New insights into sucking, swallowing and breathing central generators: A complexity analysis of rhythmic motor behaviors.

PubMed

Samson, Nathalie; Praud, Jean-Paul; Quenet, Brigitte; Similowski, Thomas; Straus, Christian

2017-01-18

Sucking, swallowing and breathing are dynamic motor behaviors. Breathing displays features of chaos-like dynamics, in particular nonlinearity and complexity, which take their source in the automatic command of breathing. In contrast, buccal/gill ventilation in amphibians is one of the rare motor behaviors that do not display nonlinear complexity. This study aimed at assessing whether sucking and swallowing would also follow nonlinear complex dynamics in the newborn lamb. Breathing movements were recorded before, during and after bottle-feeding. Sucking pressure and the integrated EMG of the thyroartenoid muscle, as an index of swallowing, were recorded during bottle-feeding. Nonlinear complexity of the whole signals was assessed through the calculation of the noise limit value (NL). Breathing and swallowing always exhibited chaos-like dynamics. The NL of breathing did not change significantly before, during or after bottle-feeding. On the other hand, sucking inconsistently and significantly less frequently than breathing exhibited a chaos-like dynamics. Therefore, the central pattern generator (CPG) that drives sucking may be functionally different from the breathing CPG. Furthermore, the analogy between buccal/gill ventilation and sucking suggests that the latter may take its phylogenetic origin in the gill ventilation CPG of the common ancestor of extant amphibians and mammals. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

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

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

Probabilistic analysis of a materially nonlinear structure

NASA Technical Reports Server (NTRS)

Millwater, H. R.; Wu, Y.-T.; Fossum, A. F.

1990-01-01

A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.

Nonlinear acoustic techniques for landmine detection.

PubMed

Korman, Murray S; Sabatier, James M

2004-12-01

Measurements of the top surface vibration of a buried (inert) VS 2.2 anti-tank plastic landmine reveal significant resonances in the frequency range between 80 and 650 Hz. Resonances from measurements of the normal component of the acoustically induced soil surface particle velocity (due to sufficient acoustic-to-seismic coupling) have been used in detection schemes. Since the interface between the top plate and the soil responds nonlinearly to pressure fluctuations, characteristics of landmines, the soil, and the interface are rich in nonlinear physics and allow for a method of buried landmine detection not previously exploited. Tuning curve experiments (revealing "softening" and a back-bone curve linear in particle velocity amplitude versus frequency) help characterize the nonlinear resonant behavior of the soil-landmine oscillator. The results appear to exhibit the characteristics of nonlinear mesoscopic elastic behavior, which is explored. When two primary waves f1 and f2 drive the soil over the mine near resonance, a rich spectrum of nonlinearly generated tones is measured with a geophone on the surface over the buried landmine in agreement with Donskoy [SPIE Proc. 3392, 221-217 (1998); 3710, 239-246 (1999)]. In profiling, particular nonlinear tonals can improve the contrast ratio compared to using either primary tone in the spectrum.

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.

Measured and predicted structural behavior of the HiMAT tailored composite wing

NASA Technical Reports Server (NTRS)

Nelson, Lawrence H.

1987-01-01

A series of load tests was conducted on the HiMAT tailored composite wing. Coupon tests were also run on a series of unbalanced laminates, including the ply configuration of the wing, the purpose of which was to compare the measured and predicted behavior of unbalanced laminates, including - in the case of the wing - a comparison between the behavior of the full scale structure and coupon tests. Both linear and nonlinear finite element (NASTRAN) analyses were carried out on the wing. Both linear and nonlinear point-stress analyses were performed on the coupons. All test articles were instrumented with strain gages, and wing deflections measured. The leading and trailing edges were found to have no effect on the response of the wing to applied loads. A decrease in the stiffness of the wing box was evident over the 27-test program. The measured load-strain behavior of the wing was found to be linear, in contrast to coupon tests of the same laminate, which were nonlinear. A linear NASTRAN analysis of the wing generally correlated more favorably with measurements than did a nonlinear analysis. An examination of the predicted deflections in the wing root region revealed an anomalous behavior of the structural model that cannot be explained. Both hysteresis and creep appear to be less significant in the wing tests than in the corresponding laminate coupon tests.

A review of human factors challenges of complex adaptive systems: discovering and understanding chaos in human performance.

PubMed

Karwowski, Waldemar

2012-12-01

In this paper, the author explores a need for a greater understanding of the true nature of human-system interactions from the perspective of the theory of complex adaptive systems, including the essence of complexity, emergent properties of system behavior, nonlinear systems dynamics, and deterministic chaos. Human performance, more often than not, constitutes complex adaptive phenomena with emergent properties that exhibit nonlinear dynamical (chaotic) behaviors. The complexity challenges in the design and management of contemporary work systems, including service systems, are explored. Examples of selected applications of the concepts of nonlinear dynamics to the study of human physical performance are provided. Understanding and applications of the concepts of theory of complex adaptive and dynamical systems should significantly improve the effectiveness of human-centered design efforts of a large system of systems. Performance of many contemporary work systems and environments may be sensitive to the initial conditions and may exhibit dynamic nonlinear properties and chaotic system behaviors. Human-centered design of emergent human-system interactions requires application of the theories of nonlinear dynamics and complex adaptive system. The success of future human-systems integration efforts requires the fusion of paradigms, knowledge, design principles, and methodologies of human factors and ergonomics with those of the science of complex adaptive systems as well as modern systems engineering.

Nonlinear behavior of the tarka flute's distinctive sounds.

PubMed

Gérard, Arnaud; Yapu-Quispe, Luis; Sakuma, Sachiko; Ghezzi, Flavio; Ramírez-Ávila, Gonzalo Marcelo

2016-09-01

The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

Nonlinear behavior of the tarka flute's distinctive sounds

NASA Astrophysics Data System (ADS)

Gérard, Arnaud; Yapu-Quispe, Luis; Sakuma, Sachiko; Ghezzi, Flavio; Ramírez-Ávila, Gonzalo Marcelo

2016-09-01

The Andean tarka flute generates multiphonic sounds. Using spectral techniques, we verify two distinctive musical behaviors and the nonlinear nature of the tarka. Through nonlinear time series analysis, we determine chaotic and hyperchaotic behavior. Experimentally, we observe that by increasing the blow pressure on different fingerings, peculiar changes from linear to nonlinear patterns are produced, leading ultimately to quenching.

A Comparison of the Quasi-static Mechanical and Nonlinear Viscoelastic Properties of the Human Semitendinosus and Gracilis Tendons

PubMed Central

Abramowitch, Steven D.; Zhang, Xiaoyan; Curran, Molly; Kilger, Robert

2010-01-01

Background Over fifty-percent of anterior cruciate ligament reconstructions are performed using semitendinosus and gracilis tendon autografts. Despite their increased use, there remains little quantitative data on their mechanical behavior. Therefore, the objective of this study was to investigate the quasi-static mechanical and nonlinear viscoelastic properties of human semitendinosus and gracilis tendons, as well as the variation of these properties along their length. Methods Specimens were subjected to a series of uniaxial tensile tests: one-hour static stress-relaxation test, 30-cycle cyclic stress-relaxation test and load to failure test. To describe the nonlinear viscoelastic behavior, the quasi-linear viscoelastic theory was utilized to model data from the static stress relaxation experiment. Findings The constants describing the viscoelastic behavior were similar between the proximal and distal halves of the gracilis tendon. The proximal half of the semitendinosus tendon, however, had a greater viscous response than its distal half, which was also significantly higher than the proximal gracilis tendon. In terms of the quasi-static mechanical properties, the properties were similar between the proximal and distal halves of the semitendinosus tendon. However, the distal gracilis tendon showed a significantly higher tangent modulus and ultimate stress compared to its proximal half, which was also significantly higher than the distal semitendinosus tendon. Interpretation The results of this study demonstrate differences between the semitendinosus and gracilis tendons in terms of their quasi-static mechanical and nonlinear viscoelastic properties. These results are important for establishing surgical preconditioning protocols and graft selection. PMID:20092917

Spatial nonlinearities: Cascading effects in the earth system

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

2006-01-01

Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

Mathematical nonlinear optics

NASA Astrophysics Data System (ADS)

McLaughlin, David W.

1995-08-01

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

Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics

NASA Astrophysics Data System (ADS)

Bun Tse, Bosco Chun

This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.

Nonlinearity in cytoplasm viscosity can generate an essential symmetry breaking in cellular behaviors.

PubMed

Tachikawa, Masashi; Mochizuki, Atsushi

2015-01-07

The cytoplasms of ameboid cells are nonlinearly viscous. The cell controls this viscosity by modulating the amount, localization and interactions of bio-polymers. Here we investigated how the nonlinearity infers the cellular behaviors and whether nonlinearity-specific behaviors exist. We modeled the developed plasmodium of the slime mold Physarum polycephalum as a network of branching tubes and examined the linear and nonlinear viscous cytoplasm flows in the tubes. We found that the nonlinearity in the cytoplasm׳s viscosity induces a novel type of symmetry breaking in the protoplasmic flow. We also show that symmetry breaking can play an important role in adaptive behaviors, namely, connection of behavioral modes implemented on different time scales and transportation of molecular signals from the front to the rear of the cell during cellular locomotion. Copyright © 2014 Elsevier Ltd. All rights reserved.

Significant Association of Urinary Toxic Metals and Autism-Related Symptoms—A Nonlinear Statistical Analysis with Cross Validation

PubMed Central

Adams, James; Kruger, Uwe; Geis, Elizabeth; Gehn, Eva; Fimbres, Valeria; Pollard, Elena; Mitchell, Jessica; Ingram, Julie; Hellmers, Robert; Quig, David; Hahn, Juergen

2017-01-01

Introduction A number of previous studies examined a possible association of toxic metals and autism, and over half of those studies suggest that toxic metal levels are different in individuals with Autism Spectrum Disorders (ASD). Additionally, several studies found that those levels correlate with the severity of ASD. Methods In order to further investigate these points, this paper performs the most detailed statistical analysis to date of a data set in this field. First morning urine samples were collected from 67 children and adults with ASD and 50 neurotypical controls of similar age and gender. The samples were analyzed to determine the levels of 10 urinary toxic metals (UTM). Autism-related symptoms were assessed with eleven behavioral measures. Statistical analysis was used to distinguish participants on the ASD spectrum and neurotypical participants based upon the UTM data alone. The analysis also included examining the association of autism severity with toxic metal excretion data using linear and nonlinear analysis. “Leave-one-out” cross-validation was used to ensure statistical independence of results. Results and Discussion Average excretion levels of several toxic metals (lead, tin, thallium, antimony) were significantly higher in the ASD group. However, ASD classification using univariate statistics proved difficult due to large variability, but nonlinear multivariate statistical analysis significantly improved ASD classification with Type I/II errors of 15% and 18%, respectively. These results clearly indicate that the urinary toxic metal excretion profiles of participants in the ASD group were significantly different from those of the neurotypical participants. Similarly, nonlinear methods determined a significantly stronger association between the behavioral measures and toxic metal excretion. The association was strongest for the Aberrant Behavior Checklist (including subscales on Irritability, Stereotypy, Hyperactivity, and Inappropriate Speech), but significant associations were found for UTM with all eleven autism-related assessments with cross-validation R2 values ranging from 0.12–0.48. PMID:28068407

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

PubMed

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

2017-03-01

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

The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

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

Correction of photoresponse nonuniformity for matrix detectors based on prior compensation for their nonlinear behavior.

PubMed

Ferrero, Alejandro; Campos, Joaquin; Pons, Alicia

2006-04-10

What we believe to be a novel procedure to correct the nonuniformity that is inherent in all matrix detectors has been developed and experimentally validated. This correction method, unlike other nonuniformity-correction algorithms, consists of two steps that separate two of the usual problems that affect characterization of matrix detectors, i.e., nonlinearity and the relative variation of the pixels' responsivity across the array. The correction of the nonlinear behavior remains valid for any illumination wavelength employed, as long as the nonlinearity is not due to power dependence of the internal quantum efficiency. This method of correction of nonuniformity permits the immediate calculation of the correction factor for any given power level and for any illuminant that has a known spectral content once the nonuniform behavior has been characterized for a sufficient number of wavelengths. This procedure has a significant advantage compared with other traditional calibration-based methods, which require that a full characterization be carried out for each spectral distribution pattern of the incident optical radiation. The experimental application of this novel method has achieved a 20-fold increase in the uniformity of a CCD array for response levels close to saturation.

Solitary waves of surface plasmon polariton via phase shifts under Doppler broadening and Kerr nonlinearity

NASA Astrophysics Data System (ADS)

Ahmad, S.; Ahmad, A.; Bacha, B. A.; Khan, A. A.; Abdul Jabar, M. S.

