting from the arbitrariness of the layering direction, are derived and exploited. The static results motivate an examination of dynamic fluctuation effects. A new sound-damping experiment is proposed that would probe singular dependence of viscosities on applied stress. A theory of Procaccia and Gitterman that reaction rates of chemically reacting binary mixtures are drastically reduced near their thermodynamic critical points is analyzed. Hydrodynamic arguments and Van Hove theory are applied, concluding that the PG idea is drastically slowed, and spatially varying composition fluctuations are at best slowed down over a narrow range of wavenumbers.
Continuous control of the nonlinearity phase for harmonic generations.
Li, Guixin; Chen, Shumei; Pholchai, Nitipat; Reineke, Bernhard; Wong, Polis Wing Han; Pun, Edwin Yue Bun; Cheah, Kok Wai; Zentgraf, Thomas; Zhang, Shuang
2015-06-01
The capability of locally engineering the nonlinear optical properties of media is crucial in nonlinear optics. Although poling is the most widely employed technique for achieving locally controlled nonlinearity, it leads only to a binary nonlinear state, which is equivalent to a discrete phase change of π in the nonlinear polarizability. Here, inspired by the concept of spin-rotation coupling, we experimentally demonstrate nonlinear metasurfaces with homogeneous linear optical properties but spatially varying effective nonlinear polarizability with continuously controllable phase. The continuous phase control over the local nonlinearity is demonstrated for second and third harmonic generation by using nonlinear metasurfaces consisting of nanoantennas of C3 and C4 rotational symmetries, respectively. The continuous phase engineering of the effective nonlinear polarizability enables complete control over the propagation of harmonic generation signals. Therefore, this method seamlessly combines the generation and manipulation of harmonic waves, paving the way for highly compact nonlinear nanophotonic devices. PMID:25849530
NASA Astrophysics Data System (ADS)
Wu, Fen; Hays, Scott
2013-09-01
This paper investigates nonlinear gain-scheduling control approaches for a class of polynomial nonlinear systems, containing an output-dependent vector field with input saturation. Using the polytopic differential inclusion and norm-bounded differential inclusion (NDI) of saturation and dead-zone functions, the nonlinear plants are transformed into systems with measurable parameters. For the polytopic differential inclusion description, a quasi-linear parameter varying (quasi-LPV) output-feedback controller will be sought for saturation control. On the other hand, the NDI model leads to a nonlinear fractional transformation (NFT) output-feedback controller for saturated nonlinear systems. The quasi-LPV and NFT output-feedback control synthesis conditions are derived in the forms of output-dependent matrix inequalities. They can be reformulated as sum-of-squares (SOS) optimisations and solved efficiently using SOS programming. The proposed nonlinear gain-scheduling saturation control approaches will be demonstrated using the Van der Pol equation.
Shahnazi, Reza
2015-01-01
An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations.
Shahnazi, Reza
2015-01-01
An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations. PMID:25104646
On a Nonlinear Model in Adiabatic Evolutions
NASA Astrophysics Data System (ADS)
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Electrifying photonic metamaterials for tunable nonlinear optics.
Kang, Lei; Cui, Yonghao; Lan, Shoufeng; Rodrigues, Sean P; Brongersma, Mark L; Cai, Wenshan
2014-08-11
Metamaterials have not only enabled unprecedented flexibility in producing unconventional optical properties that are not found in nature, they have also provided exciting potential to create customized nonlinear media with high-order properties correlated to linear behaviour. Two particularly compelling directions are active metamaterials, whose optical properties can be purposely tailored by external stimuli in a reversible manner, and nonlinear metamaterials, which enable intensity-dependent frequency conversion of light waves. Here, by exploring the interaction of these two directions, we leverage the electrical and optical functions simultaneously supported in nanostructured metals and demonstrate electrically controlled nonlinear optical processes from a metamaterial. Both second harmonic generation and optical rectification, enhanced by the resonance behaviour in the metamaterial absorber, are modulated externally with applied voltage signals. Our results reveal an opportunity to exploit optical metamaterials as self-contained, dynamic electro-optic systems with intrinsically embedded electrical functions and optical nonlinearities.
Nonlinear Dynamics of Structures with Material Degradation
NASA Astrophysics Data System (ADS)
Soltani, P.; Wagg, D. J.; Pinna, C.; Whear, R.; Briody, C.
2016-09-01
Structures usually experience deterioration during their working life. Oxidation, corrosion, UV exposure, and thermo-mechanical fatigue are some of the most well-known mechanisms that cause degradation. The phenomenon gradually changes structural properties and dynamic behaviour over their lifetime, and can be more problematic and challenging in the presence of nonlinearity. In this paper, we study how the dynamic behaviour of a nonlinear system changes as the thermal environment causes certain parameters to vary. To this end, a nonlinear lumped mass modal model is considered and defined under harmonic external force. Temperature dependent material functions, formulated from empirical test data, are added into the model. Using these functions, bifurcation parameters are defined and the corresponding nonlinear responses are observed by numerical continuation. A comparison between the results gives a preliminary insight into how temperature induced properties affects the dynamic response and highlights changes in stability conditions of the structure.
Nonlinear regimes of forced magnetic reconnection
Vekstein, G.; Kusano, K.
2015-09-15
This letter presents a self-consistent description of nonlinear forced magnetic reconnection in Taylor's model of this process. If external boundary perturbation is strong enough, nonlinearity in the current sheet evolution becomes important before resistive effects come into play. This terminates the current sheet shrinking that takes place at the linear stage and brings about its nonlinear equilibrium with a finite thickness. Then, in theory, this equilibrium is destroyed by a finite plasma resistivity during the skin-time, and further reconnection proceeds in the Rutherford regime. However, realization of such a scenario is unlikely because of the plasmoid instability, which is fast enough to develop before the transition to the Rutherford phase occurs. The suggested analytical theory is entirely different from all previous studies and provides proper interpretation of the presently available numerical simulations of nonlinear forced magnetic reconnection.
Evaluation of radiation damage using nonlinear ultrasound
Matlack, K. H.; Wall, J. J.; Kim, J.-Y.; Qu, J.; Jacobs, L. J.; Viehrig, H.-W.
2012-03-01
Nonlinear ultrasound was used to monitor radiation damage in two reactor pressure vessel (RPV) steels. The microstructural changes associated with radiation damage include changes in dislocation density and the formation of precipitates, and nonlinear ultrasonic waves are known to be sensitive to such changes. Six samples each of two different RPV steels were previously irradiated in the Rheinsberg power reactor to two fluence levels, up to 10{sup 20} n/cm{sup 2} (E > 1 MeV). Longitudinal waves were used to measure the acoustic nonlinearity in these samples, and the results show a clear increase in the measured acoustic nonlinearity from the unirradiated state to the medium dose, and then a decrease from medium dose to high dose.
Soliton production with nonlinear homogeneous lines
Elizondo-Decanini, Juan M.; Coleman, Phillip D.; Moorman, Matthew W.; Petney, Sharon Joy Victor; Dudley, Evan C.; Youngman, Kevin; Penner, Tim Dwight; Fang, Lu; Myers, Katherine M.
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
Non-linearity in Johnson noise thermometry
NASA Astrophysics Data System (ADS)
White, D. R.
2012-12-01
This paper discusses the effects of non-linearity, some of the mechanisms responsible for non-linearity, and methods for measuring non-linearity in Johnson noise thermometry. Mechanisms considered include quantum tunnelling, bipolar junction transistor and junction field-effect transistor amplifiers, feedback, clipping, output-stage crossover, quantization and dither. It is found that even- and odd-order effects behave differently in correlator-based noise thermometers, with the dominant even-order effects contributing as intermodulation products whereas the dominant odd-order contributions are third-order and at the same frequencies as the parent signals. Possible test methods include the use of discrete tones, changes in spectral shape, and direct measurement using reference noise powers. For correlators operated at constant noise power, direct measurement of non-linearity using reference noise powers enables corrections to be made with negligible additional uncertainty and measurement time.
Rotating black string with nonlinear source
Hendi, S. H.
2010-09-15
In this paper, we derive rotating black string solutions in the presence of two kinds of nonlinear electromagnetic fields, so-called Born-Infeld and power Maxwell invariant. Investigation of the solutions show that for the Born-Infeld black string the singularity is timelike and the asymptotic behavior of the solutions is anti-de Sitter, but for power Maxwell invariant solutions, depending on the values of nonlinearity parameter, the singularity may be timelike as well as spacelike and the solutions are not asymptotically anti-de Sitter for all values of the nonlinearity parameter. Next, we calculate the conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the nonlinearity parameter. We also compute the entropy, temperature, the angular velocity, the electric charge, and the electric potential of the solutions, in which the conserved and thermodynamics quantities satisfy the first law of thermodynamics.
Nonlinear realizations and the orbit method
Gonera, Joanna
2013-11-15
Given a symmetry group one can construct the invariant dynamics using the technique of nonlinear realizations or the orbit method. The relationship between these methods is discussed. Few examples are presented.
Testing of Nonlinear Filters For Coloured Noise
NASA Astrophysics Data System (ADS)
Macek, Wieslaw M.; Redaelli, Stefano; Plewczynski, Dariusz
We focus on nonlinearity and deterministic behaviour of classical model systems cor- rupted by white or coloured noise. Therefore, we use nonlinear filters to give a faith- ful representation of nonlinear behaviour of the systems. We also analyse time series of a real system, namely, we study velocities of of the solar wind plasma including Alfvénic fluctuations measured in situ by the Helios spacecraft in the inner helio- sphere. We demonstrate that the influence of white and coloured noise in the data records can be efficiently reduced by a nonlinear filter. We show that due to this non- linear noise reduction we get with much reliability estimates of the largest Lyapunov exponent and the Kolmogorov entropy.
Soliton production with nonlinear homogeneous lines
Elizondo-Decanini, Juan M.; Coleman, Phillip D.; Moorman, Matthew W.; Petney, Sharon Joy Victor; Dudley, Evan C.; Youngman, Kevin; Penner, Tim Dwight; Fang, Lu; Myers, Katherine M.
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 output 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.
Modeling of Nonlinear Beat Signals of TAE's
NASA Astrophysics Data System (ADS)
Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin
2012-03-01
Experiments on Alcator C-Mod reveal Toroidal Alfven Eigenmodes (TAE) together with signals at various beat frequencies, including those at twice the mode frequency. The beat frequencies are sidebands driven by quadratic nonlinear terms in the MHD equations. These nonlinear sidebands have not yet been quantified by any existing codes. We extend the AEGIS code to capture nonlinear effects by treating the nonlinear terms as a driving source in the linear MHD solver. Our goal is to compute the spatial structure of the sidebands for realistic geometry and q-profile, which can be directly compared with experiment in order to interpret the phase contrast imaging diagnostic measurements and to enable the quantitative determination of the Alfven wave amplitude in the plasma core
Synthesis of higher order nonlinear circuit elements
NASA Astrophysics Data System (ADS)
Chua, L. O.; Szeto, E. W.
1984-02-01
Higher and mixed-order n-port circuit elements were introduced recently to provide a logically complete formulation for nonlinear circuit theory. In this paper, higher order mutators are defined and used to synthesize these elements. The class of all higher order mutators is shown to form a group under cascade interconnections. Each mutator is realized using only linear capacitors, linear inductors and linear controlled sources. An upper bound on each type of element needed to realize a mutator is also given. Each higher or mixed-order n-port element is realized by cascading approprimate mutators across each port of a nonlinear n-port resistor. The main theorem shows that any higher or mixed-order nonlinear n-port element with a constitutive relation defined on a compact set can be realized using linear capacitors, inductors, and controlled sources, and 2-terminal nonlinear resistors.
Electromagnetic nonlinear gyrokinetics with polarization drift
Duthoit, F.-X.; Hahm, T. S.; Wang, Lu
2014-08-15
A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.
Nonlinear Acoustical Assessment of Precipitate Nucleation
NASA Technical Reports Server (NTRS)
Cantrell, John H.; Yost, William T.
2004-01-01
The purpose of the present work is to show that measurements of the acoustic nonlinearity parameter in heat treatable alloys as a function of heat treatment time can provide quantitative information about the kinetics of precipitate nucleation and growth in such alloys. Generally, information on the kinetics of phase transformations is obtained from time-sequenced electron microscopical examination and differential scanning microcalorimetry. The present nonlinear acoustical assessment of precipitation kinetics is based on the development of a multiparameter analytical model of the effects on the nonlinearity parameter of precipitate nucleation and growth in the alloy system. A nonlinear curve fit of the model equation to the experimental data is then used to extract the kinetic parameters related to the nucleation and growth of the targeted precipitate. The analytical model and curve fit is applied to the assessment of S' precipitation in aluminum alloy 2024 during artificial aging from the T4 to the T6 temper.
Epistemological and Treatment Implications of Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
Stein, A. H.
The treatment implications of understanding mind as solely epiphenomenal to nonlinearly founded neurobiology are discussed. G. Klimovsky's epistemological understanding of psychoanalysis as a science is rejected and treatment approaches integrating W. R. Bion's and D. W. Winnicott's work are supported.
Piezoelectric monolayers as nonlinear energy harvesters.
López-Suárez, Miquel; Pruneda, Miguel; Abadal, Gabriel; Rurali, Riccardo
2014-05-01
We study the dynamics of h-BN monolayers by first performing ab-initio calculations of the deformation potential energy and then solving numerically a Langevine-type equation to explore their use in nonlinear vibration energy harvesting devices. An applied compressive strain is used to drive the system into a nonlinear bistable regime, where quasi-harmonic vibrations are combined with low-frequency swings between the minima of a double-well potential. Due to its intrinsic piezoelectric response, the nonlinear mechanical harvester naturally provides an electrical power that is readily available or can be stored by simply contacting the monolayer at its ends. Engineering the induced nonlinearity, a 20 nm2 device is predicted to harvest an electrical power of up to 0.18 pW for a noisy vibration of 5 pN. PMID:24722065
Nonlinear modeling of MEMS piezoelectric energy harvesters
NASA Astrophysics Data System (ADS)
Wang, Y. C.; Huang, T. W.; Shu, Y. C.; Lin, S. C.; Wu, W. J.
2016-04-01
This article presents the modeling of nonlinear response of micro piezoelectric energy harvesters under amplified base excitation. The micro transducer is a composite cantilever beam made of the PZT thick film deposited on the stainless-steel substrate. The model is developed based on the Euler-Bernoulli beam theory considering geometric and inertia nonlinearities, and the reduced formulation is derived based on the Hamiltonian variational principle. The harmonic balance method is used to simulate the nonlinear frequency response under various magnitudes of excitation and electric loads. The hardening type of nonlinearity is predicted and is found to be in good agreement with experiment. However, the softening response is also observed in different samples fabricated under different conditions. Such disagreement is under investigation.
On controllability of nonlinear stochastic systems
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Kim, J.-H.; Mahmudov, N. I.
2006-12-01
In this paper, complete controllability for nonlinear stochastic systems is studied. First this paper addresses the problem of complete controllability of nonlinear stochastic systems with standard Brownian motion. Then this result is extended to establish complete controllability criterion for stochastic systems with fractional Brownian motion. A fixed point approach is employed for achieving the required result. The solutions are given by a variation of constants formula which allows us to study the complete controllability for nonlinear stochastic systems. In this paper, we prove the complete controllability of nonlinear stochastic system under the natural assumption that the associated linear control system is completely controllable. Finally, an illustrative example is provided to show the usefulness of the proposed technique.
Nonlinear principal component analysis of climate data
Boyle, J.; Sengupta, S.
1995-06-01
This paper presents the details of the nonlinear principal component analysis of climate data. Topic discussed include: connection with principal component analysis; network architecture; analysis of the standard routine (PRINC); and results.
Acoustic nonlinearity in fluorinert FC-43
Pantea, Cristian; Sinha, Dipen N; Osterhoudt, Curtis F; Mombourquette, Paul C
2009-01-01
Fluorinert FC-43 nonlinearity was investigated using two approaches: (i) a finite amplitude method with harmonic production; and (ii) a nonlinear frequency mixing in the fluid with consequent beam profile measurement of the difference frequency. The finite amplitude method provides information on the coefficient of nonlinearity, {beta}, through the amplitudes of the fundamental and the second harmonic, at a certain transmitter-receiver distance. A calibrated hydrophone was used as a receiver, in order to obtain direct pressure measurements of the acoustic waves in the fluid. The role of transmitter-receiver distance in {beta} determination is investigated. In the second approach, a single transducer is used to provide two high-frequency beams. The collinear high-frequency beams mix nonlinearly in the fluid resulting in a difference frequency beam and higher order harmonics of the primaries. The difference frequency beam profite is investigated at lengths beyond the mixing distance. The experimental data are compured with the KZK theory.