2017-12-01

Surface Plasmon Polaritons (SPPs) are theoretically investigated at the interface of a dielectric metal and gold. The output pulse from the dielectric is used as the input pulse for the generation of SPPs. The SPPs show soliton-like behavior at the interface. The solitary form of a SPP is maintained under the effects of Kerr nonlinearity, Doppler broadening and Fresnel dragging whereas its phase shift is significantly modified. A 0.3radian phase shift is calculated in the presence of both Kerr nonlinearity and Fresnel dragging in the absence of plasma motion. The phase shift is enhanced to 60radian due to the combined effect of Doppler broadening, Kerr nonlinearity and Fresnel dragging. The results may have significant applications in nano-photonics, optical tweezers, photovoltaic devices, plasmonster and sensing technology.

Extending nonlinear analysis to short ecological time series.

PubMed

Hsieh, Chih-hao; Anderson, Christian; Sugihara, George

2008-01-01

Nonlinearity is important and ubiquitous in ecology. Though detectable in principle, nonlinear behavior is often difficult to characterize, analyze, and incorporate mechanistically into models of ecosystem function. One obvious reason is that quantitative nonlinear analysis tools are data intensive (require long time series), and time series in ecology are generally short. Here we demonstrate a useful method that circumvents data limitation and reduces sampling error by combining ecologically similar multispecies time series into one long time series. With this technique, individual ecological time series containing as few as 20 data points can be mined for such important information as (1) significantly improved forecast ability, (2) the presence and location of nonlinearity, and (3) the effective dimensionality (the number of relevant variables) of an ecological system.

Superconducting nanowires as nonlinear inductive elements for qubits

NASA Astrophysics Data System (ADS)

Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey

2011-03-01

We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a ``crater'' at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. NSF DMR-1005645, DOE DO-FG02-07ER46453.

Vagal-dependent nonlinear variability in the respiratory pattern of anesthetized, spontaneously breathing rats

PubMed Central

Dhingra, R. R.; Jacono, F. J.; Fishman, M.; Loparo, K. A.; Rybak, I. A.

2011-01-01

Physiological rhythms, including respiration, exhibit endogenous variability associated with health, and deviations from this are associated with disease. Specific changes in the linear and nonlinear sources of breathing variability have not been investigated. In this study, we used information theory-based techniques, combined with surrogate data testing, to quantify and characterize the vagal-dependent nonlinear pattern variability in urethane-anesthetized, spontaneously breathing adult rats. Surrogate data sets preserved the amplitude distribution and linear correlations of the original data set, but nonlinear correlation structure in the data was removed. Differences in mutual information and sample entropy between original and surrogate data sets indicated the presence of deterministic nonlinear or stochastic non-Gaussian variability. With vagi intact (n = 11), the respiratory cycle exhibited significant nonlinear behavior in templates of points separated by time delays ranging from one sample to one cycle length. After vagotomy (n = 6), even though nonlinear variability was reduced significantly, nonlinear properties were still evident at various time delays. Nonlinear deterministic variability did not change further after subsequent bilateral microinjection of MK-801, an N-methyl-d-aspartate receptor antagonist, in the Kölliker-Fuse nuclei. Reversing the sequence (n = 5), blocking N-methyl-d-aspartate receptors bilaterally in the dorsolateral pons significantly decreased nonlinear variability in the respiratory pattern, even with the vagi intact, and subsequent vagotomy did not change nonlinear variability. Thus both vagal and dorsolateral pontine influences contribute to nonlinear respiratory pattern variability. Furthermore, breathing dynamics of the intact system are mutually dependent on vagal and pontine sources of nonlinear complexity. Understanding the structure and modulation of variability provides insight into disease effects on respiratory patterning. PMID:21527661

Nonlinear aspects of the EEG during sleep in children

NASA Astrophysics Data System (ADS)

Berryman, Matthew J.; Coussens, Scott W.; Pamula, Yvonne; Kennedy, Declan; Lushington, Kurt; Shalizi, Cosma; Allison, Andrew; Martin, A. James; Saint, David; Abbott, Derek

2005-05-01

Electroencephalograph (EEG) analysis enables the dynamic behavior of the brain to be examined. If the behavior is nonlinear then nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal children and children with mild OSAS are evaluated for nonlinear brain behaviour. We found that there were differences in the nonlinearity of the brain behaviour between different sleep stages, and between the two groups of children.

Nonlinear plasmonic imaging techniques and their biological applications

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Varying Degrees of Nonlinear Mechanical Behavior Arising From Geometric Differences of Urogynecological Meshes

PubMed Central

Feola, Andrew; Pal, Siladitya; Moalli, Pamela; Maiti, Spandan; Abramowitch, Steven

2014-01-01

Synthetic polypropylene meshes were designed to restore pelvic organ support for women suffering from pelvic organ prolapse; however, the FDA released two notifications regarding the potential complications associated with mesh implantation. Our aim was to characterize the structural properties of Restorelle and UltraPro subjected to uniaxial tension along perpendicular directions, and then model the tensile behavior of these meshes utilizing a co-rotational finite element model, with an imbedded linear or fiber-recruitment local stress-strain relationship. Both meshes exhibited highly nonlinear stress-strain behavior; Restorelle had no significant differences between the two perpendicular directions, while UltraPro had a 93% difference in the low (initial) stiffness (p=0.009) between loading directions. Our model predicted that early alignment of the mesh segments in the loading direction and subsequent stretching could explain the observed nonlinear tensile behavior. However, a nonlinear stress-strain response in the stretching regime, that may be inherent to the mesh segment, was required to better capture experimental results. Utilizing a nonlinear fiber recruitment model with two parameters A and B, we observed improved agreement between the simulations and the experimental results. An inverse analysis found A=120 MPa and B=1.75 for Restorelle (RMSE=0.36). This approach yielded A=30 MPa and B=3.5 for UltraPro along one direction (RMSE=0.652), while the perpendicular orientation resulted in A=130 MPa and B=4.75 (RMSE=4.36). From the uniaxial protocol, Restorelle was found to have little variance in structural properties along these two perpendicular directions; however, UltraPro was found to behave anisotropically. PMID:25011619

Nonlinearity and Scaling Behavior in Lead Zirconate Titanate Piezoceramic

NASA Astrophysics Data System (ADS)

Mueller, V.

1998-03-01

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

Sexual affordances, perceptual-motor invariance extraction and intentional nonlinear dynamics: sexually deviant and non-deviant patterns in male subjects.

PubMed

Renaud, Patrice; Goyette, Mathieu; Chartier, Sylvain; Zhornitski, Simon; Trottier, Dominique; Rouleau, Joanne-L; Proulx, Jean; Fedoroff, Paul; Bradford, John-P; Dassylva, Benoit; Bouchard, Stephane

2010-10-01

Sexual arousal and gaze behavior dynamics are used to characterize deviant sexual interests in male subjects. Pedophile patients and non-deviant subjects are immersed with virtual characters depicting relevant sexual features. Gaze behavior dynamics as indexed from correlation dimensions (D2) appears to be fractal in nature and significantly different from colored noise (surrogate data tests and recurrence plot analyses were performed). This perceptual-motor fractal dynamics parallels sexual arousal and differs from pedophiles to non-deviant subjects when critical sexual information is processed. Results are interpreted in terms of sexual affordance, perceptual invariance extraction and intentional nonlinear dynamics.

Terahertz pulse induced intervalley scattering in photoexcited GaAs.

PubMed

Su, F H; Blanchard, F; Sharma, G; Razzari, L; Ayesheshim, A; Cocker, T L; Titova, L V; Ozaki, T; Kieffer, J-C; Morandotti, R; Reid, M; Hegmann, F A

2009-06-08

Nonlinear transient absorption bleaching of intense few-cycle terahertz (THz) pulses is observed in photoexcited GaAs using opticalpump--THz-probe techniques. A simple model of the electron transport dynamics shows that the observed nonlinear response is due to THz-electric- field-induced intervalley scattering over sub-picosecond time scales as well as an increase in the intravalley scattering rate attributed to carrier heating. Furthermore, the nonlinear nature of the THz pulse transmission at high peak fields leads to a measured terahertz conductivity in the photoexcited GaAs that deviates significantly from the Drude behavior observed at low THz fields, emphasizing the need to explore nonlinear THz pulse interactions with materials in the time domain.

Non-linear behavior of fiber composite laminates

NASA Technical Reports Server (NTRS)

Hashin, Z.; Bagchi, D.; Rosen, B. W.

1974-01-01

The non-linear behavior of fiber composite laminates which results from lamina non-linear characteristics was examined. The analysis uses a Ramberg-Osgood representation of the lamina transverse and shear stress strain curves in conjunction with deformation theory to describe the resultant laminate non-linear behavior. A laminate having an arbitrary number of oriented layers and subjected to a general state of membrane stress was treated. Parametric results and comparison with experimental data and prior theoretical results are presented.

Experimental Investigation of the Acoustic Nonlinear Behavior in Granular Polymer Bonded Explosives with Progressive Fatigue Damage

PubMed Central

Yang, Zhanfeng; Tian, Yong; Li, Weibin; Zhou, Haiqiang; Zhang, Weibin; Li, Jingming

2017-01-01

The measurement of acoustic nonlinear response is known as a promising technique to characterize material micro-damages. In this paper, nonlinear ultrasonic approach is used to characterize the evolution of fatigue induced micro-cracks in polymer bonded explosives. The variations of acoustic nonlinearity with respect to fatigue cycles in the specimens are obtained in this investigation. The present results show a significant increase of acoustic nonlinearity with respect to fatigue cycles. The experimental observation of the correlation between the acoustic nonlinearity and fatigue cycles in carbon/epoxy laminates, verifies that an acoustic nonlinear response can be used to evaluate the progressive fatigue damage in the granular polymer bonded explosives. The sensitivity comparison of nonlinear and linear parameters of ultrasonic waves in the specimens shows that nonlinear acoustic parameters are more promising indicators to fatigue induced micro-damage than linear ones. The feasibility study of the micro-damage assessment of polymer bonded explosives by nonlinear ultrasonic technique in this work can be applied to damage identification, material degradation monitoring, and lifetime prediction of the explosive parts. PMID:28773017

Experimental Investigation of the Acoustic Nonlinear Behavior in Granular Polymer Bonded Explosives with Progressive Fatigue Damage.

PubMed

Yang, Zhanfeng; Tian, Yong; Li, Weibin; Zhou, Haiqiang; Zhang, Weibin; Li, Jingming

2017-06-16

The measurement of acoustic nonlinear response is known as a promising technique to characterize material micro-damages. In this paper, nonlinear ultrasonic approach is used to characterize the evolution of fatigue induced micro-cracks in polymer bonded explosives. The variations of acoustic nonlinearity with respect to fatigue cycles in the specimens are obtained in this investigation. The present results show a significant increase of acoustic nonlinearity with respect to fatigue cycles. The experimental observation of the correlation between the acoustic nonlinearity and fatigue cycles in carbon/epoxy laminates, verifies that an acoustic nonlinear response can be used to evaluate the progressive fatigue damage in the granular polymer bonded explosives. The sensitivity comparison of nonlinear and linear parameters of ultrasonic waves in the specimens shows that nonlinear acoustic parameters are more promising indicators to fatigue induced micro-damage than linear ones. The feasibility study of the micro-damage assessment of polymer bonded explosives by nonlinear ultrasonic technique in this work can be applied to damage identification, material degradation monitoring, and lifetime prediction of the explosive parts.

Aeroelasticity of Axially Loaded Aerodynamic Structures for Truss-Braced Wing Aircraft

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Lebofsky, Sonia

2015-01-01

This paper presents an aeroelastic finite-element formulation for axially loaded aerodynamic structures. The presence of axial loading causes the bending and torsional sitffnesses to change. For aircraft with axially loaded structures such as the truss-braced wing aircraft, the aeroelastic behaviors of such structures are nonlinear and depend on the aerodynamic loading exerted on these structures. Under axial strain, a tensile force is created which can influence the stiffness of the overall aircraft structure. This tension stiffening is a geometric nonlinear effect that needs to be captured in aeroelastic analyses to better understand the behaviors of these types of aircraft structures. A frequency analysis of a rotating blade structure is performed to demonstrate the analytical method. A flutter analysis of a truss-braced wing aircraft is performed to analyze the effect of geometric nonlinear effect of tension stiffening on the flutter speed. The results show that the geometric nonlinear tension stiffening effect can have a significant impact on the flutter speed prediction. In general, increased wing loading results in an increase in the flutter speed. The study illustrates the importance of accounting for the geometric nonlinear tension stiffening effect in analyzing the truss-braced wing aircraft.

An Analysis of the Macroscopic Tensile Behavior of a Nonlinear Nylon Reinforced Elastomeric Composite System Using MAC/GMC

NASA Technical Reports Server (NTRS)

Assaad, Mahmoud; Arnold, Steven M.

1999-01-01

A special class of composite laminates composed of soft rubbery matrices and stiff reinforcements made of steel wires or synthetic fibers is examined, where each constituent behaves in a nonlinear fashion even in the small strain domain. Composite laminates made of piles stacked at alternating small orientation angles with respect to the applied axial strain are primarily dominated by the nonlinear behavior of the reinforcing fibers. However; composites with large ply orientations or those perpendicular to the loading axis, will approximate the behavior of the matrix phase and respond in even a more complex fashion for arbitrarily stacked piles. The geometric nonlinearity due to small cord rotations during loading was deemed here to have a second order effect and consequently dropped from any consideration. The user subroutine USRMAT within the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC), was utilized to introduce the constituent material nonlinear behavior. Stress-strain behavior at the macro level was experimentally generated for single and multi ply composites comprised of continuous Nylon-66 reinforcements embedded in a carbon black loaded rubbery matrix. Comparisons between the predicted macro composite behavior and experimental results are excellent when material nonlinearity is included in the analysis. In this paper, a brief review of GMC is provided, along with a description of the nonlinear behavior of the constituents and associated constituent constitutive relations, and the improved macro (or composite) behavior predictions are documented and illustrated.

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.

Nonlinear analysis of a rotor-bearing system using describing functions

NASA Astrophysics Data System (ADS)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Drive-level dependence of doubly rotated langasite resonators with different configurations.

PubMed

Zhang, Haifeng; Kosinski, John; Xie, Yuan; Turner, Joseph

2013-05-01

The miniaturization of crystal resonators and filters toward the micro electromechanical systems (MEMS) and nano-structured scales demands improvement of nonlinear piezoelectricity theory and a better understanding of the nonlinear behavior of new crystal materials. The nonlinearities affect the quality factor and acoustic behavior of MEMS and nano-structured resonators and filters. Among these nonlinear effects, drive-level dependence (DLD), which describes the instability of the resonator frequency resulting from voltage level and/or power density, is a potentially significant problem for miniaturized resonators. Langasite, a promising new piezoelectric material, is of current interest for a variety of applications because of its good temperature behavior, good piezoelectric coupling, low acoustic loss, and high Q-factor. It has been recently used to make high-temperature MEMS. In this paper, we report experimental measurements of the DLD of langasite resonators with different resonator configurations (plano-plano, single bevel, and double bevel). The results show that the resonator configuration affects the DLD of the langasite resonator. The DLD measurement results for langasite are compared with literature values for quartz, langaniste, and langatate, and with additional new measurements for a GaPO4 resonator of type R-30 (-11.1° rotated Y-cut). Uncertainty analysis for the measured drive-level sensitivity is performed as well.

Optimal filtering and Bayesian detection for friction-based diagnostics in machines.

PubMed

Ray, L R; Townsend, J R; Ramasubramanian, A

2001-01-01

Non-model-based diagnostic methods typically rely on measured signals that must be empirically related to process behavior or incipient faults. The difficulty in interpreting a signal that is indirectly related to the fundamental process behavior is significant. This paper presents an integrated non-model and model-based approach to detecting when process behavior varies from a proposed model. The method, which is based on nonlinear filtering combined with maximum likelihood hypothesis testing, is applicable to dynamic systems whose constitutive model is well known, and whose process inputs are poorly known. Here, the method is applied to friction estimation and diagnosis during motion control in a rotating machine. A nonlinear observer estimates friction torque in a machine from shaft angular position measurements and the known input voltage to the motor. The resulting friction torque estimate can be analyzed directly for statistical abnormalities, or it can be directly compared to friction torque outputs of an applicable friction process model in order to diagnose faults or model variations. Nonlinear estimation of friction torque provides a variable on which to apply diagnostic methods that is directly related to model variations or faults. The method is evaluated experimentally by its ability to detect normal load variations in a closed-loop controlled motor driven inertia with bearing friction and an artificially-induced external line contact. Results show an ability to detect statistically significant changes in friction characteristics induced by normal load variations over a wide range of underlying friction behaviors.

Application of nonlinear rheology to assess the effect of secondary nanofiller on network structure of hybrid polymer nanocomposites

NASA Astrophysics Data System (ADS)

Kamkar, Milad; Aliabadian, Ehsan; Shayesteh Zeraati, Ali; Sundararaj, Uttandaraman

2018-02-01

Carbon nanotube (CNT)/polymer nanocomposites exhibit excellent electrical properties by forming a percolated network. Adding a secondary filler can significantly affect the CNTs' network, resulting in changing the electrical properties. In this work, we investigated the effect of adding manganese dioxide nanowires (MnO2NWs) as a secondary nanofiller on the CNTs' network structure inside a poly(vinylidene fluoride) (PVDF) matrix. Incorporating MnO2NWs to PVDF/CNT samples produced a better state of dispersion of CNTs, as corroborated by light microscopy and transmission electron microscopy. The steady shear and oscillatory shear flows were employed to obtain a better insight into the nanofiller structure and viscoelastic behavior of the nanocomposites. The transient response under steady shear flow revealed that the stress overshoot of hybrid nanocomposites (two-fillers), PVDF/CNT/MnO2NWs, increased dramatically in comparison to binary nanocomposites (single-filler), PVDF/CNT and PVDF/MnO2NWs. This can be attributed to microstructural changes. Large amplitude oscillatory shear characterization was also performed to further investigate the effect of the secondary nanofiller on the nonlinear viscoelastic behavior of the samples. The nonlinear rheological observations were explained using quantitative nonlinear parameters [strain-stiffening ratio (S) and shear-thickening ratio (T)] and Lissajous-Bowditch plots. Results indicated that a more rigid nanofiller network was formed for the hybrid nanocomposites due to the better dispersion state of CNTs and this led to a more nonlinear viscoelastic behavior.

Superconducting nanowires as nonlinear inductive elements for qubits

NASA Astrophysics Data System (ADS)

Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey

2010-10-01

We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a “crater” at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. We also propose a concept of a nanowire-based qubit that relies on the current dependence of the kinetic inductance of a superconducting nanowire.

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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

Liu, Rumeng; Wang, Lifeng, E-mail: walfe@nuaa.edu.cn

The nonlinear thermal vibration behavior of a single-walled carbon nanotube (SWCNT) is investigated by molecular dynamics simulation and a nonlinear, nonplanar beam model. Whirling motion with energy transfer between flexural motions is found in the free vibration of the SWCNT excited by the thermal motion of atoms where the geometric nonlinearity is significant. A nonlinear, nonplanar beam model considering the coupling in two vertical vibrational directions is presented to explain the whirling motion of the SWCNT. Energy in different vibrational modes is not equal even over a time scale of tens of nanoseconds, which is much larger than the periodmore » of fundamental natural vibration of the SWCNT at equilibrium state. The energy of different modes becomes equal when the time scale increases to the microsecond range.« less

Nonlinear Acoustic Landmine Detection: Profiling Soil Surface Vibrations and Modeling Mesoscopic Elastic Behavior

DTIC Science & Technology

2007-05-04

TITLE AND SUBTITLE Nonlinear Acoustic Landmine Detection: Profiling Soil Surface Vibrations and Modeling Mesoscopic Elastic Behavior 6. AUTHOR(S...project report; no. 352 (2007) NONLINEAR ACOUSTIC LANDMINE DETECTION: PROFILING SOIL SURFACE VIBRATIONS AND MODELING MESOSCOPIC ELASTIC... model (Caughey 1966). Nonlinear acoustic landmine detection experiments are performed in the anechoic chamber facility using both a buried acrylic

Some Aspects of Nonlinear Dynamics and CFD

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Merriam, Marshal (Technical Monitor)

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 examples of spurious behavior observed in CFD computations.

Nonlinear optical response in graphene nanoribbons: The critical role of electron scattering

NASA Astrophysics Data System (ADS)

Karimi, F.; Davoody, A. H.; Knezevic, I.

2018-06-01

Nonlinear nanophotonics has many potential applications, such as in mode locking, frequency-comb generation, and all-optical switching. The development of materials with large nonlinear susceptibility is key to realizing nonlinear nanophotonics. Nanostructured graphene systems, such as graphene nanoribbons and nanoislands, have been predicted to have a strong plasmon-enhanced nonlinear optical behavior in the nonretarded regime. Plasmons concentrate the light field down to subwavelength scales and can enhance the nonlinear optical effects; however, plasmon resonances are narrowband and sensitive to the nanostructure geometry. Here we show that graphene nanoribbons, particularly armchair graphene nanoribbons, have a remarkably strong nonlinear optical response in the long-wavelength regime and over a broad frequency range, from terahertz to the near infrared. We use a quantum-mechanical master equation with a detailed treatment of scattering and show that, in the retarded regime, electron scattering has a critical effect on the optical nonlinearity of graphene nanoribbons, which cannot be captured via the commonly used relaxation-time approximation. At terahertz frequencies, where intraband optical transitions dominate, the strong nonlinearity (in particular, third-order Kerr nonlinearity) stems from the jagged shape of the electron energy distribution, caused by the interband electron scattering mechanisms along with the intraband inelastic scattering mechanisms. We show that the relaxation-time approximation fails to capture this quantum-mechanical phenomenon and results in a significant underestimation of the intraband nonlinearity. At the midinfrared to near infrared frequencies, where interband optical transitions dominate, the Kerr nonlinearity is significantly overestimated within the relaxation-time approximation. These findings unveil the critical effect of electron scattering on the optical nonlinearity of nanostructured graphene, and also underscore the capability of this class of materials for nonlinear nanophotonic applications.

Emotions as Proximal Causes of Word of Mouth: A Nonlinear Approach.

PubMed

Lopes, Rita Rueff; Navarro, José; Silva, Ana Junca

2018-01-01

Service research tends to operationalize word of mouth (WOM) behavior as one of the many responses to service satisfaction. In this sense, little is known about its antecedents or moderators. The objective of this study was to investigate the role of customers' emotions during service experiences on WOM, applying nonlinear techniques and exploring the moderating role of customers' propensity for emotional contagion. Using the critical incidents technique, 122 customers recalled significant service experiences and the emotions they aroused, and reported if they shared said experiences with other individuals. We found that, whereas linear methods presented non-significant results in the emotions-WOM relationship, nonlinear ones (artificial neural networks) explained 46% of variance. Negative emotions were stronger predictors of WOM and the importance of emotions for WOM was significantly higher for individuals with high propensity for emotional contagion (R^2 = .79) than for those with lower levels (R^2 = .48). Theoretical and practical implications are discussed.

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

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

Harlim, John, E-mail: jharlim@psu.edu; Mahdi, Adam, E-mail: amahdi@ncsu.edu; Majda, Andrew J., E-mail: jonjon@cims.nyu.edu

2014-01-15

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partialmore » noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.« less

Phase walk analysis of leptokurtic time series.

PubMed

Schreiber, Korbinian; Modest, Heike I; Räth, Christoph

2018-06-01

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases. The method, being called phase walk analysis, is based on well established measures from random walk analysis, which are now applied to the unwrapped Fourier phases of time series. We provide an analytical description of its functionality and demonstrate its capabilities on systematically controlled leptokurtic noise. Hereby, we investigate the properties of leptokurtic time series and their influence on the Fourier phases of time series. The phase walk analysis is applied to measured and simulated intermittent time series, whose probability density distribution is approximated by power laws. We use the day-to-day returns of the Dow-Jones industrial average, a synthetic time series with tailored nonlinearities mimicing the power law behavior of the Dow-Jones and the acceleration of the wind at an Atlantic offshore site. Testing for nonlinearities by means of surrogates shows that the new method yields strong significances for nonlinear behavior. Due to the drastically decreased computing time as compared to embedding space methods, the number of surrogate realizations can be increased by orders of magnitude. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Plasticity - Theory and finite element applications.

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H. S.

1972-01-01

A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.

Size effects in non-linear heat conduction with flux-limited behaviors

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

Is there evidence for the existence of nonlinear behavior within the interplanetary solar sector structure?

NASA Astrophysics Data System (ADS)

Brown, A. G.; Francis, N. M.; Broomhead, D. S.; Cannon, P. S.; Akram, A.

1999-06-01

Using data from the Sweden and Britain Radar Experiment (SABRE) VHF coherent radar, Yeoman et al. [1990] found evidence for two and four sector structures during the declining phase of solar cycle (SC) 21. No such obvious harmonic features were present during the ascending phase of SC 22. It was suggested that the structure of the heliospheric current sheet might exhibit nonlinear behavior during the latter period. A direct test of this suggestion, using established nonlinear methods, would require the computation of the fractal dimension of the data, for example. However, the quality of the SABRE data is insufficient for this purpose. Therefore we have tried to answer a simpler question: Is there any evidence that the SABRE data was generated by a (low-dimensional) nonlinear process? If this were the case, it would be a powerful indicator of nonlinear behavior in the solar current sheet. Our approach has been to use a system of orthogonal linear filters to separate the data into linearly uncorrelated time series. We then look for nonlinear dynamical relationships between these time series, using radial basis function models (which can be thought of as a class of neural networks). The presence of such a relationship, indicated by the ability to model one filter output given another, would equate to the presence of nonlinear properties within the data. Using this technique, evidence is found for the presence of low-level nonlinear behavior during both phases of the solar cycle investigated in this study. The evidence for nonlinear behavior is stronger during the descending phase of SC 21. However, it is not possible to distinguish between nonlinear dynamics and a nonlinearly transformed colored Gaussian noise process in either instance, using the available data. Therefore, in conclusion, we find insufficient evidence within the SABRE data set to support the suggestion of increased nonlinear dynamical behavior during the ascending phase of SC 22. In fact, nonlinear dynamics would seem to exert very little influence within the measurement time series at all, given the observed data. Therefore it is likely that stochastic or unresolved high-dimensional nonlinear mechanisms are responsible for the observed spectrum complexity during the ascending phase of SC 22.