Discrete time learning control in nonlinear systems
NASA Technical Reports Server (NTRS)
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Nonlinear multiferroic phase shifters for microwave frequencies
Ustinov, Alexey B.; Kalinikos, Boris A.; Srinivasan, G.
2014-02-03
A nonlinear microwave phase shifter based on a planar multiferroic composite has been studied. The multiferroic structure is fabricated in the form of a bilayer consisting of yttrium iron garnet and barium strontium titanate. The principle of operation of the device is based on the linear and nonlinear control of the phase shift of the hybrid spin-electromagnetic waves propagating in the bilayer. The linear control is realized with magnetic and electric fields. The nonlinear control is provided by the input power of microwave signal. The device showed a nonlinear phase shift up to 250°, electric field induced phase shift up to 330°, and magnetic field induced phase shift of more than 180°.
The nonlinear physics of musical instruments
NASA Astrophysics Data System (ADS)
Fletcher, N. H.
1999-05-01
Musical instruments are often thought of as linear harmonic systems, and a first-order description of their operation can indeed be given on this basis, once we recognise a few inharmonic exceptions such as drums and bells. A closer examination, however, shows that the reality is very different from this. Sustained-tone instruments, such as violins, flutes and trumpets, have resonators that are only approximately harmonic, and their operation and harmonic sound spectrum both rely upon the extreme nonlinearity of their driving mechanisms. Such instruments might be described as `essentially nonlinear'. In impulsively excited instruments, such as pianos, guitars, gongs and cymbals, however, the nonlinearity is `incidental', although it may produce striking aural results, including transitions to chaotic behaviour. This paper reviews the basic physics of a wide variety of musical instruments and investigates the role of nonlinearity in their operation.
Nonlinear Analysis of Surface EMG Time Series
NASA Astrophysics Data System (ADS)
Zurcher, Ulrich; Kaufman, Miron; Sung, Paul
2004-04-01
Applications of nonlinear analysis of surface electromyography time series of patients with and without low back pain are presented. Limitations of the standard methods based on the power spectrum are discussed.
Linear and nonlinear light bullets: recent developments
NASA Astrophysics Data System (ADS)
Mihalache, Dumitru
2013-06-01
The spatiotemporal optical solitons (alias nonlinear "light bullets") are nondiffracting and nondispersing wave packets propagating in nonlinear optical media. The three-dimensional spatiotemporal solitons are localized (self-guided) in two transverse (spatial) dimensions and in the direction of propagation due to the balance of anomalous group-velocity dispersion of the medium in which they form and nonlinear self-phase modulation. The formation of fully threedimensional spatiotemporal optical solitons in two-dimensional photonic lattices was reported in recent experiments. Also, linear light bullets, which are robust and versatile localized wave packets combining Bessel beams in the transverse plane with temporal Airy pulses have been reported experimentally. A brief up-to-date survey of recent theoretical and experimental studies of the formation, stability and robustness of linear and nonlinear light bullets in various physical settings is given.
Radiation-pressure-induced nonlinearity in microdroplets.
Zhang, Peng; Jung, Sunghwan; Lee, Aram; Xu, Yong
2015-12-01
High quality (Q) factor whispering gallery modes (WGMs) can induce nonlinear effects in liquid droplets through mechanisms such as radiation pressure, Kerr nonlinearity, and thermal effects. However, such nonlinear effects, especially those due to radiation pressure, have yet to be thoroughly investigated and compared in the literature. In this study, we present an analytical approach that can exactly calculate the droplet deformation induced by the radiation pressure. The accuracy of the analytical approach is confirmed through numerical analyses based on the boundary element method. We show that the nonlinear optofluidic effect induced by the radiation pressure is stronger than the Kerr effect and the thermal effect under a large variety of realistic conditions. Using liquids with ultralow and experimentally attainable interfacial tension, we further confirm the prediction that it may only take a few photons to produce measurable WGM resonance shift through radiation-pressure-induced droplet deformation. PMID:26764829
Nonlinear response of unidirectional boron/aluminum
NASA Technical Reports Server (NTRS)
Pindera, M.-J.; Herakovich, C. T.; Becker, W.; Aboudi, J.
1990-01-01
Experimental results obtained for unidirectional boron/aluminum subjected to combined loading using off-axis tension, compression and Iosipescu shear specimens are correlated with a nonlinear micromechanics model. It is illustrated that the nonlinear response in the principal material directions is markedly influenced by the different loading modes and different ratios of the applied stress components. The observed nonlinear response under pure and combined loading is discussed in terms of initial yielding, subsequent hardening, stress-interaction effects and unloading-reloading characteristics. The micromechanics model is based on the concept of a repeating unit cell representative of the composite-at-large and employs the unified theory of Bodner and Partom to model the inelastic response of the matrix. It is shown that the employed micromechanics model is sufficiently general to predict the observed nonlinear response of unidirectional boron/aluminum with good accuracy.
Nonlinear theory of kinetic instabilities near threshold
Berk, H.L.; Pekker, M.S.; Breizman, B.N. |
1997-05-01
A new nonlinear equation has been derived and solved for the evolution of an unstable collective mode in a kinetic system close to the threshold of linear instability. The resonant particle response produces the dominant nonlinearity, which can be calculated iteratively in the near-threshold regime as long as the mode doe snot trap resonant particles. With sources and classical relaxation processes included, the theory describes both soft nonlinear regimes, where the mode saturation level is proportional to an increment above threshold, and explosive nonlinear regimes, where the mode grows to a level that is independent of the closeness to threshold. The explosive solutions exhibit mode frequency shifting. For modes that exist in the absence of energetic particles, the frequency shift is both upward and downward. For modes that require energetic particles for their existence, there is a preferred direction of the frequency shift. The frequency shift continues even after the mode traps resonant particles.
NASA Astrophysics Data System (ADS)
Tchinang Tchameu, J. D.; Togueu Motcheyo, A. B.; Tchawoua, C.
2016-09-01
The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW.
Nonlinear transient analysis via energy minimization
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Knight, N. F., Jr.
1978-01-01
The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose.
Variational algorithms for nonlinear smoothing applications
NASA Technical Reports Server (NTRS)
Bach, R. E., Jr.
1977-01-01
A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.
Classical Mechanics as Nonlinear Quantum Mechanics
Nikolic, Hrvoje
2007-12-03
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics.
Multifrequency gap solitons in nonlinear photonic crystals.
Xie, Ping; Zhang, Zhao-Qing
2003-11-21
We predict the existence of multifrequency gap solitons (MFGSs) in both one- and two-dimensional nonlinear photonic crystals. A MFGS is a single intrinsic mode possessing multiple frequencies inside the gap. Its existence is a result of synergic nonlinear coupling among solitons or soliton trains at different frequencies. Its formation can either lower the threshold fields of the respective frequency components or stabilize their excitations. These MFGSs form a new class of stable gap solitons.
Research in nonlinear structural and solid mechanics
NASA Technical Reports Server (NTRS)
Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)
1981-01-01
Recent and projected advances in applied mechanics, numerical analysis, computer hardware and engineering software, and their impact on modeling and solution techniques in nonlinear structural and solid mechanics are discussed. The fields covered are rapidly changing and are strongly impacted by current and projected advances in computer hardware. To foster effective development of the technology perceptions on computing systems and nonlinear analysis software systems are presented.
Two Color Interferometry with Nonlinear Refractive Properties
NASA Technical Reports Server (NTRS)
Vikram, Chandra S.; Witherow, William K.
2002-01-01
Using nonlinear refractive properties of salt-water solution at two wavelengths, numerical analysis has been performed to extract temperature and concentration from virtual interferometric fringe data. The theoretical study, using a commercially available equation solving tool, starts with critical fringe counting needs and the role of nonlinear refractive properties in such measurements. Finally, methodology of the analysis, developed codes, and fringe counting accuracy needs are described in detail.
Solitons in PT-symmetric nonlinear lattices
Abdullaev, Fatkhulla Kh.; Konotop, Vladimir V.; Zezyulin, Dmitry A.; Kartashov, Yaroslav V.
2011-04-15
The existence of localized modes supported by the PT-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems, it possesses families (branches) of solutions, which can be parametrized by the propagation constant; relatively narrow localized modes appear to be stable, even when the conservative nonlinear lattice potential is absent; and finally, the system supports stable multipole solutions.
Recent advances in nonlinear passive vibration isolators
NASA Astrophysics Data System (ADS)
Ibrahim, R. A.
2008-07-01
The theory of nonlinear vibration isolation has witnessed significant developments due to pressing demands for the protection of structural installations, nuclear reactors, mechanical components, and sensitive instruments from earthquake ground motion, shocks, and impact loads. In view of these demands, engineers and physicists have developed different types of nonlinear vibration isolators. This article presents a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means. It does not deal with other means of linear or nonlinear vibration absorbers. It begins with the basic concept and features of nonlinear isolators and inherent nonlinear phenomena. Specific types of nonlinear isolators are then discussed, including ultra-low-frequency isolators. For vertical vibration isolation, the treatment of the Euler spring isolator is based on the post-buckling dynamic characteristics of the column elastica and axial stiffness. Exact and approximate analyses of axial stiffness of the post-buckled Euler beam are outlined. Different techniques of reducing the resonant frequency of the isolator are described. Another group is based on the Gospodnetic-Frisch-Fay beam, which is free to slide on two supports. The restoring force of this beam resembles to a great extent the restoring roll moment of biased ships. The base isolation of buildings, bridges, and liquid storage tanks subjected to earthquake ground motion is then described. Base isolation utilizes friction elements, laminated-rubber bearings, and the friction pendulum. Nonlinear viscoelastic and composite material springs, and smart material elements are described in terms of material mechanical characteristics and the dependence of their transmissibility on temperature and excitation amplitude. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research directions.
Nonlinear Dynamics of Parametrically Excited Gyroscopic Systems
Namachchivaya. N.S.
2001-06-01
The primary objective of this project is to determine how some of the powerful geometric methods of dynamical systems can be applied to study nonlinear gyroscopic systems. We proposed to develop techniques to predict local and global behavior and instability mechanisms and to analyze the interactions between noise, stability, and nonlinearities inherent in gyroscopic systems. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools.
Computer aided nonlinear electrical networks analysis
NASA Technical Reports Server (NTRS)
Slapnicar, P.
1977-01-01
Techniques used in simulating an electrical circuit with nonlinear elements for use in computer-aided circuit analysis programs are described. Elements of the circuit include capacitors, resistors, inductors, transistors, diodes, and voltage and current sources (constant or time varying). Simulation features are discussed for dc, ac, and/or transient circuit analysis. Calculations are based on the model approach of formulating the circuit equations. A particular solution of transient analysis for nonlinear storage elements is described.
Nonlinear ring resonator: spatial pattern generation
NASA Astrophysics Data System (ADS)
Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.
2000-03-01
We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.
Nonlinear refraction in aqueous colloidal gold
NASA Astrophysics Data System (ADS)
Mehendale, S. C.; Mishra, S. R.; Bindra, K. S.; Laghate, M.; Dhami, T. S.; Rustagi, K. C.
1997-02-01
Nonlinear refraction in aqueous colloidal gold at 527 nm was studied using the z-scan technique. While a z-scan with a 35 ns laser showed a large negative lensing, a z-scan with a 4 ps laser showed no measurable refraction. The observed nonlinear refraction is shown to be of thermal origin resulting from energy transfer from gold particles to the water molecules.
Giant optical nonlinearity of plasmonic nanostructures
Melentiev, P N; Afanasev, A E; Balykin, V I
2014-06-30
The experimental studies of giant optical nonlinearity of single metal nanostructures are briefly reviewed. A new hybrid nanostructure – split-hole resonator (SHR) – is investigated. This structure is characterised by a record-high efficiency of third-harmonic generation and multiphoton luminescence (its nonlinearity exceeds that of a single nanohole by five orders of magnitude) and an unprecedently high sensitivity to light polarisation (extinction coefficient 4 × 10{sup 4}). (extreme light fields and their applications)
Nonlinear longitudinal control of a supermaneuverable aircraft
NASA Technical Reports Server (NTRS)
Garrard, William L.; Snell, Anthony; Enns, Dale F.
1989-01-01
A technique is described which can be used for design of feedback controllers for high-performance aircraft operating in flight conditions in which nonlinearities significantly affect performance. Designs are performed on a mathematical model of the longitudinal dynamics of a hypothetical aircraft similar to proposed supermaneuverable flight test vehicles. Nonlinear controller designs are performed using truncated solutions of the Hamilton-Jacobi-Bellman equation. Preliminary results show that the method yields promising results.
Concurrent processing in nonlinear structural stability
NASA Technical Reports Server (NTRS)
Darbhamulla, S. P.; Razzaq, Z.; Storaasli, O. O.
1986-01-01
A concurrent processing algorithm is developed for materially nonlinear stability analysis of imperfect columns with biaxial partial rotational end restraints. The algorithm for solving the governing nonlinear ordinary differential equations is implemented on a multiprocessor computer called the 'Finite Element Machine', developed at the NASA Langley Research Center. Numerical results are obtained on up to nine concurrent processors. A substantial computational gain is achieved in using the parallel processing approach.
Artificial muscle using nonlinear elastomers
NASA Astrophysics Data System (ADS)
Ratna, Banahalli
2002-03-01
Anisotropic freestanding films or fibers of nematic elastomers from laterally attached side-chain polymers show muscle-like mechanical properties. The orientational order of the liquid crystal side groups imposes a conformational anisotropy in the polymer backbone. When a large change in the order parameter occurs, as at the nematic-isotropic phase transition, there is a concomitant loss of order in the backbone which results in a contraction of the film in the direction of the director orientation. The crosslinked network imposes a symmetry-breaking field on the nematic and drives the nematic-isotropic transition towards a critical point with the application of external stress. Isostrain studies on these nonlinear elastomers, show that there are large deviations from ideal classical rubber elasticity and the contributions from total internal energy to the elastic restoring force cannot be ignored. The liquid crystal elastomers exhibiting anisoptopic contraction/extension coupled with a graded strain response to an applied external stimulus provide an excellent framework for mimicking muscular action. Liquid crystal elastomers by their very chemical nature have a number of ‘handles’ such as the liquid crystalline phase range, density of crosslinking, flexibility of the backbone, coupling between the backbone and the mesogen and the coupling between the mesogen and the external stimulus, that can be tuned to optimize the mechanical properties. We have demonstrated actuation in nematic elastomers under thermal and optical stimuli. We have been able to dope the elastomers with dyes to make them optically active. We have also doped them with carbon nanotubes in order to increase the thermal and electrical conductivity of the elastomer.
Forced nonlinear Schrödinger equation with arbitrary nonlinearity.
Cooper, Fred; Khare, Avinash; Quintero, Niurka R; Mertens, Franz G; Saxena, Avadh
2012-04-01
We consider the nonlinear Schrödinger equation (NLSE) in 1+1 dimension with scalar-scalar self-interaction g(2)/κ+1(ψ*ψ)(κ+1) in the presence of the external forcing terms of the form re(-i(kx+θ))-δψ. We find new exact solutions for this problem and show that the solitary wave momentum is conserved in a moving frame where v(k)=2k. These new exact solutions reduce to the constant phase solutions of the unforced problem when r→0. In particular we study the behavior of solitary wave solutions in the presence of these external forces in a variational approximation which allows the position, momentum, width, and phase of these waves to vary in time. We show that the stationary solutions of the variational equations include a solution close to the exact one and we study small oscillations around all the stationary solutions. We postulate that the dynamical condition for instability is that dp(t)/dq ̇(t)<0, where p(t) is the normalized canonical momentum p(t)=1/M(t)∂L/∂q ̇, and q ̇(t) is the solitary wave velocity. Here M(t)=∫dxψ*(x,t)ψ(x,t). Stability is also studied using a "phase portrait" of the soliton, where its dynamics is represented by two-dimensional projections of its trajectory in the four-dimensional space of collective coordinates. The criterion for stability of a soliton is that its trajectory is a closed single curve with a positive sense of rotation around a fixed point. We investigate the accuracy of our variational approximation and these criteria using numerical simulations of the NLSE. We find that our criteria work quite well when the magnitude of the forcing term is small compared to the amplitude of the unforced solitary wave. In this regime the variational approximation captures quite well the behavior of the solitary wave. PMID:22680598
NASA Astrophysics Data System (ADS)
Ranjbar, Monireh; Bahari, Ali
2016-09-01
Four-wave mixing in propagation of cylindrical waves in a homogeneous nonlinear optical media has been investigated theoretically. An explicit analytical expression which contains all the main nonlinear optical effects, including third harmonic generation, sum and difference frequency generation has been obtained. A comparison between sum frequency efficiency for exact and approximation expression in a homogeneous nonlinear medium has been done. The effect of increasing the nonlinear optical coefficient (χeff(3)) and increasing the frequency difference between two adjacent waves (Δ ω) , on the efficiency of sum frequency generation in homogeneous media has been investigated.
Mäkelä, J T A; Korhonen, R K
2016-06-14
Modern fibril-reinforced computational models of articular cartilage can include inhomogeneous tissue composition and structure, and nonlinear mechanical behavior of collagen, proteoglycans and fluid. These models can capture well experimental single step creep and stress-relaxation tests or measurements under small strains in unconfined and confined compression. Yet, it is known that in indentation, especially at high strain velocities, cartilage can express highly nonlinear response. Different fibril reinforced poroelastic and poroviscoelastic models were used to assess measured highly nonlinear stress-relaxation response of rabbit articular cartilage in indentation. Experimentally measured depth-dependent volume fractions of different tissue constituents and their mechanical nonlinearities were taken into account in the models. In particular, the collagen fibril network was modeled using eight separate models that implemented five different constitutive equations to describe the nonlinearity. These consisted of linear elastic, nonlinear viscoelastic and multiple nonlinear elastic representations. The model incorporating the most nonlinearly increasing Young׳s modulus of collagen fibrils as a function of strain captured best the experimental data. Relative difference between the model and experiment was ~3%. Surprisingly, the difference in the peak forces between the experiment and the model with viscoelastic collagen fibrils was almost 20%. Implementation of the measured volume fractions did not improve the ability of the model to capture the measured mechanical data. These results suggest that a highly nonlinear formulation for collagen fibrils is needed to replicate multi-step stress-relaxation response of rabbit articular cartilage in indentation with high strain rates. PMID:27130474
Mäkelä, J T A; Korhonen, R K
2016-06-14
Modern fibril-reinforced computational models of articular cartilage can include inhomogeneous tissue composition and structure, and nonlinear mechanical behavior of collagen, proteoglycans and fluid. These models can capture well experimental single step creep and stress-relaxation tests or measurements under small strains in unconfined and confined compression. Yet, it is known that in indentation, especially at high strain velocities, cartilage can express highly nonlinear response. Different fibril reinforced poroelastic and poroviscoelastic models were used to assess measured highly nonlinear stress-relaxation response of rabbit articular cartilage in indentation. Experimentally measured depth-dependent volume fractions of different tissue constituents and their mechanical nonlinearities were taken into account in the models. In particular, the collagen fibril network was modeled using eight separate models that implemented five different constitutive equations to describe the nonlinearity. These consisted of linear elastic, nonlinear viscoelastic and multiple nonlinear elastic representations. The model incorporating the most nonlinearly increasing Young׳s modulus of collagen fibrils as a function of strain captured best the experimental data. Relative difference between the model and experiment was ~3%. Surprisingly, the difference in the peak forces between the experiment and the model with viscoelastic collagen fibrils was almost 20%. Implementation of the measured volume fractions did not improve the ability of the model to capture the measured mechanical data. These results suggest that a highly nonlinear formulation for collagen fibrils is needed to replicate multi-step stress-relaxation response of rabbit articular cartilage in indentation with high strain rates.
Quaternion-valued nonlinear adaptive filtering.
Ujang, Bukhari Che; Took, Clive Cheong; Mandic, Danilo P
2011-08-01
A class of nonlinear quaternion-valued adaptive filtering algorithms is proposed based on locally analytic nonlinear activation functions. To circumvent the stringent standard analyticity conditions which are prohibitive to the development of nonlinear adaptive quaternion-valued estimation models, we use the fact that stochastic gradient learning algorithms require only local analyticity at the operating point in the estimation space. It is shown that the quaternion-valued exponential function is locally analytic, and, since local analyticity extends to polynomials, products, and ratios, we show that a class of transcendental nonlinear functions can serve as activation functions in nonlinear and neural adaptive models. This provides a unifying framework for the derivation of gradient-based learning algorithms in the quaternion domain, and the derived algorithms are shown to have the same generic form as their real- and complex-valued counterparts. To make such models second-order optimal for the generality of quaternion signals (both circular and noncircular), we use recent developments in augmented quaternion statistics to introduce widely linear versions of the proposed nonlinear adaptive quaternion valued filters. This allows full exploitation of second-order information in the data, contained both in the covariance and pseudocovariances to cater rigorously for second-order noncircularity (improperness), and the corresponding power mismatch in the signal components. Simulations over a range of circular and noncircular synthetic processes and a real world 3-D noncircular wind signal support the approach. PMID:21712159
Nonlinear dynamics in a SPEAR wiggler
NASA Astrophysics Data System (ADS)
Safranek, J.; Limborg, C.; Terebilo, A.; Blomqvist, K. I.; Elleaume, P.; Nosochkov, Y.
2002-01-01
BL11, the most recently installed wiggler in the SPEAR storage ring at the Stanford Synchrotron Radiation Laboratory, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and closed orbit shifts were used to characterize the nonlinear fields. Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different from the magnetic measurements made along a straight line with a stretched wire. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Because of the relatively large dispersion (1.2 m) at BL11, the nonlinearities particularly reduced the off-energy dynamic aperture. Because of the nature of these nonlinear fields, it is impossible, even theoretically, to cancel them completely with short multipole correctors. Magic finger corrector magnets were built, however, that partially correct the nonlinear perturbation, greatly improving the storage ring performance.
Internal resonance for nonlinear vibration energy harvesting
NASA Astrophysics Data System (ADS)
Cao, D. X.; Leadenham, S.; Erturk, A.
2015-11-01
The transformation of waste vibration energy into low-power electricity has been heavily researched over the last decade to enable self-sustained wireless electronic components. Monostable and bistable nonlinear oscillators have been explored by several research groups in an effort to enhance the frequency bandwidth of operation. Linear two-degree-of-freedom (2-DOF) configurations as well as the combination of a nonlinear single-DOF harvester with a linear oscillator to constitute a nonlinear 2-DOF harvester have also been explored to develop broadband energy harvesters. In the present work, the concept of nonlinear internal resonance in a continuous frame structure is explored for broadband energy harvesting. The L-shaped beam-mass structure with quadratic nonlinearity was formerly studied in the nonlinear dynamics literature to demonstrate modal energy exchange and the saturation phenomenon when carefully tuned for two-to-one internal resonance. In the current effort, piezoelectric coupling and an electrical load are introduced, and electromechanical equations of the L-shaped energy harvester are employed to explore primary resonance behaviors around the first and the second linear natural frequencies for bandwidth enhancement. Simulations using approximate analytical frequency response equations as well as numerical solutions reveal significant bandwidth enhancement as compared to a typical linear 2-DOF counterpart. Vibration and voltage responses are explored, and the effects of various system parameters on the overall dynamics of the internal resonance-based energy harvesting system are reported.
Photorefractive surface nonlinearly chirped waveguide arrays
NASA Astrophysics Data System (ADS)
Qi, Pengfei; Feng, Tianrun; Wang, Sainan; Han, Rong; Hu, Zhijian; Zhang, Tianhao; Tian, Jianguo; Xu, Jingjun
2016-05-01
We report an alternate type of nonlinear waveguides, photorefractive surface nonlinearly chirped waveguide arrays, which can be directly induced by photorefractive surface waves in virtue of diffusion and drift nonlinearities. The amplitude of such nonlinearly chirped waveguide arrays has an apodized envelope owing to the diffusion nonlinearity. The refractive-index change of the apodized tails converges to a nonzero value which can be handily adjusted by an external electric field. Moreover, the chirp parameters such as amplitude, sign (positive or negative), and initial position can be conveniently adjusted by an external electric field, background illumination, incident beam, etc. Then the guided-wave properties of this type of waveguide arrays are analyzed by using the transfer matrix method. Owing to the flexible tail and the nonlinear chirp, the dispersion curves of the index-guided modes can be tailored by an external electric field and the dispersion curves of ordinary and extraordinary Bragg guided modes couple, intertwine, and anticross with each other. Meanwhile, there is a clear "competition" in the coupling hybrid mode near anticrossing.
Towards the nonlinear acousto-magneto-plasmonics
NASA Astrophysics Data System (ADS)
Temnov, Vasily V.; Razdolski, Ilya; Pezeril, Thomas; Makarov, Denys; Seletskiy, Denis; Melnikov, Alexey; Nelson, Keith A.
2016-09-01
We review the recent progress in experimental and theoretical research of interactions between the acoustic, magnetic and plasmonic transients in hybrid metal-ferromagnet multilayer structures excited by ultrashort laser pulses. The main focus is on understanding the nonlinear aspects of the acoustic dynamics in materials as well as the peculiarities in the nonlinear optical and magneto-optical response. For example, the nonlinear optical detection is illustrated in detail by probing the static magneto-optical second harmonic generation in gold–cobalt–silver trilayer structures in Kretschmann geometry. Furthermore, we show experimentally how the nonlinear reshaping of giant ultrashort acoustic pulses propagating in gold can be quantified by time-resolved plasmonic interferometry and how these ultrashort optical pulses dynamically modulate the optical nonlinearities. An effective medium approximation for the optical properties of hybrid multilayers enables the understanding of novel optical detection techniques. In the discussion we also highlight recent works on the nonlinear magneto-elastic interactions, and strain-induced effects in semiconductor quantum dots.
Topological aspects of nonlinear optical responses
NASA Astrophysics Data System (ADS)
Morimoto, Takahiro; Nagaosa, Naoto
There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. A recent remarkable progress in the photovoltaic effect is the high efficiency solar cell action in perovskite oxides without inversion symmetry. The crystal structure lacking inversion replaces the role of artificial structures such as p-n junctions in conventional solar cells. One of the proposed mechanisms for this phenomenon is the shift-current which is supported by a band structure lacking inversion and is related to the Berry connection of Bloch wavefunctions. Motivated by these, we explore topological aspects of the nonlinear optical responses. To this end, we employ the Keldysh method combined with the Floquet formalism, where effective band structures can be defined under an electric field periodic in time. This enables us to describe the shift-current, nonlinear Kerr rotation, photovoltaic effect, and the photo-induced change in the order parameters in a unified fashion. We connect these nonlinear optical responses to topological quantities involving the Berry connection and Berry curvature. It is found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses.
Measuring Acoustic Nonlinearity by Collinear Mixing Waves
NASA Astrophysics Data System (ADS)
Liu, M.; Tang, G.; Jacobs, L. J.; Qu, J.
2011-06-01
It is well known that the acoustic nonlinearity parameter β is correlated to fatigue damage in metallic materials. Various methods have been developed to measure β. One of the most often used methods is the harmonic generation technique, in which β is obtained by measuring the magnitude of the second order harmonic waves. An inherent weakness of this method is the difficulty in distinguishing material nonlinearity from the nonlinearity of the measurement system. In this paper, we demonstrate the possibility of using collinear mixing waves to measure β. The wave mixing method is based on the interaction between two incident waves in a nonlinear medium. Under certain conditions, such interactions generate a third wave of different frequency. This generated third wave is also called resonant wave, because its amplitude is unbounded if the medium has no attenuation. Such resonant waves are less sensitive to the nonlinearity of the measurement system, and have the potential to identify the source location of the nonlinearity. In this work, we used a longitudinal wave and a shear wave as the incident waves. The resonant shear wave is measured experimentally on samples made of aluminum and steel, respectively. Numerical simulations of the tests were also performed using a finite difference method.
Quaternion-valued nonlinear adaptive filtering.
Ujang, Bukhari Che; Took, Clive Cheong; Mandic, Danilo P
2011-08-01
A class of nonlinear quaternion-valued adaptive filtering algorithms is proposed based on locally analytic nonlinear activation functions. To circumvent the stringent standard analyticity conditions which are prohibitive to the development of nonlinear adaptive quaternion-valued estimation models, we use the fact that stochastic gradient learning algorithms require only local analyticity at the operating point in the estimation space. It is shown that the quaternion-valued exponential function is locally analytic, and, since local analyticity extends to polynomials, products, and ratios, we show that a class of transcendental nonlinear functions can serve as activation functions in nonlinear and neural adaptive models. This provides a unifying framework for the derivation of gradient-based learning algorithms in the quaternion domain, and the derived algorithms are shown to have the same generic form as their real- and complex-valued counterparts. To make such models second-order optimal for the generality of quaternion signals (both circular and noncircular), we use recent developments in augmented quaternion statistics to introduce widely linear versions of the proposed nonlinear adaptive quaternion valued filters. This allows full exploitation of second-order information in the data, contained both in the covariance and pseudocovariances to cater rigorously for second-order noncircularity (improperness), and the corresponding power mismatch in the signal components. Simulations over a range of circular and noncircular synthetic processes and a real world 3-D noncircular wind signal support the approach.
Nonlinear compressional waves in marine sediments
NASA Astrophysics Data System (ADS)
McDonald, B. Edward
2005-09-01
A theory for nonlinear waves in marine sediments must account for the presence of a granular frame filled with water and possibly gas bubbles. When grains are in full contact, the stress-strain relation for the sediment contains a contribution varying as strain to the power 3/2, referred to as the Hertz force. The quadratic nonlinearity parameter derived from the second pressure derivative with respect to density thus diverges in the limit of small strain. We present a simple nonlinear wave equation model (a variant of the NPE) for compressional waves in marine sediments that avoids Taylor expansion and the problem of diverging nonlinearity parameter. An equation of state for partially consolidated sediments is derived from consolidation test results. Pressure is found to increase with overdensity to the power 5/2, indicating an increase in the number of contacts per grain as density increases. Numerical results for nonlinear compressional waves show agreement with analytic self-similar profiles derived from the nonlinear wave equation. [Work supported by the ONR.
Locally nonlinear transformation for facial image superresolution
NASA Astrophysics Data System (ADS)
Zeng, Xiao; Huang, Hua
2013-02-01
Reconstruction of a high-resolution face image, from a low-resolution observation based on a set of high- and low-resolution training image pairs, is an important problem for optical engineering applications. In this paper, we study this facial superresolution problem and propose a novel locally nonlinear transformation based approach. Multiple locally nonlinear transformation are utilized to approximate the global nonlinear connections between low resolution (LR)/high resolution (HR) images. LR/HR images are initially divided into multiple pairs of patches with the corresponding position information. As facial images are highly structured, patches at the same position spanned a subspace. Since the curse of dimensionality is avoided in these subspaces (patches in the same position), the Euclidean distance can express the intrinsic "radial" between samples in the same subspace. Therefore, multiple radial basis functions are utilized to approximate the nonlinear mapping between LR/HR pairs at each position from training examples. The proposed locally nonlinear transformation (LNT)-based reconstruction is achieved by applying the learned nonlinear transformation to each position patch of an LR input. The final SR results are obtained by refining the LNT reconstruction by the projection onto a convex sets algorithm using the consistency constraint. Extensive experiments on benchmark databases and real world images validate the superiority of the proposed method.
Tunable Resonators for Nonlinear Modal Interactions
NASA Astrophysics Data System (ADS)
Ramini, Abdallah H.; Hajjaj, Amal Z.; Younis, Mohammad I.
2016-10-01
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.
Towards the nonlinear acousto-magneto-plasmonics
NASA Astrophysics Data System (ADS)
Temnov, Vasily V.; Razdolski, Ilya; Pezeril, Thomas; Makarov, Denys; Seletskiy, Denis; Melnikov, Alexey; Nelson, Keith A.
2016-09-01
We review the recent progress in experimental and theoretical research of interactions between the acoustic, magnetic and plasmonic transients in hybrid metal-ferromagnet multilayer structures excited by ultrashort laser pulses. The main focus is on understanding the nonlinear aspects of the acoustic dynamics in materials as well as the peculiarities in the nonlinear optical and magneto-optical response. For example, the nonlinear optical detection is illustrated in detail by probing the static magneto-optical second harmonic generation in gold-cobalt-silver trilayer structures in Kretschmann geometry. Furthermore, we show experimentally how the nonlinear reshaping of giant ultrashort acoustic pulses propagating in gold can be quantified by time-resolved plasmonic interferometry and how these ultrashort optical pulses dynamically modulate the optical nonlinearities. An effective medium approximation for the optical properties of hybrid multilayers enables the understanding of novel optical detection techniques. In the discussion we also highlight recent works on the nonlinear magneto-elastic interactions, and strain-induced effects in semiconductor quantum dots.
Tunable Resonators for Nonlinear Modal Interactions
Ramini, Abdallah H.; Hajjaj, Amal Z.; Younis, Mohammad I.
2016-01-01
Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way. PMID:27698455
Application of a nonlinear slug test model
McElwee, C.D.