Nonlinear laminate analysis for metal matrix fiber composites

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sinclair, J. H.

1981-01-01

A nonlinear laminate analysis is described for predicting the mechanical behavior (stress-strain relationships) of angleplied laminates in which the matrix is strained nonlinearly by both the residual stress and the mechanical load and in which additional nonlinearities are induced due to progressive fiber fractures and ply relative rotations. The nonlinear laminate analysis (NLA) is based on linear composite mechanics and a piece wise linear laminate analysis to handle the nonlinear responses. Results obtained by using this nonlinear analysis on boron fiber/aluminum matrix angleplied laminates agree well with experimental data. The results shown illustrate the in situ ply stress-strain behavior and synergistic strength enhancement.

Nonlinear optical behavior of two tetrathiafulvalene derivatives in the picosecond regime

NASA Astrophysics Data System (ADS)

Marcovicz, Crislaine; Ferreira, Rudson C.; Santos, Arthur B. S.; Reyna, Albert S.; de Araújo, Cid B.; Malvestiti, Ivani; Falcão, Eduardo H. L.

2018-06-01

We report the microwave-assisted synthesis of two symmetrical tetrathiafulvalene (TTF) derivatives via trialkyl phosphite-promoted coupling of a DMIT precursor. The microwave irradiation led to an increase in the reaction yield and significantly reduced the reaction time, affording the 2,3,6,7-tetrakis(2‧-methylacetatethio)tetrathiafulvalene (4) in 74% isolated yield. Hydrolysis of 4 yielded the tetraacid 5 in excellent yield. The nonlinear optical properties of both TTF compounds at 532 nm were studied by using the Z-scan technique in the picosecond regime exhibiting large third-order refractive index and saturated nonlinear absorption with promising applications in optical limiting devices.

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

NASA Astrophysics Data System (ADS)

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

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

Temperature-dependent differences in the nonlinear acoustic behavior of ultrasound contrast agents revealed by high-speed imaging and bulk acoustics.

PubMed

Mulvana, Helen; Stride, Eleanor; Tang, Mengxing; Hajnal, Jo V; Eckersley, Robert

2011-09-01

Previous work by the authors has established that increasing the temperature of the suspending liquid from 20°C to body temperature has a significant impact on the bulk acoustic properties and stability of an ultrasound contrast agent suspension (SonoVue, Bracco Suisse SA, Manno, Lugano, Switzerland). In this paper the influence of temperature on the nonlinear behavior of microbubbles is investigated, because this is one of the most important parameters in the context of diagnostic imaging. High-speed imaging showed that raising the temperature significantly influences the dynamic behavior of individual microbubbles. At body temperature, microbubbles exhibit greater radial excursion and oscillate less spherically, with a greater incidence of jetting and gas expulsion, and therefore collapse, than they do at room temperature. Bulk acoustics revealed an associated increase in the harmonic content of the scattered signals. These findings emphasize the importance of conducting laboratory studies at body temperature if the results are to be interpreted for in vivo applications. Copyright © 2011 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Understanding the Percolation Characteristics of Nonlinear Composite Dielectrics

PubMed Central

Yang, Xiao; Hu, Jun; Chen, Shuiming; He, Jinliang

2016-01-01

Nonlinear composite dielectrics can function as smart materials for stress control and field grading in all fields of electrical insulations. The percolation process is a significant issue of composite dielectrics. However, the classic percolation theory mainly deals with traditional composites in which the electrical parameters of both insulation matrix and conducting fillers are independent of the applied electric field. This paper measured the nonlinear V-I characteristics of ZnO microvaristors/silicone rubber composites with several filler concentrations around an estimated percolation threshold. For the comparison with the experiment, a new microstructural model is proposed to simulate the nonlinear conducting behavior of the composite dielectrics modified by metal oxide fillers, which is based on the Voronoi network and considers the breakdown feature of the insulation matrix for near percolated composites. Through both experiment and simulation, the interior conducting mechanism and percolation process of the nonlinear composites were presented and a specific percolation threshold was determined as 33%. This work has provided a solution to better understand the characteristics of nonlinear composite dielectrics. PMID:27476998

Understanding the Percolation Characteristics of Nonlinear Composite Dielectrics

NASA Astrophysics Data System (ADS)

Yang, Xiao; Hu, Jun; Chen, Shuiming; He, Jinliang

2016-08-01

Nonlinear composite dielectrics can function as smart materials for stress control and field grading in all fields of electrical insulations. The percolation process is a significant issue of composite dielectrics. However, the classic percolation theory mainly deals with traditional composites in which the electrical parameters of both insulation matrix and conducting fillers are independent of the applied electric field. This paper measured the nonlinear V-I characteristics of ZnO microvaristors/silicone rubber composites with several filler concentrations around an estimated percolation threshold. For the comparison with the experiment, a new microstructural model is proposed to simulate the nonlinear conducting behavior of the composite dielectrics modified by metal oxide fillers, which is based on the Voronoi network and considers the breakdown feature of the insulation matrix for near percolated composites. Through both experiment and simulation, the interior conducting mechanism and percolation process of the nonlinear composites were presented and a specific percolation threshold was determined as 33%. This work has provided a solution to better understand the characteristics of nonlinear composite dielectrics.

Tensile and compressive behavior of Borsic/aluminum

NASA Technical Reports Server (NTRS)

Herakovich, C. T.; Davis, J. G., Jr.; Viswanathan, C. N.

1977-01-01

The results of an experimental investigation of the mechanical behavior of Borsic/aluminum are presented. Composite laminates were tested in tension and compression for monotonically increasing load and also for variable loading cycles in which the maximum load was increased in each successive cycle. It is shown that significant strain-hardening, and corresponding increase in yield stress, is exhibited by the metal matrix laminates. For matrix dominated laminates, the current yield stress is essentially identical to the previous maximum stress, and unloading is essentially linear with large permanent strains after unloading. For laminates with fiber dominated behavior, the yield stress increases with increase in the previous maximum stress, but the increase in yield stress does not keep pace with the previous maximum stress. These fiber dominated laminates exhibit smaller nonlinear strains, reversed nonlinear behavior during unloading, and smaller permanent strains after unloading. Compression results from sandwich beams and flat coupons are shown to differ considerably. Results from beam specimens tend to exhibit higher values for modulus, yield stress, and strength.

Bifurcation and response analysis of a nonlinear flexible rotating disc immersed in bounded compressible fluid

NASA Astrophysics Data System (ADS)

Remigius, W. Dheelibun; Sarkar, Sunetra; Gupta, Sayan

2017-03-01

Use of heavy gases in centrifugal compressors for enhanced oil extraction have made the impellers susceptible to failures through acousto-elastic instabilities. This study focusses on understanding the dynamical behavior of such systems by considering the effects of the bounded fluid housed in a casing on a rotating disc. First, a mathematical model is developed that incorporates the interaction between the rotating impeller - modelled as a flexible disc - and the bounded compressible fluid medium in which it is immersed. The nonlinear effects arising due to large deformations of the disc have been included in the formulation so as to capture the post flutter behavior. A bifurcation analysis is carried out with the disc rotational speed as the bifurcation parameter to investigate the dynamical behavior of the coupled system and estimate the stability boundaries. Parametric studies reveal that the relative strengths of the various dissipation mechanisms in the coupled system play a significant role that affect the bifurcation route and the post flutter behavior in the acousto-elastic system.

Nonlinear modeling of crystal system transition of black phosphorus using continuum-DFT model.

PubMed

Setoodeh, A R; Farahmand, H

2018-01-24

In this paper, the nonlinear behavior of black phosphorus crystals is investigated in tandem with dispersion-corrected density functional theory (DFT-D) analysis under uniaxial loadings. From the identified anisotropic behavior of black phosphorus due to its morphological anisotropy, a hyperelastic anisotropic (HA) model named continuum-DFT is established to predict the nonlinear behavior of the material. In this respect, uniaxial Cauchy stresses are employed on both the DFT-D and HA models along the zig-zag and armchair directions. Simultaneously, the transition of the crystal system is recognized at about 4.5 GPa of the applied uniaxial tensile stress along the zig-zag direction on the DFT-D simulation in the nonlinear region. In order to develop the nonlinear continuum model, unknown constants are surveyed with the optimized least square technique. In this regard, the continuum model is obtained to reproduce the Cauchy stress-stretch and density of strain-stretch results of the DFT-D simulation. Consequently, the modified HA model is introduced to characterize the nonlinear behavior of black phosphorus along the zig-zag direction. More importantly, the specific transition of the crystal system is successfully predicted in the new modified continuum-DFT model. The results reveal that the multiscale continuum-DFT model is well defined to replicate the nonlinear behavior of black phosphorus along the zig-zag and armchair directions.

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

PubMed

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

Human responses at work may exhibit nonlinear properties where small changes in the initial task conditions can lead to large changes in system behavior. Therefore, it is important to study such nonlinearity to gain a better understanding of human performance under a variety of physical, perceptual, and cognitive tasks conditions. The main objective of this study was to investigate whether the human trunk kinematics data during a manual lifting task exhibits nonlinear behavior in terms of determinist chaos. Data related to kinematics of the trunk with respect to the pelvis were collected using Industrial Lumbar Motion Monitor (ILMM), and analyzed applying the nonlinear dynamical systems methodology. Nonlinear dynamics quantifiers of Lyapunov exponents and Kaplan-Yorke dimensions were calculated and analyzed under different task conditions. The study showed that human trunk kinematics during manual lifting exhibits chaotic behavior in terms of trunk sagittal angular displacement, velocity and acceleration. The findings support the importance of accounting for nonlinear dynamical properties of biomechanical responses to lifting tasks.

High frequency measures of OHC nonlinear capacitance (NLC) and their significance: Why measures stray away from predictions

NASA Astrophysics Data System (ADS)

Santos-Sacchi, Joseph

2018-05-01

Measures of membrane capacitance (Cm) can be used to assess important characteristics of voltage-dependent membrane proteins (e.g., channels and transporters). In particular, a protein's time-dependent voltage-sensor charge movement is equivalently represented as a frequency-dependent component of Cm, telling much about the kinetics of the protein's conformational behavior. Recently, we have explored the frequency dependence of OHC voltage-dependent capacitance (aka nonlinear capacitance, NLC) to query rates of conformational switching within prestin (SLC26a5), the cell's lateral membrane molecular motor 1. Following removal of confounding stray capacitance effects, high frequency Cm measures using wide-band stimuli accurately reveal unexpected low pass behavior in prestin's molecular motions.

Electrospun microcrimped fibers with nonlinear mechanical properties enhance ligament fibroblast phenotype.

PubMed

Grace Chao, Pen-hsiu; Hsu, Hsiang-Yi; Tseng, Hsiao-Yun

2014-09-01

Fiber structure and order greatly impact the mechanical behavior of fibrous materials. In biological tissues, the nonlinear mechanics of fibrous scaffolds contribute to the functionality of the material. The nonlinear mechanical properties of the wavy structure (crimp) in collagen allow tissue flexibility while preventing over-extension. A number of approaches have tried to recreate this complex mechanical functionality. We generated microcrimped fibers by briefly heating electrospun parallel fibers over the glass transition temperature or by ethanol treatment. The crimp structure is similar to those of collagen fibers found in native aorta, intestines, or ligaments. Using poly-L-lactic acid fibers, we demonstrated that the bulk materials exhibit changed stress-strain behaviors with a significant increase in the toe region in correlation to the degree of crimp, similar to those observed in collagenous tissues. In addition to mimicking the stress-strain behavior of biological tissues, the microcrimped fibers are instructive in cell morphology and promote ligament phenotypic gene expression. This effect can be further enhanced by dynamic tensile loading, a physiological perturbation in vivo. This rapid and economical approach for microcrimped fiber production provides an accessible platform to study structure-function relationships and a novel functional scaffold for tissue engineering and cell mechanobiology studies.

Nonlinear analysis of dynamic signature

NASA Astrophysics Data System (ADS)

Rashidi, S.; Fallah, A.; Towhidkhah, F.