2001-01-01
Knowledge of the hydraulic conductivity distribution is of utmost importance in understanding the dynamics of an aquifer and in planning the consequences of any action taken upon that aquifer. Slug tests have been used extensively to measure hydraulic conductivity in the last 50 years since Hvorslev's (1951) work. A general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the wellbore, and a Hvorslev model for the aquifer has been implemented in this work. The nonlinear model has three parameters: ??, which is related primarily to radius changes in the water column; A, which is related to the nonlinear head losses; and K, the hydraulic conductivity. An additional parameter has been added representing the initial velocity of the water column at slug initiation and is incorporated into an analytical solution to generate the first time step before a sequential numerical solution generates the remainder of the time solution. Corrections are made to the model output for acceleration before it is compared to the experimental data. Sensitivity analysis and least squares fitting are used to estimate the aquifer parameters and produce some diagnostic results, which indicate the accuracy of the fit. Finally, an example of field data has been presented to illustrate the application of the model to data sets that exhibit nonlinear behavior. Multiple slug tests should be taken at a given location to test for nonlinear effects and to determine repeatability.
Extremely nonlinear and switchable SQUID metamaterial
NASA Astrophysics Data System (ADS)
Zhang, Daimeng; Trepanier, Melissa; Mukhanov, Oleg; Jung, Philipp; Butz, Susanne; Ustinov, Alexey; Anlage, Steven
2014-03-01
We present experimental results on a superconducting metamaterial with remarkably nonlinear and switchable properties in the microwave range. The meta-atoms are RF Superconducting Quantum Interference Devices (SQUIDs), a superconducting loop interrupted by a single Josephson Junction. RF SQUIDs are similar to split-ring resonators except that the inductance is tunable due to the nonlinear Josephson inductance. This metamaterial has high tunability via DC magnetic field, temperature and applied RF power. Here we focus on the nonlinearity in our metamaterial due to the Josephson effect. The intermodulation measurements show a highly nonlinear response from the metamaterial. In an RF power dependence experiment we observed hysteretic behavior in transmission which indicates the metamaterial is a nonlinear multi-state system. As a result, we can control the transmission by switching between metastable states via manipulating the applied RF power. We also observe a unique self-induced transparency of meta-atoms in a certain applied RF power range. This extremely nonlinear metamaterial has potential application for next-generation digital RF receiver systems. This work is supported by the NSF-GOALI and OISE programs through grant # ECCS-1158644, and CNAM.
Nonlinear Learning Underpinning Pedagogy: Evidence, Challenges, and Implications
ERIC Educational Resources Information Center
Chow, Jia Yi
2013-01-01
This article provides a brief overview of the framework of nonlinear pedagogy and evidence emanating from motor learning literature that underpins a nonlinear pedagogical approach. In addition, challenges for nonlinear pedagogy and a discussion on how nonlinear pedagogy support the work of physical education (PE) teachers will be shared. Evidence…
Guided wave methods and apparatus for nonlinear frequency generation
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.
A principle of similarity for nonlinear vibration absorbers
NASA Astrophysics Data System (ADS)
Habib, G.; Kerschen, G.
2016-10-01
This paper develops a principle of similarity for the design of a nonlinear absorber, the nonlinear tuned vibration absorber (NLTVA), attached to a nonlinear primary system. Specifically, for effective vibration mitigation, we show that the NLTVA should feature a nonlinearity possessing the same mathematical form as that of the primary system. A compact analytical formula for the nonlinear coefficient of the absorber is then derived. The formula, valid for any polynomial nonlinearity in the primary system, is found to depend only on the mass ratio and on the nonlinear coefficient of the primary system. When the primary system comprises several polynomial nonlinearities, we demonstrate that the NLTVA obeys a principle of additivity, i.e., each nonlinear coefficient can be calculated independently of the other nonlinear coefficients using the proposed formula.
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.
Stochastic inflation and nonlinear gravity
NASA Astrophysics Data System (ADS)
Salopek, D. S.; Bond, J. R.
1991-02-01
We show how nonlinear effects of the metric and scalar fields may be included in stochastic inflation. Our formalism can be applied to non-Gaussian fluctuation models for galaxy formation. Fluctuations with wavelengths larger than the horizon length are governed by a network of Langevin equations for the physical fields. Stochastic noise terms arise from quantum fluctuations that are assumed to become classical at horizon crossing and that then contribute to the background. Using Hamilton-Jacobi methods, we solve the Arnowitt-Deser-Misner constraint equations which allows us to separate the growing modes from the decaying ones in the drift phase following each stochastic impulse. We argue that the most reasonable choice of time hypersurfaces for the Langevin system during inflation is T=ln(Ha), where H and a are the local values of the Hubble parameter and the scale factor, since T is the natural time for evolving the short-wavelength scalar field fluctuations in an inhomogeneous background. We derive a Fokker-Planck equation which describes how the probability distribution of scalar field values at a given spatial point evolves in T. Analytic Green's-function solutions obtained for a single scalar field self-interacting through an exponential potential are used to demonstrate (1) if the initial condition of the Hubble parameter is chosen to be consistent with microwave-background limits, H(φ0)/mρ<~10-4, then the fluctuations obey Gaussian statistics to a high precision, independent of the time hypersurface choice and operator-ordering ambiguities in the Fokker-Planck equation, and (2) for scales much larger than our present observable patch of the Universe, the distribution is non-Gaussian, with a tail extending to large energy densities; although there are no observable manifestations, it does show eternal inflation. Lattice simulations of our Langevin network for the exponential potential demonstrate how spatial correlations are incorporated. An initially
Probing Acoustic Nonlinearity by Mixing Surface Acoustic Waves
Hurley, David Howard; Telschow, Kenneth Louis
2000-07-01
Measurement methods aimed at determining material properties through nonlinear wave propagation are sensitive to artifacts caused by background nonlinearities inherent in the ultrasonic generation and detection methods. The focus of this paper is to describe our investigation of nonlinear mixing of surface acoustic waves (SAWs) as a means to decrease sensitivity to background nonlinearity and increase spatial sensitivity to acoustic nonlinearity induced by material microstructure.
The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models
NASA Technical Reports Server (NTRS)
Hesse, Michael; Birn, Joachim
2011-01-01
Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.
Nonlinear Dynamics of Single Bunch Instability
Stupakov, G.V.; Breizman, B.N.; Pekker, M.S.; /Texas U.
2011-09-09
A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations. Microwave single bunch instability in circular accelerators has been observed in many machines. The instability usually arises when the number of particles in the bunch exceeds some critical value, Nc, which varies depending on the parameters of the accelerating regime. Recent observations on the SLC damping rings at SLAC with a new low-impedance vacuum chamber revealed new interesting features of the instability. In some cases, after initial exponential growth, the instability eventually saturated at a level that remained constant through the accumulation cycle. In other regimes, relaxation-type oscillations were measured in nonlinear phase of the instability. In many cases, the instability was characterized by a frequency close to the second harmonic of the synchrotron oscillations. Several attempts have been made to address the nonlinear stage of the instability based on either computer simulations or some specific assumptions regarding the structure of the unstable mode. An attempt of a more general consideration of the problem is carried out in this paper. We adopt an approach recently developed in plasma physics for analysis of nonlinear behavior of weakly unstable modes in dynamic systems. Assuming that the growth rate of the instability is much smaller than its frequency, we find a time dependent solution to Vlasov equation and derive an equation for the complex amplitude of the oscillations valid in the nonlinear regime. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Nonlinear Fourier analysis with cnoidal waves
Osborne, A.R.
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
On Dynamic Nonlinear Elasticity and Small Strain
NASA Astrophysics Data System (ADS)
Johnson, P. A.; Sutin, A.; Guyer, R. A.; Tencate, J. A.
2002-12-01
We are addressing the question of whether or not there is a threshold strain behavior where anomalous nonlinear fast dynamics (ANFD) commences in rock and other similar solids, or if the elastic nonlinearity persists to the smallest measurable values. In qualitative measures of many rock types and other materials that behave in the same manner, we have not observed a threshold; however the only careful, small strain level study conducted under controlled conditions that we are aware of is that of TenCate et al. in Berea sandstone (Phys. Rev. Lett. 85, 1020-1024 (2000)). This work indicates that in Berea sandstone, the elastic nonlinearity persists to the minimum measured strains of at least 10-8. Recently, we have begun controlled experiments in other materials that exhibit ANFD in order to see whether or not they behave as Berea sandstone does. We are employing Young's mode resonance to study resonance peak shift and amplitude variations as a function of drive level and detected strain level. In this type of experiment, the time average amplitude is recorded as the sample is driven by a continuous wave source from below to above the fundamental mode resonance. The drive level is increased, and the measurement is repeated progressively over larger and larger drive levels. Experiments are conducted at ambient pressure. Pure alumina ceramic is a material that is highly, elastically-nonlinear and nonporous, and therefore the significant influence of relative humidity on elastic nonlinear response that rock suffers is avoided. Temperature is carefully monitored. Measurements on pure alumina ceramic show that, like Berea sandstone, there is no threshold of elastic nonlinearity within our measurement capability. We are now studying other solids that exhibit ANFD including rock and mixed phase metal. These results indicate that elastic nonlinearity influences all elastic measurments on these solids including modulus and Q at ambient conditions. There appears to be no
Supratransmission in a disordered nonlinear periodic structure
NASA Astrophysics Data System (ADS)
Yousefzadeh, B.; Phani, A. Srikantha
2016-10-01
We study the interaction among dispersion, nonlinearity, and disorder effects in the context of wave transmission through a discrete periodic structure, subjected to continuous harmonic excitation in its stop band. We consider a damped nonlinear periodic structure of finite length with disorder. Disorder is introduced throughout the structure by small changes in the stiffness parameters drawn from a uniform statistical distribution. Dispersion effects forbid wave transmission within the stop band of the linear periodic structure. However, nonlinearity leads to supratransmission phenomenon, by which enhanced wave transmission occurs within the stop band of the periodic structure when forced at an amplitude exceeding a certain threshold. The frequency components of the transmitted waves lie within the pass band of the linear structure, where disorder is known to cause Anderson localization. There is therefore a competition between dispersion, nonlinearity, and disorder in the context of supratransmission. We show that supratransmission persists in the presence of disorder. The influence of disorder decreases in general as the forcing frequency moves away from the pass band edge, reminiscent of dispersion effects subsuming disorder effects in linear periodic structures. We compute the dependence of the supratransmission force threshold on nonlinearity and strength of coupling between units. We observe that nonlinear forces are confined to the driven unit for weakly coupled systems. This observation, together with the truncation of higher-order nonlinear terms, permits us to develop closed-form expressions for the supratransmission force threshold. In sum, in the frequency range studied here, disorder does not influence the supratransmission force threshold in the ensemble-average sense, but it does reduce the average transmitted wave energy.
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.
2015-09-15
Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.
Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Konotop, Vladimir V.
2008-04-25
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schroedinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.
Quenching phenomena for second-order nonlinear parabolic equation with nonlinear source
NASA Astrophysics Data System (ADS)
Mingyou, Zhang; Huichao, Xu; Runzhang, Xu
2012-09-01
In this paper, we investigate the quenching phenomena of the Cauchy problem for the second-order nonlinear parabolic equation on unbounded domain. It is shown that the solution quenches in finite time under some assumptions on the exponents and the initial data. Our main tools are comparison principle and maximum principle. We extend the result to the case of more generally nonlinear absorption.
Torello, David; Kim, Jin-Yeon; Qu, Jianmin; Jacobs, Laurence J.
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation
NASA Technical Reports Server (NTRS)
Spangler, Steven R.
1990-01-01
A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.
Identifying nonlinear biomechanical models by multicriteria analysis
NASA Astrophysics Data System (ADS)
Srdjevic, Zorica; Cveticanin, Livija
2012-02-01
In this study, the methodology developed by Srdjevic and Cveticanin (International Journal of Industrial Ergonomics 34 (2004) 307-318) for the nonbiased (objective) parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n-degree of freedom (DOF) nonlinear biomechanical models. The dynamic performance of the n-DOF nonlinear model is described in terms of response functions in the frequency domain, such as the driving-point mechanical impedance and seat-to-head transmissibility function. For randomly generated parameters of the model, nonlinear equations of motion are solved using the Runge-Kutta method. The appropriate data transformation from the time-to-frequency domain is performed by a discrete Fourier transformation. Squared deviations of the response functions from the target values are used as the model performance evaluation criteria, thus shifting the problem into the multicriteria framework. The objective weights of criteria are obtained by applying the Shannon entropy concept. The suggested methodology is programmed in Pascal and tested on a 4-DOF nonlinear lumped parameter biomechanical model. The identification process over the 2000 generated sets of parameters lasts less than 20 s. The model response obtained with the imbedded identified parameters correlates well with the target values, therefore, justifying the use of the underlying concept and the mathematical instruments and numerical tools applied. It should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model.
Nonlinear coupling in the human motor system
Chen, C.C.; Kilner, J.M.; Friston, K.J.; Kiebel, S. J.; Jolly, R.K.; Ward, N. S.
2010-01-01
The synchronous discharge of neuronal assemblies is thought to facilitate communication between areas within distributed networks in the human brain. This oscillatory activity is especially interesting, given the pathological modulation of specific frequencies in diseases affecting the motor system. Many studies investigating oscillatory activity have focussed on same frequency, or linear, coupling between areas of a network. In this study, our aim was to establish a functional architecture in the human motor system responsible for induced responses as measured in normal subjects with magnetoencephalography. Specifically, we looked for evidence for additional nonlinear (between-frequency) coupling among neuronal sources and, in particular, whether nonlinearities were found predominantly in connections within areas (intrinsic), between areas (extrinsic) or both. We modelled the event-related modulation of spectral responses during a simple hand-grip using dynamic casual modelling. We compared models with and without nonlinear connections under conditions of symmetric and asymmetric interhemispheric connectivity. Bayesian model comparison suggested that the task-dependent motor network was asymmetric during right hand movements. Furthermore, it revealed very strong evidence for nonlinear coupling between sources in this distributed network, but interactions among frequencies within a source appeared linear in nature. Our results provide empirical evidence for nonlinear coupling among distributed neuronal sources in the motor system and that these play an important role in modulating spectral responses under normal conditions. PMID:20573886
Nonlinear fitness landscape of a molecular pathway.
Perfeito, Lilia; Ghozzi, Stéphane; Berg, Johannes; Schnetz, Karin; Lässig, Michael
2011-07-01
Genes are regulated because their expression involves a fitness cost to the organism. The production of proteins by transcription and translation is a well-known cost factor, but the enzymatic activity of the proteins produced can also reduce fitness, depending on the internal state and the environment of the cell. Here, we map the fitness costs of a key metabolic network, the lactose utilization pathway in Escherichia coli. We measure the growth of several regulatory lac operon mutants in different environments inducing expression of the lac genes. We find a strikingly nonlinear fitness landscape, which depends on the production rate and on the activity rate of the lac proteins. A simple fitness model of the lac pathway, based on elementary biophysical processes, predicts the growth rate of all observed strains. The nonlinearity of fitness is explained by a feedback loop: production and activity of the lac proteins reduce growth, but growth also affects the density of these molecules. This nonlinearity has important consequences for molecular function and evolution. It generates a cliff in the fitness landscape, beyond which populations cannot maintain growth. In viable populations, there is an expression barrier of the lac genes, which cannot be exceeded in any stationary growth process. Furthermore, the nonlinearity determines how the fitness of operon mutants depends on the inducer environment. We argue that fitness nonlinearities, expression barriers, and gene-environment interactions are generic features of fitness landscapes for metabolic pathways, and we discuss their implications for the evolution of regulation. PMID:21814515
Cooperative Nonlinearities in Auditory Cortical Neurons
Atencio, Craig A.; Sharpee, Tatyana O.; Schreiner, Christoph E.
2008-01-01
SUMMARY Cortical receptive fields represent the signal preferences of sensory neurons. Receptive fields are thought to provide a representation of sensory experience from which the cerebral cortex may make interpretations. While it is essential to determine a neuron’s receptive field, it remains unclear which features of the acoustic environment are specifically represented by neurons in the primary auditory cortex (AI). We characterized cat AI spectrotemporal receptive fields (STRFs) by finding both the spike-triggered average (STA) and stimulus dimensions that maximized the mutual information between response and stimulus. We derived a nonlinearity relating spiking to stimulus projection onto two maximally informative dimensions (MIDs). The STA was highly correlated with the first MID. Generally, the nonlinearity for the first MID was asymmetric and often monotonic in shape, while the second MID nonlinearity was symmetric and non-monotonic. The joint nonlinearity for both MIDs revealed that most first and second MIDs were synergistic, and thus should be considered conjointly. The difference between the nonlinearities suggests different possible roles for the MIDs in auditory processing. PMID:18579084
The role of nonlinearity in inverse problems
NASA Astrophysics Data System (ADS)
Snieder, Roel
1998-06-01
In many practical inverse problems, one aims to retrieve a model that has infinitely many degrees of freedom from a finite amount of data. It follows from a simple variable count that this cannot be done in a unique way. Therefore, inversion entails more than estimating a model: any inversion is not complete without a description of the class of models that is consistent with the data; this is called the appraisal problem. Nonlinearity makes the appraisal problem particularly difficult. The first reason for this is that nonlinear error propagation is a difficult problem. The second reason is that for some nonlinear problems the model parameters affect the way in which the model is being interrogated by the data. Two examples are given of this, and it is shown how the nonlinearity may make the problem more ill-posed. Finally, three attempts are shown to carry out the model appraisal for nonlinear inverse problems that are based on an analytical approach, a numerical approach and a common sense approach.