2013-12-01

Signature is a long trained motor skill resulting in well combination of segments like strokes and loops. It is a physical manifestation of complex motor processes. The problem, generally stated, is that how relative simplicity in behavior emerges from considerable complexity of perception-action system that produces behavior within an infinitely variable biomechanical and environmental context. To solve this problem, we present evidences which indicate that motor control dynamic in signing process is a chaotic process. This chaotic dynamic may explain a richer array of time series behavior in motor skill of signature. Nonlinear analysis is a powerful approach and suitable tool which seeks for characterizing dynamical systems through concepts such as fractal dimension and Lyapunov exponent. As a result, they can be analyzed in both horizontal and vertical for time series of position and velocity. We observed from the results that noninteger values for the correlation dimension indicates low dimensional deterministic dynamics. This result could be confirmed by using surrogate data tests. We have also used time series to calculate the largest Lyapunov exponent and obtain a positive value. These results constitute significant evidence that signature data are outcome of chaos in a nonlinear dynamical system of motor control.

Ultrasonic Nondestructive Characterization of Adhesive Bonds

NASA Technical Reports Server (NTRS)

Qu, Jianmin

1997-01-01

Qualitative measurements of adhesion or binding forces can be accomplished, for example, by using the reflection coefficient of an ultrasound or by using thermal waves (Light and Kwun, 1989, Achenbach and Parikh, 1991, and Bostrom and wickham, 1991). However, a quantitative determination of binding forces is rather difficult. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasound passes through a nonlinear material. It seems that such non-linearity can be effectively used to characterize the bond strength. Several theories have been developed to model this nonlinear effect (Adler and Nagy, 1991; Achenbach and Parikh, 1991; Parikh and Achenbach, 1992; and Hirose and Kitahara, 1992; Anastasi and Roberts, 1992). Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented by Pangraz and Arnold (1994). Recently, Tang, Cheng and Achenbach (1997) made a comparison between the experimental and simulated results based on this theoretical model. A water immersion mode-converted shear wave through-transmission setup was used by Berndt and Green (1997) to analyze the nonlinear acoustic behavior of the adhesive bond. In this project, the nonlinear responses of an adhesive joint was investigated through transmission tests of ultrasonic wave and analyzed by the finite element simulations. The higher order harmonics were obtained in the tests. It is found that the amplitude of higher harmonics increases as the aging increases, especially the 3dorder harmonics. Results from the numerical simulation show that the material nonlinearity does indeed generate higher order harmonics. In particular, the elastic-perfect plastic behavior generates significant 3rd and 5th order harmonics.

Cubical Mass-Spring Model design based on a tensile deformation test and nonlinear material model.

PubMed

San-Vicente, Gaizka; Aguinaga, Iker; Tomás Celigüeta, Juan

2012-02-01

Mass-Spring Models (MSMs) are used to simulate the mechanical behavior of deformable bodies such as soft tissues in medical applications. Although they are fast to compute, they lack accuracy and their design remains still a great challenge. The major difficulties in building realistic MSMs lie on the spring stiffness estimation and the topology identification. In this work, the mechanical behavior of MSMs under tensile loads is analyzed before studying the spring stiffness estimation. In particular, the performed qualitative and quantitative analysis of the behavior of cubical MSMs shows that they have a nonlinear response similar to hyperelastic material models. According to this behavior, a new method for spring stiffness estimation valid for linear and nonlinear material models is proposed. This method adjusts the stress-strain and compressibility curves to a given reference behavior. The accuracy of the MSMs designed with this method is tested taking as reference some soft-tissue simulations based on nonlinear Finite Element Method (FEM). The obtained results show that MSMs can be designed to realistically model the behavior of hyperelastic materials such as soft tissues and can become an interesting alternative to other approaches such as nonlinear FEM.

The influence of and the identification of nonlinearity in flexible structures

NASA Technical Reports Server (NTRS)

Zavodney, Lawrence D.

1988-01-01

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

Nonlinear absorption and optical limiting in gold-precipitated glasses induced by a femtosecond laser

NASA Astrophysics Data System (ADS)

Qu, Shiliang; Gao, Yachen; Jiang, Xiongwei; Zeng, Huidan; Song, Yinglin; Qiu, Jianrong; Zhu, Congshan; Hirao, K.

2003-09-01

Nonlinear absorptions of Au nanoparticles precipitated silicate glasses by irradiation of a focused femtosecond pulsed laser were investigated using Z-scan technique with 8 ns pulses at 532 nm. Optical limiting (OL) effects in such glasses have been also measured. It is observed that the behaviors of transition from saturable absorption to reverse saturable absorption and the OL performances for different samples are significantly different, which depend drastically on the irradiation power density of the femtosecond laser used for the Au nanoparticles precipitation in the glass. Strong nonlinear absorptions in these samples are mainly attributed to the surface plasmon resonance (SPR) and free carrier absorptions of the precipitated Au nanoparticles.

Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

NASA Astrophysics Data System (ADS)

Virella, Juan C.; Prato, Carlos A.; Godoy, Luis A.

2008-05-01

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.

Experimental study of the reversible behavior of modulational instability in optical fibers

NASA Astrophysics Data System (ADS)

van Simaeys, Gaetan; Emplit, Philippe; Haelterman, Marc

2002-03-01

We report what is to our knowledge the first clear-cut experimental evidence of the reversibility of modulational instability in dispersive Kerr media. It was possible to perform this experiment with standard telecommunication fiber because we used a specially designed 550-ps square-pulse laser source based on the two-wavelength configuration of a nonlinear optical loop mirror. Our observations demonstrate that reversibility is due to well-balanced and synchronous energy transfer among a significant number of spectral wave components. These results provide what we believe is the first evidence, in the field of nonlinear optics, of the universal Fermi-Pasta-Ulam recurrence phenomenon that has been predicted for a large number of conservative nonlinear systems, including those described by a nonlinear Schrödinger equation that is relevant to the context of the present study.

Augmented twin-nonlinear two-box behavioral models for multicarrier LTE power amplifiers.

PubMed

Hammi, Oualid

2014-01-01

A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients.

Experimental and Model Studies on Loading Path-Dependent and Nonlinear Gas Flow Behavior in Shale Fractures

NASA Astrophysics Data System (ADS)

Li, Honglian; Lu, Yiyu; Zhou, Lei; Tang, Jiren; Han, Shuaibin; Ao, Xiang

2018-01-01

Interest in shale gas as an energy source is growing worldwide. Because the rock's natural fracture system can contribute to gas production, it is important to understand the flow behavior of natural fractures in shale. Previous studies on the flow characteristics in shale fractures were limited and did not consider the effect of nonlinearity. To understand the basic mechanics of the gas flow behavior in shale fractures, laboratory investigations with consideration of the fluid pressure gradient, the confining stress, the loading history and the fracture geometry were conducted in this paper. Izbash's equation was used to analyze the nonlinearity of the flow. The results show that the behavior of the friction factors is similar to that shown in flow tests in smooth and rough pipes. The increase of the confining stress and the irreversible damage to the shale decreased the hydraulic aperture and increased the relative roughness. Thus, turbulent flow could appear at a low Reynolds number, resulting in a significant pressure loss. The limits of the cubic law and the existing correction factor for transmissivity are discussed. It is found that the previous friction models overestimate the friction factor in the laminar regime and underestimate the friction factor in the turbulent regime. For this reason, a new friction model based on a linear combination of the Reynolds number and the relative roughness was developed.

Detailed puncture analyses tank cars : analysis of different impactor threats and impact conditions.

DOT National Transportation Integrated Search

2013-03-01

There has been significant research in recent years to analyze and improve the impact behavior and puncture resistance of railroad tank cars. Much of this research has been performed using detailed nonlinear finite element analyses supported by full ...

Six different roles for crossover inhibition in the retina: correcting the nonlinearities of synaptic transmission.

PubMed

Werblin, Frank S

2010-03-01

Early retinal studies categorized ganglion cell behavior as either linear or nonlinear and rectifying as represented by the familiar X- and Y-type ganglion cells in cat. Nonlinear behavior is in large part a consequence of the rectifying nonlinearities inherent in synaptic transmission. These nonlinear signals underlie many special functions in retinal processing, including motion detection, motion in motion, and local edge detection. But linear behavior is also required for some visual processing tasks. For these tasks, the inherently nonlinear signals are "linearized" by "crossover inhibition." Linearization utilizes a circuitry whereby nonlinear ON inhibition adds with nonlinear OFF excitation or ON excitation adds with OFF inhibition to generate a more linear postsynaptic voltage response. Crossover inhibition has now been measured in most bipolar, amacrine, and ganglion cells. Functionally crossover inhibition enhances edge detection, allows ganglion cells to recognize luminance-neutral patterns with their receptive fields, permits ganglion cells to distinguish contrast from luminance, and maintains a more constant conductance during the light response. In some cases, crossover extends the operating range of cone-driven OFF ganglion cells into the scotopic levels. Crossover inhibition is also found in neurons of the lateral geniculate nucleus and V1.

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

PubMed

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

2007-04-01

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

Generalized Weierstrass-Mandelbrot Function Model for Actual Stocks Markets Indexes with Nonlinear Characteristics

NASA Astrophysics Data System (ADS)

Zhang, L.; Yu, C.; Sun, J. Q.

2015-03-01

It is difficult to simulate the dynamical behavior of actual financial markets indexes effectively, especially when they have nonlinear characteristics. So it is significant to propose a mathematical model with these characteristics. In this paper, we investigate a generalized Weierstrass-Mandelbrot function (WMF) model with two nonlinear characteristics: fractal dimension D where 2 > D > 1.5 and Hurst exponent (H) where 1 > H > 0.5 firstly. And then we study the dynamical behavior of H for WMF as D and the spectrum of the time series γ change in three-dimensional space, respectively. Because WMF and the actual stock market indexes have two common features: fractal behavior using fractal dimension and long memory effect by Hurst exponent, we study the relationship between WMF and the actual stock market indexes. We choose a random value of γ and fixed value of D for WMF to simulate the S&P 500 indexes at different time ranges. As shown in the simulation results of three-dimensional space, we find that γ is important in WMF model and different γ may have the same effect for the nonlinearity of WMF. Then we calculate the skewness and kurtosis of actual Daily S&P 500 index in different time ranges which can be used to choose the value of γ. Based on these results, we choose appropriate γ, D and initial value into WMF to simulate Daily S&P 500 indexes. Using the fit line method in two-dimensional space for the simulated values, we find that the generalized WMF model is effective for simulating different actual stock market indexes in different time ranges. It may be useful for understanding the dynamical behavior of many different financial markets.

Nonlinear DC Conduction Behavior in Graphene Nanoplatelets/Epoxy Resin Composites

NASA Astrophysics Data System (ADS)

Yuan, Yang; Wang, Qingguo; Qu, Zhaoming

2018-01-01

Graphene nanoplatelets (GNPs)/Epoxy resin (ER) with a low percolation threshold were fabricated. Then the nonlinear DC conduction behavior of GNPs/ER composites was investigated, which indicates that dispersion, exfoliation level and conductivity of GNPs in specimens are closely related to the conduction of composites. Moreover, it could be seen that the modified graphene nanoplatelets made in this paper could be successfully used for increasing the electric conductivity of the epoxy resin, and the GNPs/ER composites with nonlinear conduction behavior have a good application prospects in the field of intelligent electromagnetic protection.

Nonlinear analysis for high-temperature multilayered fiber composite structures. M.S. Thesis; [turbine blades

NASA Technical Reports Server (NTRS)

Hopkins, D. A.

1984-01-01

A unique upward-integrated top-down-structured approach is presented for nonlinear analysis of high-temperature multilayered fiber composite structures. Based on this approach, a special purpose computer code was developed (nonlinear COBSTRAN) which is specifically tailored for the nonlinear analysis of tungsten-fiber-reinforced superalloy (TFRS) composite turbine blade/vane components of gas turbine engines. Special features of this computational capability include accounting of; micro- and macro-heterogeneity, nonlinear (stess-temperature-time dependent) and anisotropic material behavior, and fiber degradation. A demonstration problem is presented to mainfest the utility of the upward-integrated top-down-structured approach, in general, and to illustrate the present capability represented by the nonlinear COBSTRAN code. Preliminary results indicate that nonlinear COBSTRAN provides the means for relating the local nonlinear and anisotropic material behavior of the composite constituents to the global response of the turbine blade/vane structure.

Augmented Twin-Nonlinear Two-Box Behavioral Models for Multicarrier LTE Power Amplifiers

PubMed Central

2014-01-01

A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients. PMID:24624047

Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.

PubMed

Jin, Leisheng; Li, Lijie

2017-12-01

In this work, nonlinear dynamics of silicon nanowire resonator considering nonlocal effect has been investigated. For the first time, dynamical parameters (e.g., resonant frequency, Duffing coefficient, and the damping ratio) that directly influence the nonlinear dynamics of the nanostructure have been derived. Subsequently, by calculating their response with the varied nonlocal coefficient, it is unveiled that the nonlocal effect makes more obvious impacts at the starting range (from zero to a small value), while the impact of nonlocal effect becomes weaker when the nonlocal term reaches to a certain threshold value. Furthermore, to characterize the role played by nonlocal effect in exerting influence on nonlinear behaviors such as bifurcation and chaos (typical phenomena in nonlinear dynamics of nanoscale devices), we have calculated the Lyapunov exponents and bifurcation diagram with and without nonlocal effect, and results shows the nonlocal effect causes the most significant effect as the device is at resonance. This work advances the development of nanowire resonators that are working beyond linear regime.