Nonlinear ADC with digitally selectable quantizing characteristics
Lygouras, J.N.
1988-10-01
In this paper a method is presented for generating linear or nonlinear functions digitally. The Nonlinear Analog to Digital Conversion (NLADC) is accomplished using the Pulse Width Modulation (PWM) of the analog input voltage. The conversion is done according to a special Quantizing Characteristic Function (Q.C.F.), which depends on the specific application. This special Q.C.F. sampled, quantized and coded has been stored in an EPROM. The quantizing characteristic can be any monotonically increasing function of any type (e.g. linear, square, exponential e.t.c.) resulting in a very flexible linear or nonlinear A/D converter. More than one Q.C.F. can be stored in the EPROM. Such a NLADC could be used for the expansion or compression of the dynamic range in Nuclear Science measurements, in robotics for the cartesian space path planning, as in the case of Pulse Code Modulation (PCM) nonlinear quantization, e.t.c. The corresponding nonlinear Digital to Analog Converter is described.
Optimization approaches to nonlinear model predictive control
Biegler, L.T. . Dept. of Chemical Engineering); Rawlings, J.B. . Dept. of Chemical Engineering)
1991-01-01
With the development of sophisticated methods for nonlinear programming and powerful computer hardware, it now becomes useful and efficient to formulate and solve nonlinear process control problems through on-line optimization methods. This paper explores and reviews control techniques based on repeated solution of nonlinear programming (NLP) problems. Here several advantages present themselves. These include minimization of readily quantifiable objectives, coordinated and accurate handling of process nonlinearities and interactions, and systematic ways of dealing with process constraints. We motivate this NLP-based approach with small nonlinear examples and present a basic algorithm for optimization-based process control. As can be seen this approach is a straightforward extension of popular model-predictive controllers (MPCs) that are used for linear systems. The statement of the basic algorithm raises a number of questions regarding stability and robustness of the method, efficiency of the control calculations, incorporation of feedback into the controller and reliable ways of handling process constraints. Each of these will be treated through analysis and/or modification of the basic algorithm. To highlight and support this discussion, several examples are presented and key results are examined and further developed. 74 refs., 11 figs.
Interactive Workshop Discusses Nonlinear Waves and Chaos
NASA Astrophysics Data System (ADS)
Tsurutani, Bruce; Morales, George; Passot, Thierry
2010-07-01
Eighth International Nonlinear Wave Workshop; La Jolla, California, 1-5 March 2010; Nonlinear waves and chaos were the focus of a weeklong series of informal and interactive discussions at the Eighth International Nonlinear Wave Workshop (NWW8), held in California. The workshop gathered nonlinear plasma and water wave experts from the United States, France, Czech Republic, Germany, Greece, Holland, India, and Japan. Attendees were from the fields of space, laboratory, and fusion plasma physics, astrophysics, and applied mathematics. Special focus was placed on nonlinear waves and turbulence in the terrestrial environment as well as in the interstellar medium from observational, laboratory, and theoretical perspectives. Discussions covered temperature anisotropies and related instabilities, the properties and origin of the so-called dissipation range, and various coherent structures of electromagnetic as well as electrostatic nature. Reconnection and shocks were also topics of discussion, as were properties of magnetospheric whistler and chorus waves. Examples and analysis techniques for superdiffusion and subdiffusion were identified. On this last topic, a good exchange of ideas and results occurred between a water wave expert and a plasma expert, with the rest of the audience listening intently.
Nonlinear diffusion filtering influenced by mean curvature
NASA Astrophysics Data System (ADS)
Kollár, Michal; Mikula, Karol; Čunderlík, Róbert
2016-04-01
The presentation introduces a new nonlinear diffusion filtering method on closed surfaces such as a sphere, ellipsoid or the Earth's surface. Our new model extends the regularized surface Perona-Malik model by including a local extrema detector based on a mean curvature of processed data. The model is thus represented by a nonlinear diffusion equation which filters noise while preserves main edges, local extrema and details important for a correct interpretation of data. We define a surface finite-volume method to approximate numerically the nonlinear parabolic partial differential equation on a closed surface. The closed surface is approximated by a polyhedral surface created by planar triangles representing subdivision of an initial icosahedron grid and we use a piece-wise linear approximation of a solution in space and the backward Euler time discretization. Numerical experiments present nonlinear diffusion filtering of artificial data and real measurements, namely the GOCE satellite observations. They aim to point out a main advantage of the new nonlinear model which, on the contrary of Perona-Malik model, preserves local extremal values of filtered data.
Reliability of Complex Nonlinear Numerical Simulations
NASA Technical Reports Server (NTRS)
Yee, H. C.
2004-01-01
This work describes some of the procedure to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.
Nonlinear frequency response analysis of structural vibrations
NASA Astrophysics Data System (ADS)
Weeger, Oliver; Wever, Utz; Simeon, Bernd
2014-12-01
In this paper we present a method for nonlinear frequency response analysis of mechanical vibrations of 3-dimensional solid structures. For computing nonlinear frequency response to periodic excitations, we employ the well-established harmonic balance method. A fundamental aspect for allowing a large-scale application of the method is model order reduction of the discretized equation of motion. Therefore we propose the utilization of a modal projection method enhanced with modal derivatives, providing second-order information. For an efficient spatial discretization of continuum mechanics nonlinear partial differential equations, including large deformations and hyperelastic material laws, we employ the concept of isogeometric analysis. Isogeometric finite element methods have already been shown to possess advantages over classical finite element discretizations in terms of higher accuracy of numerical approximations in the fields of linear vibration and static large deformation analysis. With several computational examples, we demonstrate the applicability and accuracy of the modal derivative reduction method for nonlinear static computations and vibration analysis. Thus, the presented method opens a promising perspective on application of nonlinear frequency analysis to large-scale industrial problems.
Nonlinear kinetic modeling of stimulated Raman scattering
NASA Astrophysics Data System (ADS)
Benisti, Didier
2011-10-01
Despite its importance for many applications, such as or Raman amplification or inertial confinement fusion, deriving a nonlinear estimate of Raman reflectivity in a plasma has remained quite a challenge for decades. This is mainly due to the nonlinear modification of the electron distribution function induced by the plasma wave (EPW), which, in turn, modifies the propagation of this wave. In this paper is derived an envelope equation for the EPW valid in 3D and which accounts for the nonlinear change of its collisionless (Landau-like) damping rate, group velocity, coupling to the electromagnetic drive, frequency and wave number. Our theoretical predictions for each of these terms are carefully compared against results from Vlasov simulations of stimulated Raman scattering (SRS), as well as with other theories. Moreover, our envelope model shows to be as accurate as a Vlasov code in predicting Raman threshold in 1D. Making comparisons with experimental results nevertheless requires including transverse dimensions and letting Raman start from noise. To this end, we performed a completely new derivation of the electrostatic fluctuations in a plasma, which accounts nonlinear effects. Moreover, based on our Multi-D simulations of Raman scattering with our envelope code BRAMA, we discuss the effect on SRS of wave front bowing, transverse detrapping and of a completely new defocussing effect due to the local change in the direction of the EPW group velocity induced by the nonlinear decrease of Landau damping.
Optimal singular control for nonlinear semistabilisation
NASA Astrophysics Data System (ADS)
L'Afflitto, Andrea; Haddad, Wassim M.
2016-06-01
The singular optimal control problem for asymptotic stabilisation has been extensively studied in the literature. In this paper, the optimal singular control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which is of paramount importance for consensus control of network dynamical systems. Three approaches are presented to address the nonlinear semistable singular control problem. Namely, a singular perturbation method is presented to construct a state-feedback singular controller that guarantees closed-loop semistability for nonlinear systems. In this approach, we show that for a non-negative cost-to-go function the minimum cost of a nonlinear semistabilising singular controller is lower than the minimum cost of a singular controller that guarantees asymptotic stability of the closed-loop system. In the second approach, we solve the nonlinear semistable singular control problem by using the cost-to-go function to cancel the singularities in the corresponding Hamilton-Jacobi-Bellman equation. For this case, we show that the minimum value of the singular performance measure is zero. Finally, we provide a framework based on the concepts of state-feedback linearisation and feedback equivalence to solve the singular control problem for semistabilisation of nonlinear dynamical systems. For this approach, we also show that the minimum value of the singular performance measure is zero. Three numerical examples are presented to demonstrate the efficacy of the proposed singular semistabilisation frameworks.
Nonlinear Vibrations of Ferroelectric Bimorph Cantilever
NASA Astrophysics Data System (ADS)
Ostrovskii, Igor; Nadtochiy, Andriy
2008-06-01
Nonlinear vibrations of a bimorph LiNbO3 microcantilever are investigated. A periodically poled LiNbO3 wafer is used as an initial chip. The cantilever is micro-machined near an interdomain wall between two inversely poled domains. The vibrations are excited by an applied rf-voltage, and motion of a cantilever tip is detected optically. Nonlinearity is revealed by measuring the changes in the dependencies of vibration amplitude versus frequency when amplitude increases, and by reading of sub-harmonic oscillations. A surface of the microcantilever may be modified with a silane, which is sensitive to certain biomolecules. This composite nonlinear micro-vibrator may be used for developing a smart biosensor operating in ambient atmosphere in a real time mode.
Instantaneous, stepped-frequency, nonlinear radar
NASA Astrophysics Data System (ADS)
Ranney, Kenneth; Gallagher, Kyle; Martone, Anthony; Mazzaro, Gregory; Sherbondy, Kelly; Narayanan, Ram
2015-05-01
Researchers have recently developed radar systems capable of exploiting non-linear target responses to precisely locate targets in range. These systems typically achieve the bandwidth necessary for range resolution through transmission of either a stepped-frequency or chirped waveform. The second harmonic of the reflected waveform is then analyzed to isolate the non-linear target response. In other experiments, researchers have identified certain targets through the inter-modulation products they produce in response to a multi-tone stimulus. These experiments, however, do not exploit the phase information available in the inter-modulation products. We present a method for exploiting both the magnitude and phase information available in the inter-modulation products to create an "instantaneous" stepped frequency, non-linear target response. The new approach enables us to both maintain the unambiguous range dictated by the fundamental, multi-tone separation and obtain the entire target signature from a single transmitted waveform.
Nonlinear optical properties of multipyrrole dyes
Frenette, Mathieu; Hatamimoslehabadi, Maryam; Bellinger-Buckley, Stephanie; Laoui, Samir; Bag, Seema; Dantiste, Olivier; Rochford, Jonathan; Yelleswarapu, Chandra
2014-01-01
The nonlinear optical properties of a series of pyrrolic compounds consisting of BODIPY and aza-BODIPY systems are investigated using 532 nm nanosecond laser and the Z-scan technique. Results show that 3,5-distyryl extension of BODIPY to the red shifted MeO2BODIPY dye has a dramatic impact on its nonlinear absorption properties changing it from a saturable absorber to an efficient reverse saturable absorbing material with a nonlinear absorption coefficient of 4.64 × 10−10 m/W. When plotted on a concentration scale per mole of dye in solution MeO2BODIPY far outperforms the recognized zinc(II) phthalocyanine dye and is comparable to that of zinc(II) tetraphenylporphyrin. PMID:25242819
Spin and wavelength multiplexed nonlinear metasurface holography
NASA Astrophysics Data System (ADS)
Ye, Weimin; Zeuner, Franziska; Li, Xin; Reineke, Bernhard; He, Shan; Qiu, Cheng-Wei; Liu, Juan; Wang, Yongtian; Zhang, Shuang; Zentgraf, Thomas
2016-06-01
Metasurfaces, as the ultrathin version of metamaterials, have caught growing attention due to their superior capability in controlling the phase, amplitude and polarization states of light. Among various types of metasurfaces, geometric metasurface that encodes a geometric or Pancharatnam-Berry phase into the orientation angle of the constituent meta-atoms has shown great potential in controlling light in both linear and nonlinear optical regimes. The robust and dispersionless nature of the geometric phase simplifies the wave manipulation tremendously. Benefitting from the continuous phase control, metasurface holography has exhibited advantages over conventional depth controlled holography with discretized phase levels. Here we report on spin and wavelength multiplexed nonlinear metasurface holography, which allows construction of multiple target holographic images carried independently by the fundamental and harmonic generation waves of different spins. The nonlinear holograms provide independent, nondispersive and crosstalk-free post-selective channels for holographic multiplexing and multidimensional optical data storages, anti-counterfeiting, and optical encryption.
Linear superposition solutions to nonlinear wave equations
NASA Astrophysics Data System (ADS)
Liu, Yu
2012-11-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed.
Spin and wavelength multiplexed nonlinear metasurface holography
Ye, Weimin; Zeuner, Franziska; Li, Xin; Reineke, Bernhard; He, Shan; Qiu, Cheng-Wei; Liu, Juan; Wang, Yongtian; Zhang, Shuang; Zentgraf, Thomas
2016-01-01
Metasurfaces, as the ultrathin version of metamaterials, have caught growing attention due to their superior capability in controlling the phase, amplitude and polarization states of light. Among various types of metasurfaces, geometric metasurface that encodes a geometric or Pancharatnam–Berry phase into the orientation angle of the constituent meta-atoms has shown great potential in controlling light in both linear and nonlinear optical regimes. The robust and dispersionless nature of the geometric phase simplifies the wave manipulation tremendously. Benefitting from the continuous phase control, metasurface holography has exhibited advantages over conventional depth controlled holography with discretized phase levels. Here we report on spin and wavelength multiplexed nonlinear metasurface holography, which allows construction of multiple target holographic images carried independently by the fundamental and harmonic generation waves of different spins. The nonlinear holograms provide independent, nondispersive and crosstalk-free post-selective channels for holographic multiplexing and multidimensional optical data storages, anti-counterfeiting, and optical encryption. PMID:27306147
Magnetoplasmonic RF mixing and nonlinear frequency generation
NASA Astrophysics Data System (ADS)
Firby, C. J.; Elezzabi, A. Y.
2016-07-01
We present the design of a magnetoplasmonic Mach-Zehnder interferometer (MZI) modulator facilitating radio-frequency (RF) mixing and nonlinear frequency generation. This is achieved by forming the MZI arms from long-range dielectric-loaded plasmonic waveguides containing bismuth-substituted yttrium iron garnet (Bi:YIG). The magnetization of the Bi:YIG can be driven in the nonlinear regime by RF magnetic fields produced around adjacent transmission lines. Correspondingly, the nonlinear temporal dynamics of the transverse magnetization component are mapped onto the nonreciprocal phase shift in the MZI arms, and onto the output optical intensity signal. We show that this tunable mechanism can generate harmonics, frequency splitting, and frequency down-conversion with a single RF excitation, as well as RF mixing when driven by two RF signals. This magnetoplasmonic component can reduce the number of electrical sources required to generate distinct optical modulation frequencies and is anticipated to satisfy important applications in integrated optics.
Battery electrochemical nonlinear/dynamic SPICE model
Glass, M.C.
1996-12-31
An Integrated Battery Model has been produced which accurately represents DC nonlinear battery behavior together with transient dynamics. The NiH{sub 2} battery model begins with a given continuous-function electrochemical math model. The math model for the battery consists of the sum of two electrochemical process DC currents, which are a function of the battery terminal voltage. This paper describes procedures for realizing a voltage-source SPICE model which implements the electrochemical equations using behavioral sources. The model merges the essentially DC non-linear behavior of the electrochemical model, together with the empirical AC dynamic terminal impedance from measured data. Thus the model integrates the short-term linear impedance behavior, with the long-term nonlinear DC resistance behavior. The long-duration non-Faradaic capacitive behavior of the battery is represented by a time constant. Outputs of the model include battery voltage/current, state-of-charge, and charge-current efficiency.
The maximal process of nonlinear shot noise
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2009-05-01
In the nonlinear shot noise system-model shots’ statistics are governed by general Poisson processes, and shots’ decay-dynamics are governed by general nonlinear differential equations. In this research we consider a nonlinear shot noise system and explore the process tracking, along time, the system’s maximal shot magnitude. This ‘maximal process’ is a stationary Markov process following a decay-surge evolution; it is highly robust, and it is capable of displaying both a wide spectrum of statistical behaviors and a rich variety of random decay-surge sample-path trajectories. A comprehensive analysis of the maximal process is conducted, including its Markovian structure, its decay-surge structure, and its correlation structure. All results are obtained analytically and in closed-form.