Hydrostatic Stress Effect On the Yield Behavior of Inconel 100

NASA Technical Reports Server (NTRS)

Allen, Phillip A.; Wilson, Christopher D.

2002-01-01

Classical metal plasticity theory assumes that hydrostatic stress has no effect on the yield and postyield behavior of metals. Recent reexaminations of classical theory have revealed a significant effect of hydrostatic stress on the yield behavior of notched geometries. New experiments and nonlinear finite element analyses (FEA) of Inconel 100 (IN 100) equal-arm bend and double-edge notch tension (DENT) test specimens have revealed the effect of internal hydrostatic tensile stresses on yielding. Nonlinear FEA using the von Mises (yielding is independent of hydrostatic stress) and the Drucker-Prager (yielding is linearly dependent on hydrostatic stress) yield functions was performed. In all test cases, the von Mises constitutive model, which is independent of hydrostatic pressure, overestimated the load for a given displacement or strain. Considering the failure displacements or strains, the Drucker-Prager FEMs predicted loads that were 3% to 5% lower than the von Mises values. For the failure loads, the Drucker Prager FEMs predicted strains that were 20% to 35% greater than the von Mises values. The Drucker-Prager yield function seems to more accurately predict the overall specimen response of geometries with significant internal hydrostatic stress influence.

Rogue-wave bullets in a composite (2+1)D nonlinear medium.

PubMed

Chen, Shihua; Soto-Crespo, Jose M; Baronio, Fabio; Grelu, Philippe; Mihalache, Dumitru

2016-07-11

We show that nonlinear wave packets localized in two dimensions with characteristic rogue wave profiles can propagate in a third dimension with significant stability. This unique behavior makes these waves analogous to light bullets, with the additional feature that they propagate on a finite background. Bulletlike rogue-wave singlet and triplet are derived analytically from a composite (2+1)D nonlinear wave equation. The latter can be interpreted as the combination of two integrable (1+1)D models expressed in different dimensions, namely, the Hirota equation and the complex modified Korteweg-de Vries equation. Numerical simulations confirm that the generation of rogue-wave bullets can be observed in the presence of spontaneous modulation instability activated by quantum noise.

Effect of fiber distribution and realignment on the nonlinear and inhomogeneous mechanical properties of human supraspinatus tendon under longitudinal tensile loading.

PubMed

Lake, Spencer P; Miller, Kristin S; Elliott, Dawn M; Soslowsky, Louis J

2009-12-01

Tendon exhibits nonlinear stress-strain behavior that may be partly due to movement of collagen fibers through the extracellular matrix. While a few techniques have been developed to evaluate the fiber architecture of other soft tissues, the organizational behavior of tendon under load has not been determined. The supraspinatus tendon (SST) of the rotator cuff is of particular interest for investigation due to its complex mechanical environment and corresponding inhomogeneity. In addition, SST injury occurs frequently with limited success in treatment strategies, illustrating the need for a better understanding of SST properties. Therefore, the objective of this study was to quantitatively evaluate the inhomogeneous tensile mechanical properties, fiber organization, and fiber realignment under load of human SST utilizing a novel polarized light technique. Fiber distributions were found to become more aligned under load, particularly during the low stiffness toe-region, suggesting that fiber realignment may be partly responsible for observed nonlinear behavior. Fiber alignment was found to correlate significantly with mechanical parameters, providing evidence for strong structure-function relationships in tendon. Human SST exhibits complex, inhomogeneous mechanical properties and fiber distributions, perhaps due to its complex loading environment. Surprisingly, histological grade of degeneration did not correlate with mechanical properties.

Aeroelastic flutter enhancement by exploiting the combined use of shape memory alloys and nonlinear piezoelectric circuits

NASA Astrophysics Data System (ADS)

Sousa, Vagner Candido de; Silva, Tarcísio Marinelli Pereira; De Marqui Junior, Carlos

2017-10-01

In this paper, the combined effects of semi-passive control using shunted piezoelectric material and passive pseudoelastic hysteresis of shape memory springs on the aerolastic behavior of a typical section is investigated. An aeroelastic model that accounts for the presence of both smart materials employed as mechanical energy dissipation devices is presented. The Brinson model is used to simulate the shape memory material. New expressions for the modeling of the synchronized switch damping on inductor technique (developed for enhanced piezoelectric damping) are presented, resulting in better agreement with experimental data. The individual effects of each nonlinear mechanism on the aeroelastic behavior of the typical section are first verified. Later, the combined effects of semi-passive piezoelectric control and passive shape memory alloy springs on the post-critical behavior of the system are discussed in details. The range of post-flutter airflow speeds with stable limit cycle oscillations is significantly increased due to the combined effects of both sources of energy dissipation, providing an effective and autonomous way to modify the behavior of aeroelastic systems using smart materials.

Parameter estimation of a nonlinear Burger's model using nanoindentation and finite element-based inverse analysis

NASA Astrophysics Data System (ADS)

Hamim, Salah Uddin Ahmed

Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.

Efficient techniques for forced response involving linear modal components interconnected by discrete nonlinear connection elements

NASA Astrophysics Data System (ADS)

Avitabile, Peter; O'Callahan, John

2009-01-01

Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources. Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration. Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as: equivalent reduced model technique (ERMT);modal modification response technique (MMRT); andcomponent element method (CEM); are presented in this paper and are compared to traditional methods.

Nonlinear optical behavior of DNA-functionalized gold nanoparticles

NASA Astrophysics Data System (ADS)

Kulyk, B.; Krupka, O.; Smokal, V.; Figà, V.; Czaplicki, R.; Sahraoui, B.

2018-03-01

The third-order nonlinear optical properties of gold nanoparticles embedded in the DNA-based composites were investigated by means of the third harmonic generation. With this purpose, the thin films comprising DNA-based complexes and Au nanoparticles were spin-deposited on glass substrate and their optical and nonlinear optical features were studied using the Maker-fringe technique at a laser fundamental wavelength of 1064 nm. The values of the third-order susceptibility χ (3)(- 3ω; ω, ω, ω) of the composite films based on DNA complex doped with 5 wt% of N-ethyl-N-(2-hydroxyethyl)-4-(4-nitrophenylazo)aniline were found to be significantly higher than those for pure composite films. Meanwhile, the presence of Au nanoparticles noticeable decreases the third-order nonlinear response of DNA-based composite mainly due to the enhanced absorption and scattering of laser and generated beam, respectively.

Nonlinear Dynamical Model of a Soft Viscoelastic Dielectric Elastomer

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2017-12-01

Actuated by alternating stimulation, dielectric elastomers (DEs) show a behavior of complicated nonlinear vibration, implying a potential application as dynamic electromechanical actuators. As is well known, for a vibrational system, including the DE system, the dynamic properties are significantly affected by the geometrical sizes. In this article, a nonlinear dynamical model is deduced to investigate the geometrical effects on dynamic properties of viscoelastic DEs. The DEs with square and arbitrary rectangular geometries are considered, respectively. Besides, the effects of tensile forces on dynamic performances of rectangular DEs with comparably small and large geometrical sizes are explored. Phase paths and Poincaré maps are utilized to detect the periodicity of the nonlinear vibrations of DEs. The resonance characteristics of DEs incorporating geometrical effects are also investigated. The results indicate that the dynamic properties of DEs, including deformation response, vibrational periodicity, and resonance, are tuned when the geometrical sizes vary.

Nonlinear viscoelastic characterization of human vocal fold tissues under large-amplitude oscillatory shear (LAOS)

PubMed Central

Chan, Roger W.

2018-01-01

Viscoelastic shear properties of human vocal fold tissues were previously quantified by the shear moduli (G′ and G″). Yet these small-strain linear measures were unable to describe any nonlinear tissue behavior. This study attempted to characterize the nonlinear viscoelastic response of the vocal fold lamina propria under large-amplitude oscillatory shear (LAOS) with a stress decomposition approach. Human vocal fold cover and vocal ligament specimens from eight subjects were subjected to LAOS rheometric testing with a simple-shear rheometer. The empirical total stress response was decomposed into elastic and viscous stress components, based on odd-integer harmonic decomposition approach with Fourier transform. Nonlinear viscoelastic measures derived from the decomposition were plotted in Pipkin space and as rheological fingerprints to observe the onset of nonlinearity and the type of nonlinear behavior. Results showed that both the vocal fold cover and the vocal ligament experienced intercycle strain softening, intracycle strain stiffening, as well as shear thinning both intercycle and intracycle. The vocal ligament appeared to demonstrate an earlier onset of nonlinearity at phonatory frequencies, and higher sensitivity to changes in frequency and strain. In summary, the stress decomposition approach provided much better insights into the nonlinear viscoelastic behavior of the vocal fold lamina propria than the traditional linear measures. PMID:29780189

Nonlinear viscoelastic characterization of human vocal fold tissues under large-amplitude oscillatory shear (LAOS).

PubMed

Chan, Roger W

2018-05-01

Viscoelastic shear properties of human vocal fold tissues were previously quantified by the shear moduli ( G' and G″ ). Yet these small-strain linear measures were unable to describe any nonlinear tissue behavior. This study attempted to characterize the nonlinear viscoelastic response of the vocal fold lamina propria under large-amplitude oscillatory shear (LAOS) with a stress decomposition approach. Human vocal fold cover and vocal ligament specimens from eight subjects were subjected to LAOS rheometric testing with a simple-shear rheometer. The empirical total stress response was decomposed into elastic and viscous stress components, based on odd-integer harmonic decomposition approach with Fourier transform. Nonlinear viscoelastic measures derived from the decomposition were plotted in Pipkin space and as rheological fingerprints to observe the onset of nonlinearity and the type of nonlinear behavior. Results showed that both the vocal fold cover and the vocal ligament experienced intercycle strain softening, intracycle strain stiffening, as well as shear thinning both intercycle and intracycle. The vocal ligament appeared to demonstrate an earlier onset of nonlinearity at phonatory frequencies, and higher sensitivity to changes in frequency and strain. In summary, the stress decomposition approach provided much better insights into the nonlinear viscoelastic behavior of the vocal fold lamina propria than the traditional linear measures.

PV Degradation Curves: Non-Linearities and Failure Modes

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

Jordan, Dirk C.; Silverman, Timothy J.; Sekulic, Bill

Photovoltaic (PV) reliability and durability have seen increased interest in recent years. Historically, and as a preliminarily reasonable approximation, linear degradation rates have been used to quantify long-term module and system performance. The underlying assumption of linearity can be violated at the beginning of the life, as has been well documented, especially for thin-film technology. Additionally, non-linearities in the wear-out phase can have significant economic impact and appear to be linked to different failure modes. In addition, associating specific degradation and failure modes with specific time series behavior will aid in duplicating these degradation modes in accelerated tests and, eventually,more » in service life prediction. In this paper, we discuss different degradation modes and how some of these may cause approximately linear degradation within the measurement uncertainty (e.g., modules that were mainly affected by encapsulant discoloration) while other degradation modes lead to distinctly non-linear degradation (e.g., hot spots caused by cracked cells or solder bond failures and corrosion). The various behaviors are summarized with the goal of aiding in predictions of what may be seen in other systems.« less

The Search for an Effective Clinical Behavior Analysis: The Nonlinear Thinking of Israel Goldiamond

ERIC Educational Resources Information Center

Layng, T. V. Joe

2009-01-01

This paper has two purposes; the first is to reintroduce Goldiamond's constructional approach to clinical behavior analysis and to the field of behavior analysis as a whole, which, unfortunately, remains largely unaware of his nonlinear functional analysis and its implications. The approach is not simply a set of clinical techniques; instead it…

Decrease and enhancement of third-order optical nonlinearity in metal-dielectric composite films

NASA Astrophysics Data System (ADS)

Ning, Tingyin; Lu, Heng; Zhou, Yueliang; Man, Baoyuan

2018-04-01

We investigate third-order optical nonlinearity in gold nanoparticles embedded in CaCu3Ti4O12 (CCTO) films using the Z-scan method. We observe that the effective third-order nonlinear optical susceptibilities in such composite films can not only be enhanced, in line with the conventional behavior, but also be decreased, depending on the volume concentration of gold. In particular, the nonlinear absorption behavior can be changed from saturable absorption in pure CCTO films to reversed saturable absorption in composite films, and theoretically, even zero nonlinear absorption could be obtained. These results indicate that it should be possible to tune the third-order optical nonlinearity in Au:CCTO composite films by altering the gold concentration, thus making them suitable for applications in photonic devices.

A first approach to the distortion analysis of nonlinear analog circuits utilizing X-parameters

NASA Astrophysics Data System (ADS)

Weber, H.; Widemann, C.; Mathis, W.