Nonlinear theory of a plasma Cherenkov maser
Choi, J.S.; Heo, E.G.; Choi, D.I.
1995-12-31
The nonlinear saturation state in a plasma Cherenkov maser (PCM) propagating the intense relativistic electron beam through a circular waveguide partially filled with a dense annular plasma, is analyzed from the nonlinear formulation based on the cold fluid-Maxwell equations. We obtain the nonlinear efficiency and the final operation frequency under consideration of the effects of the beam current, the beam energy and the slow wave structure. We show that the saturation mechanism of a PCM instablity is a close correspondence in that of the relativistic two stream instability by the coherent trapping of electrons in a single most-ustable wave. And the optimal conditions in PCM operation are also obtained from performing our nonliear analysis together with computer simulations.
Resolution enhancement in nonlinear photoacoustic imaging
Goy, Alexandre S.; Fleischer, Jason W.
2015-11-23
Nonlinear processes can be exploited to gain access to more information than is possible in the linear regime. Nonlinearity modifies the spectra of the excitation signals through harmonic generation, frequency mixing, and spectral shifting, so that features originally outside the detector range can be detected. Here, we present an experimental study of resolution enhancement for photoacoustic imaging of thin metal layers immersed in water. In this case, there is a threshold in the excitation below which no acoustic signal is detected. Above threshold, the nonlinearity reduces the width of the active area of the excitation beam, resulting in a narrower absorption region and thus improved spatial resolution. This gain is limited only by noise, as the active area of the excitation can be arbitrarily reduced when the fluence becomes closer to the threshold. Here, we demonstrate a two-fold improvement in resolution and quantify the image quality as the excitation fluence goes through threshold.
Resolution enhancement in nonlinear photoacoustic imaging
NASA Astrophysics Data System (ADS)
Goy, Alexandre S.; Fleischer, Jason W.
2015-11-01
Nonlinear processes can be exploited to gain access to more information than is possible in the linear regime. Nonlinearity modifies the spectra of the excitation signals through harmonic generation, frequency mixing, and spectral shifting, so that features originally outside the detector range can be detected. Here, we present an experimental study of resolution enhancement for photoacoustic imaging of thin metal layers immersed in water. In this case, there is a threshold in the excitation below which no acoustic signal is detected. Above threshold, the nonlinearity reduces the width of the active area of the excitation beam, resulting in a narrower absorption region and thus improved spatial resolution. This gain is limited only by noise, as the active area of the excitation can be arbitrarily reduced when the fluence becomes closer to the threshold. Here, we demonstrate a two-fold improvement in resolution and quantify the image quality as the excitation fluence goes through threshold.
Nonlinear acoustic impedance of thermoacoustic stack
NASA Astrophysics Data System (ADS)
Ge, Huan; Fan, Li; Xiao, Shu-yu; Tao, Sha; Qiu, Mei-chen; Zhang, Shu-yi; Zhang, Hui
2012-09-01
In order to optimize the performances of the thermoacoustic refrigerator working with the high sound pressure level, the nonlinear acoustic characteristics of the thermoacoustic stack in the resonant pipe are studied. The acoustic fluid impedance of the stack made of copper mesh and set up in a resonant pipe is measured in the acoustic fields with different intensities. It is found that when the sound pressure level in the pipe increases to a critical value, the resistance of the stack increases nonlinearly with the sound pressure, while the reactance of the stack keeps constant. Based on the experimental results, a theory model is set up to describe the acoustic characteristics of the stack, according to the rigid frame theory and Forchheimmer equation. Furthermore, the influences of the sound pressure level, operating frequency, volume porosity, and length of the stack on the nonlinear impedance of the stack are evaluated.
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.
Nonlinear Propagation of Infrasound from Large Explosions
NASA Astrophysics Data System (ADS)
de Groot-Hedlin, Catherine
2015-04-01
Atmospheric explosions release immense quantities of infrasound energy that can be detected at receivers located from hundreds to thousands of kilometers from the origin. This has led to the deployment of a global 60-station network of micro-barometer arrays to aid in nuclear explosion monitoring. Current methods of estimating the radiated source energy from remote recordings of infrasound signals use simplified empirical source-yield relations that account for stratospheric winds along the source-receiver path. These formulations apply only to direct and stratospherically ducted arrivals. More recently, considerable progress has been made in applying numerical modeling techniques to develop more accurate source-yield formulations for realistic sound and wind speed profiles. However, these methods assume linear infrasound propagation along the travel path even though nonlinear effects - which arise when the amplitude of the acoustic pressure perturbation is a finite fraction of the ambient atmospheric pressure - are known to significantly alter infrasound frequencies, velocities and amplitudes, and thus can affect derived source yield estimates. For realistic atmospheric profiles, nonlinearity can be significant both in the vicinity of a large explosive source as well as at much greater distances. Within the stratosphere, nonlinearity may arise at caustics created by ducting; in the thermosphere, nonlinearity may arise due to very low ambient pressures at high altitudes. In this study, the effects of nonlinearity on infrasound signal amplitudes and frequencies are simulated using a nonlinear finite difference, time-domain (FDTD) method. The key features that allow for accurate and efficient nonlinear synthesis of infrasound propagation through realistic media are that 1) it includes for atmospheric viscosity, and 2) the environmental models are constrained to have axial symmetry, yielding solutions relevant to a point source in a fully 3D model with rotational
Highly nonlinear layered spiral microstructured optical fiber
NASA Astrophysics Data System (ADS)
Rodrigues, Sílvia M.; Facão, Margarida M.; Latas, Sofia C.; Ferreira, Mário F.
2013-08-01
A layered spiral microstructured optical fiber (LS-MOF) is presented, which offers the possibility of a good control of both the dispersion and the nonlinear properties. The proposed design is analyzed using a finite element method considering silica and air as the materials. Zero dispersion, low confinement loss, and a record value of γ = 70.0 W-1/km for the LS-MOF nonlinear parameter are simultaneously obtained at 1.55 μm, whereas a higher value γ = 169.4 W-1/km can be achieved at 1.06 μm. Our results demonstrate the great potential of the LS-MOF for several nonlinear applications, namely for an efficient generation of the supercontinuum.
Nonlinear optical techniques for surface studies. [Monolayers
Shen, Y.R.
1981-09-01
Recent effort in developing nonlinear optical techniques for surface studies is reviewed. Emphasis is on monolayer detection of adsorbed molecules on surfaces. It is shown that surface coherent antiStokes Raman scattering (CARS) with picosecond pulses has the sensitivity of detecting submonolayer of molecules. On the other hand, second harmonic or sum-frequency generation is also sensitive enough to detect molecular monolayers. Surface-enhanced nonlinear optical effects on some rough metal surfaces have been observed. This facilitates the detection of molecular monolayers on such surfaces, and makes the study of molecular adsorption at a liquid-metal interface feasible. Advantages and disadvantages of the nonlinear optical techniques for surface studies are discussed.
Spin and wavelength multiplexed nonlinear metasurface holography.
Ye, Weimin; Zeuner, Franziska; Li, Xin; Reineke, Bernhard; He, Shan; Qiu, Cheng-Wei; Liu, Juan; Wang, Yongtian; Zhang, Shuang; Zentgraf, Thomas
2016-01-01
Metasurfaces, as the ultrathin version of metamaterials, have caught growing attention due to their superior capability in controlling the phase, amplitude and polarization states of light. Among various types of metasurfaces, geometric metasurface that encodes a geometric or Pancharatnam-Berry phase into the orientation angle of the constituent meta-atoms has shown great potential in controlling light in both linear and nonlinear optical regimes. The robust and dispersionless nature of the geometric phase simplifies the wave manipulation tremendously. Benefitting from the continuous phase control, metasurface holography has exhibited advantages over conventional depth controlled holography with discretized phase levels. Here we report on spin and wavelength multiplexed nonlinear metasurface holography, which allows construction of multiple target holographic images carried independently by the fundamental and harmonic generation waves of different spins. The nonlinear holograms provide independent, nondispersive and crosstalk-free post-selective channels for holographic multiplexing and multidimensional optical data storages, anti-counterfeiting, and optical encryption. PMID:27306147
High resolution 3D nonlinear integrated inversion
NASA Astrophysics Data System (ADS)
Li, Yong; Wang, Xuben; Li, Zhirong; Li, Qiong; Li, Zhengwen
2009-06-01
The high resolution 3D nonlinear integrated inversion method is based on nonlinear theory. Under layer control, the log data from several wells (or all wells) in the study area and seismic trace data adjacent to the wells are input to a network with multiple inputs and outputs and are integratedly trained to obtain an adaptive weight function of the entire study area. Integrated nonlinear mapping relationships are built and updated by the lateral and vertical geologic variations of the reservoirs. Therefore, the inversion process and its inversion results can be constrained and controlled and a stable seismic inversion section with high resolution with velocity inversion, impedance inversion, and density inversion sections, can be gained. Good geologic effects have been obtained in model computation tests and real data processing, which verified that this method has high precision, good practicality, and can be used for quantitative reservoir analysis.
Static Nonlinear Analysis In Concrete Structures
Hemmati, Ali
2008-07-08
Push-over analysis is a simple and applied approach which can be used for estimation of demand responses influenced by earthquake stimulations. The analysis is non-linear static analysis of the structure affected under increasing lateral loads and specifying the displacement--load diagram or structure capacity curve, draw the curve the base shear values and lateral deflection on the roof level of the building will be used. However, for estimation of the real behavior of the structure against earthquake, the non-linear dynamic analysis approaches and various accelerographs should be applied. Of course it should be noted that this approach especially in relation with tall buildings is complex and time consuming. In the article, the different patterns of lateral loading in push-over analysis have been compared with non-linear dynamic analysis approach so that the results represented accordingly. The researches indicated the uniformly--distributed loading is closer to real status.
Implications of nonlinearity for spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Sen, Sourav; Ray, Arnab K.
2014-03-01
We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order and bears a form that is very similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave on subsonic solutions, and maintaining nonlinearity in it up to the second order, we get the time dependence of the perturbation in the form of a Liénard system. A dynamical systems analysis of the Liénard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial subsonic states also adversely affects the temporal evolution of the flow toward a final and stable transonic state.
Nonlinear negative refraction by difference frequency generation
NASA Astrophysics Data System (ADS)
Cao, Jianjun; Shen, Dongyi; Feng, Yaming; Wan, Wenjie
2016-05-01
Negative refraction has attracted much interest for its promising capability in imaging applications. Such an effect can be implemented by negative index meta-materials, however, which are usually accompanied by high loss and demanding fabrication processes. Recently, alternative nonlinear approaches like phase conjugation and four wave mixing have shown advantages of low-loss and easy-to-implement, but associated problems like narrow accepting angles can still halt their practical applications. Here, we demonstrate theoretically and experimentally a scheme to realize negative refraction by nonlinear difference frequency generation with wide tunability, where a thin Beta barium borate slice serves as a negative refraction layer bending the input signal beam to the idler beam at a negative angle. Furthermore, we realize optical focusing effect using such nonlinear negative refraction, which may enable many potential applications in imaging science.
Nonlinear optomechanical measurement of mechanical motion
Brawley, G. A.; Vanner, M. R.; Larsen, P. E.; Schmid, S.; Boisen, A.; Bowen, W. P.
2016-01-01
Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications. PMID:26996234
Nonlinear nonequilibrium quasiparticle relaxation in Josephson junctions.
Krasnov, V M
2009-11-27
I solve numerically a full set of nonlinear kinetic balance equations for stacked Josephson junctions, which allows analysis of strongly nonequilibrium phenomena. It is shown that nonlinearity becomes significant already at very small disequilibrium. The following new, nonlinear effects are obtained: (i) At even-gap voltages V = 2nDelta/e (n = 2, 3, ...) nonequilibrium bosonic bands overlap. This leads to enhanced emission of Omega = 2Delta bosons and to the appearance of dips in tunnel conductance. (ii) A new type of radiative solution is found at strong disequilibrium. It is characterized by the fast stimulated relaxation of quasiparticles. A stack in this state behaves as a light emitting diode and directly converts electric power to boson emission, without utilization of the ac-Josephson effect. The phenomenon can be used for realization of a new type of superconducting cascade laser in the THz frequency range.
Thermodynamic properties of a Kerr nonlinear blackbody.
Cheng, Ze
2012-11-01
Within the framework of quantum field theory, we present the superfluid state of photons in a blackbody whose interior is filled by a Kerr nonlinear crystal. The thermodynamic properties of a Kerr nonlinear blackbody are investigated. At the transition temperature, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the superfluid state. The transition temperature is characteristic of a concrete crystal. The entropy density and specific heat capacity are monotonically increasing functions of the temperature but are monotonically decreasing functions of the Kerr nonlinear coefficient. PMID:23214733
Nonlinear ultrasonic scanning to detect material defects
NASA Technical Reports Server (NTRS)
Yost, William T. (Inventor); Cantrell, John H. (Inventor)
1998-01-01
A method and system are provided to detect defects in a material. Waves of known frequency(ies) are mixed at an interaction zone in the material. As a result, at least one of a difference wave and a sum wave are generated in the interaction zone. The difference wave occurs at a difference frequency and the sum wave occurs at a sum frequency. The amplitude of at least one nonlinear signal based on the sum and/or difference waves is then measured. The nonlinear signal is defined as the amplitude of one of the difference wave and sum wave relative to the product of the amplitude of the surface waves. The amplitude of the nonlinear signal is an indication of defects (e.g., dislocation dipole density) in the interaction zone.
Nonlinear self-adjointness through differential substitutions
NASA Astrophysics Data System (ADS)
Gandarias, M. L.
2014-10-01
It is known (Ibragimov, 2011; Galiakberova and Ibragimov, 2013) [14,18] that the property of nonlinear self-adjointness allows to associate conservation laws of the equations under study, with their symmetries. In this paper we show that, even when the equation is nonlinearly self-adjoint with a non differential substitution, finding the explicit form of the differential substitution can provide new conservation laws associated to its symmetries. By using the general theorem on conservation laws (Ibragimov, 2007) [11] and the property of nonlinear self-adjointness we find some new conservation laws for the modified Harry-Dym equation. By using a differential substitution we construct a conservation law for the Harry-Dym equation, which has not been derived before using Ibragimov method.
Biomolecular Imaging with Coherent Nonlinear Vibrational Microscopy
Chung, Chao-Yu; Boik, John; Potma, Eric O.
2014-01-01
Optical imaging with spectroscopic vibrational contrast is a label-free solution for visualizing, identifying, and quantifying a wide range of biomolecular compounds in biological materials. Both linear and nonlinear vibrational microscopy techniques derive their imaging contrast from infrared active or Raman allowed molecular transitions, which provide a rich palette for interrogating chemical and structural details of the sample. Yet nonlinear optical methods, which include both second-order sum-frequency generation (SFG) and third-order coherent Raman scattering (CRS) techniques, offer several improved imaging capabilities over their linear precursors. Nonlinear vibrational microscopy features unprecedented vibrational imaging speeds, provides strategies for higher spatial resolution, and gives access to additional molecular parameters. These advances have turned vibrational microscopy into a premier tool for chemically dissecting live cells and tissues. This review discusses the molecular contrast of SFG and CRS microscopy and highlights several of the advanced imaging capabilities that have impacted biological and biomedical research. PMID:23245525
Nonlinear acceleration of SN transport calculations
Fichtl, Erin D; Warsa, James S; Calef, Matthew T
2010-12-20
The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.
Robust nonlinear control of vectored thrust aircraft
NASA Technical Reports Server (NTRS)
Doyle, John C.; Murray, Richard; Morris, John
1993-01-01
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.
Damage detection in initially nonlinear systems
Bornn, Luke; Farrar, Charles; Park, Gyuhae
2009-01-01
The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits, SHM has been widely studied over the past decade. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state - a condition that often does not hold in complex 'real world' systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment.
Nonlinear extraordinary wave in dense plasma
Krasovitskiy, V. B.; Turikov, V. A.
2013-10-15
Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.
How to characterize the nonlinear amplifier?
NASA Technical Reports Server (NTRS)
Kallistratova, Dmitri Kouznetsov; Cotera, Carlos Flores
1994-01-01
The conception of the amplification of the coherent field is formulated. The definition of the coefficient of the amplification as the relation between the mean value of the field at the output to the value at the input and the definition of the noise as the difference between the number of photons in the output mode and square of the modulus of the mean value of the output amplitude are considered. Using a simple example it is shown that by these definitions the noise of the nonlinear amplifier may be less than the noise of the ideal linear amplifier of the same amplification coefficient. Proposals to search another definition of basic parameters of the nonlinear amplifiers are discussed. This definition should enable us to formulate the universal fundamental lower limit of the noise which should be valid for linear quantum amplifiers as for nonlinear ones.