2013-07-01

In this contribution a first approach to the distortion analysis of nonlinear 2-port-networks with X-parameters1 is presented. The X-parameters introduced by Verspecht and Root (2006) offer the possibility to describe nonlinear microwave 2-port-networks under large signal conditions. On the basis of X-parameter measurements with a nonlinear network analyzer (NVNA) behavioral models can be extracted for the networks. These models can be used to consider the nonlinear behavior during the design process of microwave circuits. The idea of the present work is to extract the behavioral models in order to describe the influence of interfering signals on the output behavior of the nonlinear circuits. Hereby, a simulator is used instead of a NVNA to extract the X-parameters. Assuming that the interfering signals are relatively small compared to the nominal input signal, the output signal can be described as a superposition of the effects of each input signal. In order to determine the functional correlation between the scattering variables, a polynomial dependency is assumed. The required datasets for the approximation of the describing functions are simulated by a directional coupler model in Cadence Design Framework. The polynomial coefficients are obtained by a least-square method. The resulting describing functions can be used to predict the system's behavior under certain conditions as well as the effects of the interfering signal on the output signal. 1 X-parameter is a registered trademark of Agilent Technologies, Inc.

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

NASA Astrophysics Data System (ADS)

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

2012-12-01

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

Nonlinear modeling of chaotic time series: Theory and applications

NASA Astrophysics Data System (ADS)

Casdagli, M.; Eubank, S.; Farmer, J. D.; Gibson, J.; Desjardins, D.; Hunter, N.; Theiler, J.

We review recent developments in the modeling and prediction of nonlinear time series. In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases, it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years, methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics, and human speech.

An Experimental and Finite Element Investigation into the Nonlinear Material Behavior of Pin-Loaded Composite Laminates

DTIC Science & Technology

1991-01-01

their midsurface counterparts due to the nature of the pin deflection and resulting load transfer. Linear elastic coupon radial stresses also followed... midsurface counterparts. The effects of the nonlinear elastic material behavior were quite evident when viewing the [(0/90)3,01, coupon intralaminar...to the midsurface of the coupon. The nonlinear elastic intralaminar shear stress-strain assumption acted to increase through thickness stresses

Experimental investigation of material nonlinearity using the Rayleigh surface waves excited and detected by angle beam wedge transducers.

PubMed

Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo; Hu, Hongwei

2018-05-12

Angle beam wedge transducers are widely used in nonlinear Rayleigh wave experiments as they can generate Rayleigh wave easily and produce high intensity nonlinear waves for detection. When such a transducer is used, the spurious harmonics (source nonlinearity) and wave diffraction may occur and will affect the measurement results, so it is essential to fully understand its acoustic nature. This paper experimentally investigates the nonlinear Rayleigh wave beam fields generated and received by angle beam wedge transducers, in which the theoretical predictions are based on the acoustic model developed previously for angle beam wedge transducers [S. Zhang, et al., Wave Motion, 67, 141-159, (2016)]. The source of the spurious harmonics is fully characterized by scrutinizing the nonlinear Rayleigh wave behavior in various materials with different driving voltages. Furthermore, it is shown that the attenuation coefficients for both fundamental and second harmonic Rayleigh waves can be extracted by comparing the measurements with the predictions when the experiments are conducted at many locations along the propagation path. A technique is developed to evaluate the material nonlinearity by making appropriate corrections for source nonlinearity, diffraction and attenuation. The nonlinear parameters of three aluminum alloy specimens - Al 2024, Al 6061 and Al 7075 - are measured, and the results indicate that the measurement results can be significantly improved using the proposed method. Copyright © 2018. Published by Elsevier B.V.

A new method for analysis of limit cycle behavior of the NASA/JPL 70-meter antenna axis servos

NASA Technical Reports Server (NTRS)

Hill, R. E.

1989-01-01

A piecewise linear method of analyzing the effects of discontinuous nonlinearities on control system performance is described. The limit cycle oscillatory behavior of the system resulting from the nonlinearities is described in terms of a sequence of linear system transient responses. The equations are derived which relate the initial and the terminal conditions of successive transients and the boundary conditions imposed by the non-linearities. The method leads to a convenient computation algorithm for prediction of limit cycle characteristics resulting from discontinuous nonlinearities such as friction, deadzones, and hysteresis.

A Novel Approach to Anharmonicity for a Wealth of Applications in Nonlinear Science Technologies

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

Hanusse, Patrick

2011-04-19

We present a new theory of the anharmonicity of nonlinear oscillations that are exhibited by many physical systems. New physical quantities are introduced that describe the departure from linear or harmonic behavior and as far as extremely anharmonic situations. In order to solve the nonlinear phase equation, the key notion of our theory, which controls the anharmonic behavior, a new and fascinating nonlinear trigonometry is designed. These results provide a general and accurate yet compact description of such signals, by far better than the Fourier description, both quantitatively and qualitatively and will benefit many application fields.

Modeling workplace bullying using catastrophe theory.

PubMed

Escartin, J; Ceja, L; Navarro, J; Zapf, D

2013-10-01

Workplace bullying is defined as negative behaviors directed at organizational members or their work context that occur regularly and repeatedly over a period of time. Employees' perceptions of psychosocial safety climate, workplace bullying victimization, and workplace bullying perpetration were assessed within a sample of nearly 5,000 workers. Linear and nonlinear approaches were applied in order to model both continuous and sudden changes in workplace bullying. More specifically, the present study examines whether a nonlinear dynamical systems model (i.e., a cusp catastrophe model) is superior to the linear combination of variables for predicting the effect of psychosocial safety climate and workplace bullying victimization on workplace bullying perpetration. According to the AICc, and BIC indices, the linear regression model fits the data better than the cusp catastrophe model. The study concludes that some phenomena, especially unhealthy behaviors at work (like workplace bullying), may be better studied using linear approaches as opposed to nonlinear dynamical systems models. This can be explained through the healthy variability hypothesis, which argues that positive organizational behavior is likely to present nonlinear behavior, while a decrease in such variability may indicate the occurrence of negative behaviors at work.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. 2; Global Asymptotic Behavior of Time Discretizations; 2. Global Asymptotic Behavior of time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Giffen Behavior and Subsistence Consumption

PubMed Central

Jensen, Robert T.

2010-01-01

This paper provides the first real-world evidence of Giffen behavior, i.e., upward sloping demand. Subsidizing the prices of dietary staples for extremely poor households in two provinces of China, we find strong evidence of Giffen behavior for rice in Hunan, and weaker evidence for wheat in Gansu. The data provide new insight into the consumption behavior of the poor, who act as though maximizing utility subject to subsistence concerns. We find that their elasticity of demand depends significantly, and nonlinearly, on the severity of their poverty. Understanding this heterogeneity is important for the effective design of welfare programs for the poor. (JEL D12, O12) PMID:21031158

Experiments and numerical simulations of nonlinear vibration responses of an assembly with friction joints - Application on a test structure named "Harmony"

NASA Astrophysics Data System (ADS)

Claeys, M.; Sinou, J.-J.; Lambelin, J.-P.; Todeschini, R.

2016-03-01

In presence of friction, the frequency response function of a metallic assembly is strongly dependent on the excitation level. The local stick-slip behavior at the friction interfaces induces energy dissipation and local stiffness softening. These phenomena are studied both experimentally and numerically on a test structure named "Harmony". Concerning the numerical part, a classical complete methodology from the finite element and friction modeling to the prediction of the nonlinear vibrational response is implemented. The well-known Harmonic Balance Method with a specific condensation process on the nonlinear frictional elements is achieved. Also, vibration experiments are performed to validate not only the finite element model of the test structure named "Harmony" at low excitation levels but also to investigate the nonlinear behavior of the system on several excitation levels. A scanning laser vibrometer is used to measure the nonlinear behavior and the local stick-slip movement near the contacts.

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

NASA Technical Reports Server (NTRS)

Ng, C. F.

1988-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Nonlinear characterization of a bolted, industrial structure using a modal framework

NASA Astrophysics Data System (ADS)

Roettgen, Daniel R.; Allen, Matthew S.

2017-02-01

This article presents measurements from a sub assembly of an off-the-shelf automotive exhaust system containing a bolted-flange connection and uses a recently proposed modal framework to develop a nonlinear dynamic model for the structure. The nonlinear identification and characterization methods used are reviewed to highlight the strengths of the current approach and the areas where further development is needed. This marks the first use of these new testing and nonlinear identification tools, and the associated modal framework, on production hardware with a realistic joint and realistic torque levels. To screen the measurements for nonlinearities, we make use of a time frequency analysis routine designed for transient responses called the zeroed early-time fast Fourier transform (ZEFFT). This tool typically reveals the small frequency shifts and distortions that tend to occur near each mode that is affected by the nonlinearity. The damping in this structure is found to be significantly nonlinear and a Hilbert transform is used to characterize the damping versus amplitude behavior. A model is presented that captures these effects for each mode individually (e.g. assuming negligible nonlinear coupling between modes), treating each mode as a single degree-of-freedom oscillator with a spring and viscous damping element in parallel with a four parameter Iwan model. The parameters of this model are identified for each of the structure's modes that exhibited nonlinearity and the resulting nonlinear model is shown to capture the stiffness and damping accurately over a large range of response amplitudes.

Nonlinear Geometric Effects in Mechanical Bistable Morphing Structures

NASA Astrophysics Data System (ADS)

Chen, Zi; Guo, Qiaohang; Majidi, Carmel; Chen, Wenzhe; Srolovitz, David J.; Haataja, Mikko P.

2012-09-01

Bistable structures associated with nonlinear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects on bistability remain elusive. We demonstrate, through both theoretical analysis and tabletop experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells.

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

PubMed

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

2012-03-01

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

Linear and nonlinear market correlations: Characterizing financial crises and portfolio optimization.

PubMed

Haluszczynski, Alexander; Laut, Ingo; Modest, Heike; Räth, Christoph

2017-12-01

Pearson correlation and mutual information-based complex networks of the day-to-day returns of U.S. S&P500 stocks between 1985 and 2015 have been constructed to investigate the mutual dependencies of the stocks and their nature. We show that both networks detect qualitative differences especially during (recent) turbulent market periods, thus indicating strongly fluctuating interconnections between the stocks of different companies in changing economic environments. A measure for the strength of nonlinear dependencies is derived using surrogate data and leads to interesting observations during periods of financial market crises. In contrast to the expectation that dependencies reduce mainly to linear correlations during crises, we show that (at least in the 2008 crisis) nonlinear effects are significantly increasing. It turns out that the concept of centrality within a network could potentially be used as some kind of an early warning indicator for abnormal market behavior as we demonstrate with the example of the 2008 subprime mortgage crisis. Finally, we apply a Markowitz mean variance portfolio optimization and integrate the measure of nonlinear dependencies to scale the investment exposure. This leads to significant outperformance as compared to a fully invested portfolio.

Linear and nonlinear market correlations: Characterizing financial crises and portfolio optimization

NASA Astrophysics Data System (ADS)

Haluszczynski, Alexander; Laut, Ingo; Modest, Heike; Räth, Christoph

2017-12-01

Pearson correlation and mutual information-based complex networks of the day-to-day returns of U.S. S&P500 stocks between 1985 and 2015 have been constructed to investigate the mutual dependencies of the stocks and their nature. We show that both networks detect qualitative differences especially during (recent) turbulent market periods, thus indicating strongly fluctuating interconnections between the stocks of different companies in changing economic environments. A measure for the strength of nonlinear dependencies is derived using surrogate data and leads to interesting observations during periods of financial market crises. In contrast to the expectation that dependencies reduce mainly to linear correlations during crises, we show that (at least in the 2008 crisis) nonlinear effects are significantly increasing. It turns out that the concept of centrality within a network could potentially be used as some kind of an early warning indicator for abnormal market behavior as we demonstrate with the example of the 2008 subprime mortgage crisis. Finally, we apply a Markowitz mean variance portfolio optimization and integrate the measure of nonlinear dependencies to scale the investment exposure. This leads to significant outperformance as compared to a fully invested portfolio.

Linear approximations of global behaviors in nonlinear systems with moderate or strong noise

NASA Astrophysics Data System (ADS)

Liang, Junhao; Din, Anwarud; Zhou, Tianshou

2018-03-01

While many physical or chemical systems can be modeled by nonlinear Langevin equations (LEs), dynamical analysis of these systems is challenging in the cases of moderate and strong noise. Here we develop a linear approximation scheme, which can transform an often intractable LE into a linear set of binomial moment equations (BMEs). This scheme provides a feasible way to capture nonlinear behaviors in the sense of probability distribution and is effective even when the noise is moderate or big. Based on BMEs, we further develop a noise reduction technique, which can effectively handle tough cases where traditional small-noise theories are inapplicable. The overall method not only provides an approximation-based paradigm to analysis of the local and global behaviors of nonlinear noisy systems but also has a wide range of applications.