Photonic surfaces for designable nonlinear power shaping
Biswas, Roshni Povinelli, Michelle L.
2015-02-09
We propose a method for designing nonlinear input-output power response based on absorptive resonances of nanostructured surfaces. We show that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the laser wavelength. We demonstrate our results in a silicon photonic crystal slab at a laser wavelength of 808 nm. We quantify the overall spectral red shift as a function of laser power. The shift results from absorptive heating and the thermo-optic effect. We then demonstrate devices with increasing, decreasing, and non-monotonic transmission as a function of laser power. The transmission changes are up to 7.5 times larger than in unpatterned silicon. The strong nonlinear transmission is due to a combination of resonantly enhanced absorption, reduced thermal conductivity, and the resonant transmission lineshape. Our results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest.
Nonlinear Optical Properties of Porous Silicon
NASA Astrophysics Data System (ADS)
Peterman, Elaine; Brewer, Christopher; Sandusky, John; Cameron, Stewart; Kirkpatrick, Sean
2003-03-01
Porous silicon (poSi) has been the focus of many studies recently due to its unique nonlinear optical properties. The nonlinear properties of poSi wafers were studied as a function of intensity using a 790nm, 75 femtosecond laser system. The effects of pulse stretching were measured as a function of beam intensity and sample porosity. Cross correlating the reflected beam off of the sample with a reference beam, the maximum second harmonic generated inside a KDP crystal was monitored as the reference line was delayed. Comparative pulse widths are presented for a bulk silicon sample, a 30sample. A z-scan was also performed on a 30to determine a nonlinear index of refraction, n2.
Eliminating material constraints for nonlinearity with plasmonic metamaterials
Neira, Andres D.; Olivier, Nicolas; Nasir, Mazhar E.; Dickson, Wayne; Wurtz, Gregory A.; Zayats, Anatoly V.
2015-01-01
Nonlinear optical materials comprise the foundation of modern photonics, offering functionalities ranging from ultrafast lasers to optical switching, harmonic and soliton generation. Optical nonlinearities are typically strong near the electronic resonances of a material and thus provide limited tuneability for practical use. Here we show that in plasmonic nanorod metamaterials, the Kerr-type nonlinearity is not limited by the nonlinear properties of the constituents. Compared with gold's nonlinearity, the measured nonlinear absorption and refraction demonstrate more than two orders of magnitude enhancement over a broad spectral range that can be engineered via geometrical parameters. Depending on the metamaterial's effective plasma frequency, either a focusing or defocusing nonlinearity is observed. The ability to obtain strong and fast optical nonlinearities in a given spectral range makes these metamaterials a flexible platform for the development of low-intensity nonlinear applications. PMID:26195182
Predicting nonlinear properties of metamaterials from the linear response.
O'Brien, Kevin; Suchowski, Haim; Rho, Junsuk; Salandrino, Alessandro; Kante, Boubacar; Yin, Xiaobo; Zhang, Xiang
2015-04-01
The discovery of optical second harmonic generation in 1961 started modern nonlinear optics. Soon after, R. C. Miller found empirically that the nonlinear susceptibility could be predicted from the linear susceptibilities. This important relation, known as Miller's Rule, allows a rapid determination of nonlinear susceptibilities from linear properties. In recent years, metamaterials, artificial materials that exhibit intriguing linear optical properties not found in natural materials, have shown novel nonlinear properties such as phase-mismatch-free nonlinear generation, new quasi-phase matching capabilities and large nonlinear susceptibilities. However, the understanding of nonlinear metamaterials is still in its infancy, with no general conclusion on the relationship between linear and nonlinear properties. The key question is then whether one can determine the nonlinear behaviour of these artificial materials from their exotic linear behaviour. Here, we show that the nonlinear oscillator model does not apply in general to nonlinear metamaterials. We show, instead, that it is possible to predict the relative nonlinear susceptibility of large classes of metamaterials using a more comprehensive nonlinear scattering theory, which allows efficient design of metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.
Detecting nonlinearity and chaos in epidemic data
Ellner, S.; Gallant, A.R.; Theiler, J. |
1993-08-01
Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude of epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.
Nonlinear Bogolyubov-Valatin transformations: Two modes
Scharnhorst, K.; Holten, J.-W. van
2011-11-15
Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper, we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes, which can be implemented by means of unitary SU(2{sup n}=4) transformations, is isomorphic to SO(6;R)/Z{sub 2}. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (linear combinations of products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington's E-numbers and can be understood in terms of the tensor product of two commuting copies of the division algebra of quaternions H. From a physical point of view, we present a method to diagonalize any arbitrary two-fermion Hamiltonians. Relying on Jordan-Wigner transformations for two-spin-1/2 and single-spin-3/2 systems, we also study nonlinear spin transformations and the related problem of diagonalizing arbitrary two-spin-1/2 and single-spin-3/2 Hamiltonians. Finally, from a calculational point of view, we pay due attention to explicit parametrizations of SU(4) and SO(6;R) matrices (of respective sizes 4x4 and 6x6) and their mutual relation. - Highlights: > Reveals the structure of nonlinear canonical transformations for two fermionic modes. > Studies nonlinear basis transformations in a Clifford algebra. > Focuses on methodological and structural aspects. > Presents a new approach to the diagonalization of 4x4 matrix Hamiltonians. > Presents the relation between
Nonlinear Interaction of Waves in Geomaterials
NASA Astrophysics Data System (ADS)
Ostrovsky, L. A.
2009-05-01
Progress of 1990s - 2000s in studying vibroacoustic nonlinearities in geomaterials is largely related to experiments in resonance samples of rock and soils. It is now a common knowledge that many such materials are very strongly nonlinear, and they are characterized by hysteresis in the dependence between the stress and strain tensors, as well as by nonlinear relaxation ("slow time"). Elastic wave propagation in such media has many peculiarities; for example, third harmonic amplitude is a quadratic (not cubic as in classical solids) function of the main harmonic amplitude, and average wave velocity is linearly (not quadratically as usual) dependent on amplitude. The mechanisms of these peculiarities are related to complex structure of a material typically consisting of two phases: a hard matrix and relatively soft inclusions such as microcracks and grain contacts. Although most informative experimental results have been obtained in rock in the form of resonant bars, few theoretical models are yet available to describe and calculate waves interacting in such samples. In this presentation, a brief overview of structural vibroacoustic nonlinearities in rock is given first. Then, a simple but rather general approach to the description of wave interaction in solid resonators is developed based on accounting for resonance nonlinear perturbations which are cumulating from period to period. In particular, the similarity and the differences between traveling waves and counter-propagating waves are analyzed for materials with different stress-strain dependences. These data can be used for solving an inverse problem, i.e. characterizing nonlinear properties of a geomaterial by its measured vibroacoustic parameters. References: 1. L. Ostrovsky and P. Johnson, Riv. Nuovo Chimento, v. 24, 1-46, 2007 (a review); 2. L. Ostrovsky, J. Acoust. Soc. Amer., v. 116, 3348-3353, 2004.
Nonlinear electromagnetic interactions in thermal QED
Brandt, F.T.; Frenkel, J. )
1995-03-06
We examine the behavior of the nonlinear interactions between electromagnetic fields at high temperature. It is shown that, in general, the ln([ital T]) dependence on the temperature of the Green functions is simply related to their UV behavior at zero temperature. We argue that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as [ital T][r arrow][infinity]. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action.
Nonlinear and adaptive estimation in reentry.
NASA Technical Reports Server (NTRS)
Jazwinski, A. H.
1972-01-01
The problem of real-time estimation of a lifting reentry vehicle trajectory of the shuttle orbiter type is considered. Simulations feature large position and velocity uncertainties at radar acquisition and realistic model errors in lift, drag and other model parameters. Radar tracking and accelerometer data are simulated. Significant nonlinearities are found to exist on spacecraft acquisition. An iterated nonlinear filter is shown to perform optimally during the radar acquisition phase. An adaptive filter is shown to track time-varying model errors, such as errors in the lift and drag coefficients, down to the noise level. Such real-time model tracking (identification) is frequently required for guidance and control implementation.
Feedback options in nonlinear numerical finance
NASA Astrophysics Data System (ADS)
Hugger, Jens; Mashayekhi, Sima
2012-09-01
Feedback options are options where information about the trading of the underlying asset is fed back into the pricing model. This results in nonlinear pricing models. A survey of the literature about feedback options in finance is presented. The pricing model for the full feedback option on an infinite slab is presented and boundary values on a bounded domain are derived. This bounded, nonlinear, 2 dimensional initial-boundary value problem is solved numerically using a number of standard finite difference schemes and the methods incorporated in the symbolic software Maple{trade mark, serif}.
Photonic nonlinearities via quantum Zeno blockade.
Sun, Yu-Zhu; Huang, Yu-Ping; Kumar, Prem
2013-05-31
Realizing optical-nonlinear effects at a single-photon level is a highly desirable but also extremely challenging task, because of both fundamental and practical difficulties. We present an avenue to surmounting these difficulties by exploiting quantum Zeno blockade in nonlinear optical systems. Considering specifically a lithium-niobate microresonator, we find that a deterministic phase gate can be realized between single photons with near-unity fidelity. Supported by established techniques for fabricating and operating such devices, our approach can provide an enabling tool for all-optical applications in both classical and quantum domains.
System characterization in nonlinear random vibration
Paez, T.L.; Gregory, D.L.
1986-01-01
Linear structural models are frequently used for structural system characterization and analysis. In most situations they can provide satisfactory results, but under some circumstances they are insufficient for system definition. The present investigation proposes a model for nonlinear structure characterization, and demonstrates how the functions describing the model can be identified using a random vibration experiment. Further, it is shown that the model is sufficient to completely characterize the stationary random vibration response of a structure that has a harmonic frequency generating form of nonlinearity. An analytical example is presented to demonstrate the plausibility of the model.
Method for conducting nonlinear electrochemical impedance spectroscopy
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1985-01-01
A model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear is considered. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1986-01-01
In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
Improved Indentation Test for Measuring Nonlinear Elasticity
NASA Technical Reports Server (NTRS)
Eldridge, Jeffrey I.
2004-01-01
A cylindrical-punch indentation technique has been developed as a means of measuring the nonlinear elastic responses of materials -- more specifically, for measuring the moduli of elasticity of materials in cases in which these moduli vary with applied loads. This technique offers no advantage for characterizing materials that exhibit purely linear elastic responses (constant moduli of elasticity, independent of applied loads). However, the technique offers a significant advantage for characterizing such important materials as plasma-sprayed thermal-barrier coatings, which, in cyclic loading, exhibit nonlinear elasticity with hysteresis related to compaction and sliding within their microstructures.
A method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Negative resistance instability due to nonlinear damping
Caussyn, D.D.; Ball, M.; Brabson, B.; Budnick, J.; Derenchuk, V.; East, G.; Ellison, M.; Friesel, D.; Hamilton, B.; Hedblom, K.; Jones, W.P.; Lee, S.Y.; Li, D.; Liu, J.Y.; Lofnes, T.; Ng, K.Y.; Riabko, A.; Sloan, T.; Wang, Y. Uppsala University, The Svedberg Laboratory, Box 533, S-75121, Uppsala Fermilab, P.O. Box 500, Batavia, Illinois 60510 )
1994-11-14
The longitudinal dynamics of a stored proton beam bunch, acted upon by a nonlinear damping force, was studied experimentally at the Indiana University Cyclotron Facility Cooler Ring. The effect of the nonlinear damping force on synchrotron motion was explored by varying the relative velocity between the cooling electron and the stored proton beams. Maintained longitudinal oscillations were observed, whose amplitude grew rapidly once a critical threshold in the relative velocity between the proton and electron beams was exceeded. We attribute this phenomenon to a negative resistance instability occurring after a Hopf bifurcation.
Narrow-band nonlinear sea waves
NASA Technical Reports Server (NTRS)
Tayfun, M. A.
1980-01-01
Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.
A spectral characterization of nonlinear normal modes
NASA Astrophysics Data System (ADS)
Cirillo, G. I.; Mauroy, A.; Renson, L.; Kerschen, G.; Sepulchre, R.
2016-09-01
This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity.
Algorithms For Integrating Nonlinear Differential Equations
NASA Technical Reports Server (NTRS)
Freed, A. D.; Walker, K. P.
1994-01-01
Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.
Nonlinear oscillations of coalescing magnetic flux ropes.
Kolotkov, Dmitrii Y; Nakariakov, Valery M; Rowlands, George
2016-05-01
An analytical model of highly nonlinear oscillations occurring during a coalescence of two magnetic flux ropes, based upon two-fluid hydrodynamics, is developed. The model accounts for the effect of electric charge separation, and describes perpendicular oscillations of the current sheet formed by the coalescence. The oscillation period is determined by the current sheet thickness, the plasma parameter β, and the oscillation amplitude. The oscillation periods are typically greater or about the ion plasma oscillation period. In the nonlinear regime, the oscillations of the ion and electron concentrations have a shape of a narrow symmetric spikes. PMID:27300993
Outlier robust nonlinear mixed model estimation.
Williams, James D; Birch, Jeffrey B; Abdel-Salam, Abdel-Salam G
2015-04-15
In standard analyses of data well-modeled by a nonlinear mixed model, an aberrant observation, either within a cluster, or an entire cluster itself, can greatly distort parameter estimates and subsequent standard errors. Consequently, inferences about the parameters are misleading. This paper proposes an outlier robust method based on linearization to estimate fixed effects parameters and variance components in the nonlinear mixed model. An example is given using the four-parameter logistic model and bioassay data, comparing the robust parameter estimates with the nonrobust estimates given by SAS(®).
Nonlinear vibration energy harvester using diamagnetic levitation
NASA Astrophysics Data System (ADS)
Liu, L.; Yuan, F. G.
2011-05-01
This letter proposes a nonlinear vibration energy harvester based on stabilized magnetic levitation using diamagnetic. Restoring forces induced by the magnetic field in harvesting vibration energy is employed instead of the forces introduced by conventional mechanical suspensions; therefore dissipation of vibration energy into heat through mechanical suspensions is eliminated. The core of the design consists of two spiral coils made of diamagnetic materials, which serve dual purposes: providing nonlinear restoring force and harnessing eddy current to power external circuits. From the theoretical analysis presented, the proposed harvester has the potential to provide wideband power outputs in low frequency range.
Nonlinear Internal Waves - Evolution and Energy Dissipation
NASA Astrophysics Data System (ADS)
Orr, M.; Mignerey, P.
2003-04-01
Nonlinear internal waves have been observed propagating up the slope of the South China Sea during the recent ONR Asian Seas International Acoustics Experiment. Energy dissipation rates have been extracted. The location of the initiation of the depression to elevation conversion has been identified. Scaling parameters have been extracted and used to initialize a two-layer evolution equation model simulation. Mode1, 2 linear and nonlinear internal waves and instabilities have been observed near the shelf break of the United States of America New Jersey Shelf. Acoustic flow visualization records will be presented. Work supported by the Office of Naval Research (ONR) Ocean Acoustics Program and ONR's NRL base funding.
On Lipschitz continuity of nonlinear differential operators
NASA Technical Reports Server (NTRS)
Keeling, Stephen L.
1987-01-01
In connection with approximations for nonlinear evolution equations, it is standard to assume that nonlinear terms are at least locally Lipschitz continuous. However, it is shown here that f = f(X,del sub u(X)) is Lipschitz continuous from the subspace W sup 1, infinity is a subset of L sub 2 into W sup 1,2, and maps W sup 2, infinity into W sup 1, infinity, if and only if f is affine with W sup 1, infinity coefficients. In fact, a local version of this claim is proved.
Nonlinear nanomechanical oscillators for ultrasensitive inertial detection
Datskos, Panagiotis George; Lavrik, Nickolay V
2013-08-13
A system for ultrasensitive mass and/or force detection of this invention includes a mechanical oscillator driven to oscillate in a nonlinear regime. The mechanical oscillator includes a piezoelectric base with at least one cantilever resonator etched into the piezoelectric base. The cantilever resonator is preferably a nonlinear resonator which is driven to oscillate with a frequency and an amplitude. The system of this invention detects an amplitude collapse of the cantilever resonator at a bifurcation frequency as the cantilever resonator stimulated over a frequency range. As mass and/or force is introduced to the cantilever resonator, the bifurcation frequency shifts along a frequency axis in proportion to the added mass.
Ionization penalty in nonlinear optical bioimaging
NASA Astrophysics Data System (ADS)
Voronin, A. A.; Zheltikov, A. M.
2010-05-01
The noninvasiveness of nonlinear optical imaging techniques is quantified in terms of the number of free electron generated in the laser-tissue interaction region per photon emitted into the nonlinear optical signal. For a broad variety of biomarker dyes and bioactivity reporter proteins, this ratio is shown to approach a critical value of unity for field intensities above 1TW/cm2 . Closed-form analytical expressions for the ionization penalty function and the critical pulse repetition rate are derived for few-cycle laser pulses.
Nonlinear neutral inclusions: assemblages of coated ellipsoids
Bolaños, Silvia Jiménez; Vernescu, Bogdan
2015-01-01
The problem of determining nonlinear neutral inclusions in (electrical or thermal) conductivity is considered. Neutral inclusions, inserted in a matrix containing a uniform applied electric field, do not disturb the field outside the inclusions. The well-known Hashin-coated sphere construction is an example of a neutral inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated ellipsoids. The proposed construction is neutral for a given applied field. PMID:26064633
Primordial fluctuations and non-linear structure
NASA Technical Reports Server (NTRS)
Little, Blane; Weinberg, David H.; Park, Changbom
1991-01-01
Several aspects of nonlinear gravitational instability are explored using two numerical experiments, each of which employs a series of 3D cosmological N-body simulations. In the first experiment, all of the initial high-frequency power is truncated above some critical wavenumber, in the second experiment, initial Fourier components are replaced with wavenumbers greater than critical by waves taken from an independent realization with the same power spectrum but with unrelated phases. These initial conditions are evolved for different values of critical wavenumbers to see how the progressive elimination or substitution of initial high-frequency components affects the final, nonlinear structure.
Stability of non-linear integrable accelerator
Batalov, I.; Valishev, A.; /Fermilab
2011-09-01
The stability of non-linear Integrable Optics Test Accelerator (IOTA) model developed in [1] was tested. The area of the stable region in transverse coordinates and the maximum attainable tune spread were found as a function of non-linear lens strength. Particle loss as a function of turn number was analyzed to determine whether a dynamic aperture limitation present in the system. The system was also tested with sextupoles included in the machine for chromaticity compensation. A method of evaluation of the beam size in the linear part of the accelerator was proposed.
Non-linear Post Processing Image Enhancement
NASA Technical Reports Server (NTRS)
Hunt, Shawn; Lopez, Alex; Torres, Angel
1997-01-01
A non-linear filter for image post processing based on the feedforward Neural Network topology is presented. This study was undertaken to investigate the usefulness of "smart" filters in image post processing. The filter has shown to be useful in recovering high frequencies, such as those lost during the JPEG compression-decompression process. The filtered images have a higher signal to noise ratio, and a higher perceived image quality. Simulation studies comparing the proposed filter with the optimum mean square non-linear filter, showing examples of the high frequency recovery, and the statistical properties of the filter are given,
Optimized spectral estimation for nonlinear synchronizing systems
NASA Astrophysics Data System (ADS)
Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn
2014-03-01
In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
Nonlinear plasma wave in magnetized plasmas
NASA Astrophysics Data System (ADS)
Bulanov, Sergei V.; Zh. Esirkepov, Timur; Kando, Masaki; Koga, James K.; Hosokai, Tomonao; Zhidkov, Alexei G.; Kodama, Ryosuke
2013-08-01
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic "Four-Ray Star" pattern.
Polydiacetylene thin films for nonlinear optical applications
NASA Technical Reports Server (NTRS)
Paley, Mark S.
1993-01-01
One very promising class of organic compounds for nonlinear optical (NLO) applications are polydiacetylenes, which are novel in that they are highly conjugated polymers which can also be crystalline. Polydiacetylenes offer several advantages over other organic materials: because of their highly conjugated electronic structures, they are capable of possessing large optical nonlinearities with fast response times; because they are crystalline, they can be highly ordered, which is essential for optimizing their NLO properties; and, last, because they are polymeric, they can be formed as thin films, which are useful for device fabrication. We have actively been carrying out ground-based research on several compounds of interest.
Evolution Of Nonlinear Waves in Compressing Plasma
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Nonlinear model of elastic field sources
NASA Astrophysics Data System (ADS)
Lev, B. I.; Zagorodny, A. G.
2016-09-01
A general concept of the long-range elastic interactions in continuous medium is proposed. The interaction is determined as a consequence of symmetry breaking of the elastic field distribution produced by the topological defect as isolated inclusions. It is proposed to treat topological defects as the source of elastic field that can be described in terms of this field. The source is considered as a nonlinear object which determines the effective charge of the field at large distances in the linear theory. The models of the nonlinear source are proposed.
A nonlinear virtual rider for motorcycles
NASA Astrophysics Data System (ADS)
Massaro, M.
2011-09-01
This work presents a virtual rider for the guidance of a nonlinear motorcycle model. The target motion is defined in terms of roll angle and speed. The virtual rider inputs are the steering torque, the rear-wheel driving/braking torque and front-wheel braking torque. The virtual rider capability is assessed by guiding the nonlinear motorcycle model in demanding manoeuvres with roll angles of 50° and longitudinal accelerations up to 0.8 g. Considerations on the effective preview distance used by the virtual rider are included.
Nonlinear electromagnetic interactions in energetic materials
Wood, Mitchell Anthony; Dalvit, Diego Alejandro; Moore, David Steven
2016-01-12
We study the scattering of electromagnetic waves in anisotropic energetic materials. Nonlinear light-matter interactions in molecular crystals result in frequency-conversion and polarization changes. Applied electromagnetic fields of moderate intensity can induce these nonlinear effects without triggering chemical decomposition, offering a mechanism for the nonionizing identification of explosives. We use molecular-dynamics simulations to compute such two-dimensional THz spectra for planar slabs made of pentaerythritol tetranitrate and ammonium nitrate. Finally, we discuss third-harmonic generation and polarization-conversion processes in such materials. These observed far-field spectral features of the reflected or transmitted light may serve as an alternative tool for standoff explosive detection.
Derivation of an applied nonlinear Schroedinger equation
Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens; Rambo, Patrick K.; Karelitz, David B.
2015-01-01
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
Hebbian Crosstalk Prevents Nonlinear Unsupervised Learning
Cox, Kingsley J. A.; Adams, Paul R.
2008-01-01
Learning is thought to occur by localized, activity-induced changes in the strength of synaptic connections between neurons. Recent work has shown that induction of change at one connection can affect changes at others (“crosstalk”). We studied the role of such crosstalk in nonlinear Hebbian learning using a neural network implementation of independent components analysis. We find that there is a sudden qualitative change in the performance of the network at a threshold crosstalk level, and discuss the implications of this for nonlinear learning from higher-order correlations in the neocortex. PMID:19826612
Primordial magnetic fields and nonlinear electrodynamics
Kunze, Kerstin E.
2008-01-15
The creation of large scale magnetic fields is studied in an inflationary universe where electrodynamics is assumed to be nonlinear. After inflation ends electrodynamics becomes linear and thus the description of reheating and the subsequent radiation dominated stage are unaltered. The nonlinear regime of electrodynamics is described by Lagrangians having a power-law dependence on one of the invariants of the electromagnetic field. It is found that there is a range of parameters for which primordial magnetic fields of cosmologically interesting strengths can be created.
Optimal Parametric Feedback Excitation of Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Braun, David J.
2016-01-01
An optimal parametric feedback excitation principle is sought, found, and investigated. The principle is shown to provide an adaptive resonance condition that enables unprecedentedly robust movement generation in a large class of oscillatory dynamical systems. Experimental demonstration of the theory is provided by a nonlinear electronic circuit that realizes self-adaptive parametric excitation without model information, signal processing, and control computation. The observed behavior dramatically differs from the one achievable using classical parametric modulation, which is fundamentally limited by uncertainties in model information and nonlinear effects inevitably present in real world applications.
Optimal Parametric Feedback Excitation of Nonlinear Oscillators.
Braun, David J
2016-01-29
An optimal parametric feedback excitation principle is sought, found, and investigated. The principle is shown to provide an adaptive resonance condition that enables unprecedentedly robust movement generation in a large class of oscillatory dynamical systems. Experimental demonstration of the theory is provided by a nonlinear electronic circuit that realizes self-adaptive parametric excitation without model information, signal processing, and control computation. The observed behavior dramatically differs from the one achievable using classical parametric modulation, which is fundamentally limited by uncertainties in model information and nonlinear effects inevitably present in real world applications. PMID:26871336
Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes
Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; Allen, Matthew S.
2015-09-15
Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less
Nonlinear traveling wave solution for the MJO skeleton model
NASA Astrophysics Data System (ADS)
Chen, S.; Stechmann, S. N.
2014-12-01
Recently, a minimal dynamical model is presented for capturing MJO's fundamental features. The model is a nonlinear oscillator model for the MJO skeleton and it involves interactions between convection, moisture and circulation. I will present the exact nonlinear traveling wave solutions for the model based on its energy conservation. The exact nonlinear solution provides for an explicit comparison of features between linear and nonlinear waves such as dispersion relations and traveling wave speeds. Moreover, the nonlinear solutions, compared with the linear ones, produce a narrow region of active convection and a wider region of suppressed convection. These predictions offer nonlinear MJO features that could potentially be targets of observational investigations.
Nonlinear response of tension leg platforms in random sea waves
Ma, R.; Li, G.
1995-12-31
The nonlinear dynamic analysis of a tension leg platform is carried out by using nonlinear spectral analysis in this paper. The nonlinear response spectrum is obtained by introducing Hermite polynomial. The study indicates that it is possible to solve nonlinear vibration problems by using spectral analysis directly. It is not necessary to linearize the nonlinear terms in this method so that the errors introduced by linearization can be eliminated. This method will provide a convenient and accurate tool for solving nonlinear random vibration problems.
Cui Weiguang; Zhang Pengjie; Yang Xiaohu
2010-05-15
A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter {zeta}, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution ({zeta}=1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < or approx. 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < or approx. 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance of including the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size, and initial redshift). We find that, the nonlinear power spectra can differ by {approx}30% for 10% deviation from GR (|{zeta}-1|=0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.
Nonlinear seismology a reality. The quantitative data
NASA Astrophysics Data System (ADS)
Marmureanu, G.; Cioflan, C. O.; Marmureanu, A.
2012-04-01
Nonlinear effects in ground motion during large earthquakes have long been a controversial issue between seismologists and geotechnical engineers. The central point of the discussion in last 10-15 years was whether soil amplification is function of earthquake magnitude. Laboratory tests made by using Hardin or Drnevich resonant columns consistently show the decreasing of dynamic torsion function(G) and increasing of torsion damping function(D%) with shear strains(γ) induced by deep strong Vrancea earthquakes; G = G(γ), respectively, D%= D%(γ),therefore nonlinear viscoelastic constitutive laws are required. Nonlinear amplification at sediments sites appears to be more pervasive than seismologists used to think...Any attempt at seismic zonation must take into account the local site condition and this nonlinear amplification (Aki, A., Local Site Effects on Weak and Strong Ground Motion, Tecto-nophysics, 218, pp.93-111, 1993). The difficulty to seismologists in demonstrating the nonlinear site effects has been due to the effect being overshadowed by the overall patterns of shock generation and propagation. In other words, the seismological detection of the nonlinear site effects requires a simultaneous understanding of the effects of earthquake source, propagation path and local geological site conditions. In main ground motion equation, ground displacement u(t) has general form: u(t)=s(t)*g(t)*i(t),where s(t),g(t) and i(t) are source, propagation and, respectively, instrument recording functions. The authors, in order to make quantitative evidence of large nonlinear effects, introduced and developed the concept of the nonlinear spectral amplification factor (SAF) as ratio between maximum spectral absolute acceleration (Sa), relative velocity (Sv ), relative displacement (Sd) from response spectra for a fraction of critical damping (ζ %) at fundamental period or any other period and peak values of acceleration (amax), velocity (vmax) and displacement (dmax
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu
2016-02-01
The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition. PMID:26497312
Quantum nonlinear optics: nonlinear optics meets the quantum world (Conference Presentation)
NASA Astrophysics Data System (ADS)
Boyd, Robert W.
2016-02-01
This presentation first reviews the historical development of the field of nonlinear optics, starting from its inception in 1961. It then reviews some of its more recent developments, including especially how nonlinear optics has become a crucial tool for the developing field of quantum technologies. Fundamental quantum processes enabled by nonlinear optics, such as the creation of squeezed and entangled light states, are reviewed. We then illustrate these concepts by means of specific applications, such as the development of secure communication systems based on the quantum states of light.
Multiply scaled constrained nonlinear equation solvers. [for nonlinear heat conduction problems
NASA Technical Reports Server (NTRS)
Padovan, Joe; Krishna, Lala
1986-01-01
To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.
Wang, Kangpeng; Ju, Yongfeng; He, Jin; Zhang, Long E-mail: lzhang@siom.ac.cn; Wang, Jun E-mail: lzhang@siom.ac.cn; Chen, Yu; Blau, Werner J.
2014-01-13
Laser propagation in a tandem structure comprising carbon nanotubes and phthalocyanines is studied by Z-scan method. Due to the different mechanisms of the two materials, the laser beam can be attenuated with different absorptivities, by changing the sequence of light passing through each material. Numerical simulations considering the effect of path length and the change of nonlinear coefficient within each material are conducted for understanding the distribution of laser intensity in the tandem system and hence, fitting of the asymmetric Z-scan curves. The results are helpful for the design of nonlinear optical devices comprising multiple nonlinear materials and mechanisms.
PREDICTION OF NONLINEAR SPATIAL FUNCTIONALS. (R827257)
Spatial statistical methodology can be useful in the arena of environmental regulation. Some regulatory questions may be addressed by predicting linear functionals of the underlying signal, but other questions may require the prediction of nonlinear functionals of the signal. ...
Nonlinear Submodels Of Orthogonal Linear Models
ERIC Educational Resources Information Center
Bechtel, Gordon G.
1973-01-01
It is the purpose of this paper to suggest the orthogonal analysis of variance as a device for simplifying either the analytic or iterative problem of finding LS (least squares) estimates for the parameters of particular nonlinear models. (Author/RK)
Nonlinear Dynamics and the Growth of Literature.
ERIC Educational Resources Information Center
Tabah, Albert N.
1992-01-01
Discussion of nonlinear dynamic mechanisms focuses on whether information production and dissemination can be described by similar mechanisms. The exponential versus linear growth of literature is discussed, the time factor is considered, an example using literature from the field of superconductivity is given, and implications for information…
Nonlinear behavior of negative phase velocity metamaterials
NASA Astrophysics Data System (ADS)
Boardman, Allan; King, Neil; Rapoport, Yuriy
2006-08-01
Negative phase velocity metamaterials (NPM) are engineered media currently enjoying a surge of interest due to their interesting properties and potential applications. Their nonlinear behaviour will be intrinsic to the Holy Grail quest for power control. This is a hot topic that is only just being explored as evidenced by a rapidly increasing number of publications over the past few years. With the introduction of power comes the possibility of solitons and it is important to recognise that damping, arising from both the environment and the material, must be offset by the introduction of gain. In this context the investigation considers what are known as dissipative solitons, within a pumping, multi-stable configuration, designed as a ring or Fabry-Perot cavity. Several exciting scenarios will be presented and particular attention is devoted to the nonlinearity displayed by well-known 'artificial' molecules such as split rings and omega particles. The desire to create metamaterials that reach out to optical frequencies is acknowledged through a discussion of scalability. Detailed studies of the cavity stability regimes lead to some novel possibilities for cavity control. The presentation will be rounded off with a generalised theory of metamaterial behaviour in nonlinear environments that is based upon a novel approach using what is sometimes called the nonlinear Lorentz lemma. Extensive new numerical results will be used to illustrate the concepts outlined above.
Photodynamics of nonlinear fullerene-containing media
NASA Astrophysics Data System (ADS)
Belousova, Inna M.; Belousov, Vlidilen P.; Danilov, Oleg B.; Grigor'ev, Vladimir A.; Kalintsev, Alexander G.; Zgonnik, V. N.; Kamanina, Natalia V.; Zhevlakov, Aleksandr P.; Kris'ko, A. V.; Mironova, N. G.; Sosnov, Eugene N.; Gavronskaya, E. A.; Smirnov, V. A.; Yur'ev, Michail S.; Ponomarev, Alexander N.; Yashin, Vladimir E.
2001-03-01
The results of theoretical and experimental studies on photodynamics and mechanism of nonlinear optical processes, responsible for optical limiting of power radiation in the wavelength range from 0.3 to 1.3 microns, are presented. Peculiarities in the mechanisms of optical limiting for different fullerene-containing matrices, including solutions, solid-state and polymer systems, are shown.