Nonlinear dynamics induced in a structure by seismic and environmental loading

DOE PAGES

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

2016-07-26

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

Nonlinear dynamics induced in a structure by seismic and environmental loading

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

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

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

Nonlinear time dependence of dark current in charge-coupled devices

NASA Astrophysics Data System (ADS)

Dunlap, Justin C.; Bodegom, Erik; Widenhorn, Ralf

2011-03-01

It is generally assumed that charge-coupled device (CCD) imagers produce a linear response of dark current versus exposure time except near saturation. We found a large number of pixels with nonlinear dark current response to exposure time to be present in two scientific CCD imagers. These pixels are found to exhibit distinguishable behavior with other analogous pixels and therefore can be characterized in groupings. Data from two Kodak CCD sensors are presented for exposure times from a few seconds up to two hours. Linear behavior is traditionally taken for granted when carrying out dark current correction and as a result, pixels with nonlinear behavior will be corrected inaccurately.

Ontology of Earth's nonlinear dynamic complex systems

NASA Astrophysics Data System (ADS)

Babaie, Hassan; Davarpanah, Armita

2017-04-01

As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity

NASA Astrophysics Data System (ADS)

Li, Qian; Matula, Thomas J.; Tu, Juan; Guo, Xiasheng; Zhang, Dong

2013-02-01

It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear ‘Cross law’ to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the ‘compression-only’ behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., ‘shear-thinning’ and ‘strain-softening’) in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.

Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity.

PubMed

Li, Qian; Matula, Thomas J; Tu, Juan; Guo, Xiasheng; Zhang, Dong

2013-02-21

It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear 'Cross law' to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the 'compression-only' behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., 'shear-thinning' and 'strain-softening') in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.

Hydrostatic Stress Effect on the Yield Behavior of Inconel 100

NASA Technical Reports Server (NTRS)

Allen, Phillip A.; Wilson, Christopher D.

2003-01-01

Classical metal plasticity theory assumes that hydrostatic stress has negligible effect on the yield and postyield behavior of metals. Recent reexaminations of classical theory have revealed a significant effect of hydrostatic stress on the yield behavior of various geometries. Fatigue tests and nonlinear finite element analyses (FEA) of Inconel 100 (IN100) equal-arm bend specimens and new monotonic tests and nonlinear finite element analyses of IN100 smooth tension, smooth compression, and double-edge notch tension (DENT) test specimens have revealed the effect of internal hydrostatic tensile stresses on yielding. Nonlinear FEA using the von Mises (yielding is independent of hydrostatic stress) and the Drucker-Prager (yielding is linearly dependent on hydrostatic stress) yield functions were performed. A new FEA constitutive model was developed that incorporates a pressure-dependent yield function with combined multilinear kinematic and multilinear isotropic hardening using the ABAQUS user subroutine (UMAT) utility. In all monotonic tensile test cases, the von Mises constitutive model, overestimated the load for a given displacement or strain. Considering the failure displacements or strains for the DENT specimen, the Drucker-Prager FEM s predicted loads that were approximately 3% lower than the von Mises values. For the failure loads, the Drucker Prager FEM s predicted strains that were up to 35% greater than the von Mises values. Both the Drucker-Prager model and the von Mises model performed equally-well in simulating the equal-arm bend fatigue test.

NOLIN: A nonlinear laminate analysis program

NASA Technical Reports Server (NTRS)

Kibler, J. J.

1975-01-01

A nonlinear, plane-stress, laminate analysis program, NOLIN, was developed which accounts for laminae nonlinearity under inplane shear and transverse extensional stress. The program determines the nonlinear stress-strain behavior of symmetric laminates subjected to any combination of inplane shear and biaxial extensional loadings. The program has the ability to treat different stress-strain behavior in tension and compression, and predicts laminate failure using any or all of maximum stress, maximum strain, and quadratic interaction failure criteria. A brief description of the program is presented including discussion of the flow of information and details of the input required. Sample problems and a complete listing of the program is also provided.

Nonlinearity characterization of temperature sensing systems for integrated circuit testing by intermodulation products monitoring.

PubMed

Altet, J; Mateo, D; Perpiñà, X; Grauby, S; Dilhaire, S; Jordà, X

2011-09-01

This work presents an alternative characterization strategy to quantify the nonlinear behavior of temperature sensing systems. The proposed approach relies on measuring the temperature under thermal sinusoidal steady state and observing the intermodulation products that are generated within the sensing system itself due to its nonlinear temperature-output voltage characteristics. From such intermodulation products, second-order interception points can be calculated as a figure of merit of the measuring system nonlinear behavior. In this scenario, the present work first shows a theoretical analysis. Second, it reports the experimental results obtained with three thermal sensing techniques used in integrated circuits. © 2011 American Institute of Physics

Anomalous behavior of nonlinear refractive indexes of CO2 and Xe in supercritical states.

PubMed

Mareev, Evgenii; Aleshkevich, Victor; Potemkin, Fedor; Bagratashvili, Victor; Minaev, Nikita; Gordienko, Vyacheslav

2018-05-14

Direct measurement of pressure dependent nonlinear refractive index of CO 2 and Xe in subcritical and supercritical states are reported. In the vicinity of the ridge (or the Widom line), corresponding to the maximum density fluctuations, the nonlinear refractive index reaches a maximum value (up to 4.8*10 -20 m 2 /W in CO 2 and 3.5*10 -20 m 2 /W in Xe). Anomalous behavior of the nonlinear refractive index in the vicinity of a ridge is caused by the cluster formation. That corresponds to the results of our theoretical assumption based on the modified Langevin theory.

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.

Descriptive Characteristics of Surface Water Quality in Hong Kong by a Self-Organising Map

PubMed Central

An, Yan; Zou, Zhihong; Li, Ranran

2016-01-01

In this study, principal component analysis (PCA) and a self-organising map (SOM) were used to analyse a complex dataset obtained from the river water monitoring stations in the Tolo Harbor and Channel Water Control Zone (Hong Kong), covering the period of 2009–2011. PCA was initially applied to identify the principal components (PCs) among the nonlinear and complex surface water quality parameters. SOM followed PCA, and was implemented to analyze the complex relationships and behaviors of the parameters. The results reveal that PCA reduced the multidimensional parameters to four significant PCs which are combinations of the original ones. The positive and inverse relationships of the parameters were shown explicitly by pattern analysis in the component planes. It was found that PCA and SOM are efficient tools to capture and analyze the behavior of multivariable, complex, and nonlinear related surface water quality data. PMID:26761018

Descriptive Characteristics of Surface Water Quality in Hong Kong by a Self-Organising Map.

PubMed

An, Yan; Zou, Zhihong; Li, Ranran

2016-01-08

In this study, principal component analysis (PCA) and a self-organising map (SOM) were used to analyse a complex dataset obtained from the river water monitoring stations in the Tolo Harbor and Channel Water Control Zone (Hong Kong), covering the period of 2009-2011. PCA was initially applied to identify the principal components (PCs) among the nonlinear and complex surface water quality parameters. SOM followed PCA, and was implemented to analyze the complex relationships and behaviors of the parameters. The results reveal that PCA reduced the multidimensional parameters to four significant PCs which are combinations of the original ones. The positive and inverse relationships of the parameters were shown explicitly by pattern analysis in the component planes. It was found that PCA and SOM are efficient tools to capture and analyze the behavior of multivariable, complex, and nonlinear related surface water quality data.

Circadian Role in Daily Pattern of Cardiovascular Risk

NASA Astrophysics Data System (ADS)

Ivanov, Plamen Ch.; Hu, Kun; Chen, Zhi; Hilton, Michael F.; Stanley, H. Eugene; Shea, Steven A.

2004-03-01

Numerous epidemiological studies demonstrate that sudden cardiac death, pulmonary embolism, myocardial infarction, and stroke have a 24-hour daily pattern with a broad peak between 9-11am. Such a daily pattern in cardiovascular risk could be attributable to external factors, such as the daily behavior patterns, including sleep-wake cycles and activity levels, or internal factors, such as the endogenous circadian pacemaker. Findings of significant alternations in the temporal organization and nonlinear properties of heartbeat fluctuations with disease and with sleep-wake transitions raise the intriguing possibility that changes in the mechanism of control associated with behavioral sleep-wake transition may be responsible for the increased cardiac instability observed in particular circadian phases. Alternatively, we hypothesize that there is a circadian clock, independent of the sleep-wake cycle, which affects the cardiac dynamics leading to increased cardiovascular risk. We analyzed continuous recordings from healthy subjects during 7 cycles of forced desynchrony routine wherein subjects' sleep-wake cycles are adjusted to 28 hours so that their behaviors occur across all circadian phases. Heartbeat data were divided into one-hour segments. For each segment, we estimated the correlations and the nonlinear properties of the heartbeat fluctuations at the corresponding circadian phase. Since the sleep and wake contributions are equally weighted in our experiment, a change of the properties of the heartbeat dynamics with circadian phase suggest a circadian rhythm. We show significant circadian-mediated alterations in the correlation and nonlinear properties of the heartbeat resembling those observed in patients with heart failure. Remarkably, these dynamical alterations are centered at 60 degrees circadian phase, coinciding with the 9-11am window of cardiac risk.

A mathematical model to describe the nonlinear elastic properties of the gastrocnemius tendon of chickens.

PubMed

Foutz, T L

1991-03-01

A phenomenological model was developed to describe the nonlinear elastic behavior of the avian gastrocnemius tendon. Quasistatic uniaxial tensile tests were used to apply a deformation and resulting load on the tendon at a deformation rate of 5 mm/min. Plots of deformation versus load indicated a nonlinear loading response. By calculating engineering stress and engineering strain, the experimental data were normalized for tendon shape. The elastic response was determined from stress-strain curves and was found to vary with engineering strain. The response to the applied engineering strain could best be described by a mathematical model that combined a linear function and a nonlinear function. Three parameters in the model were developed to represent the nonlinear elastic behavior of the tendon, thereby allowing analysis of elasticity without prior knowledge of engineering strain. This procedure reduced the amount of data needed for the statistical analysis of nonlinear elasticity.

Preparation, optical and non-linear optical power limiting properties of Cu, CuNi nanowires

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

Udayabhaskar, R.; Karthikeyan, B., E-mail: bkarthik@nitt.edu; Ollakkan, Muhamed Shafi

2014-01-06

Metallic nanowires show excellent Plasmon absorption which is tunable based on its aspect ratio and alloying nature. We prepared Cu and CuNi metallic nanowires and studied its optical and nonlinear optical behavior. Optical properties of nanowires are theoretically explained using Gans theory. Nonlinear optical behavior is studied using a single beam open aperture z-scan method with the use of 5 ns Nd: YAG laser. Optical limiting is found to arise from two-photon absorption.

Preparation, optical and non-linear optical power limiting properties of Cu, CuNi nanowires

NASA Astrophysics Data System (ADS)

Udayabhaskar, R.; Ollakkan, Muhamed Shafi; Karthikeyan, B.

2014-01-01

Metallic nanowires show excellent Plasmon absorption which is tunable based on its aspect ratio and alloying nature. We prepared Cu and CuNi metallic nanowires and studied its optical and nonlinear optical behavior. Optical properties of nanowires are theoretically explained using Gans theory. Nonlinear optical behavior is studied using a single beam open aperture z-scan method with the use of 5 ns Nd: YAG laser. Optical limiting is found to arise from two-photon absorption.

On the structure of nonlinear constitutive equations for fiber reinforced composites

NASA Technical Reports Server (NTRS)

Jansson, Stefan

1992-01-01

The structure of constitutive equations for nonlinear multiaxial behavior of transversely isotropic fiber reinforced metal matrix composites subject to proportional loading was investigated. Results from an experimental program were combined with numerical simulations of the composite behavior for complex stress to reveal the full structure of the equations. It was found that the nonlinear response can be described by a quadratic flow-potential, based on the polynomial stress invariants, together with a hardening rule that is dominated by two different hardening mechanisms.

Nonlinear modeling of chaotic time series: Theory and applications

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

Casdagli, M.; Eubank, S.; Farmer, J.D.

1990-01-01

We review recent developments in the modeling and prediction of nonlinear time series. In some cases apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifyingmore » and quantifying low-dimensional chaotic behavior. During the past few years methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics and human speech. 162 refs., 13 figs.« less

Comparison of in vivo and ex vivo viscoelastic behavior of the spinal cord.

PubMed

Ramo, Nicole L; Shetye, Snehal S; Streijger, Femke; Lee, Jae H T; Troyer, Kevin L; Kwon, Brian K; Cripton, Peter; Puttlitz, Christian M

2018-03-01

Despite efforts to simulate the in vivo environment, post-mortem degradation and lack of blood perfusion complicate the use of ex vivo derived material models in computational studies of spinal cord injury. In order to quantify the mechanical changes that manifest ex vivo, the viscoelastic behavior of in vivo and ex vivo porcine spinal cord samples were compared. Stress-relaxation data from each condition were fit to a non-linear viscoelastic model using a novel characterization technique called the direct fit method. To validate the presented material models, the parameters obtained for each condition were used to predict the respective dynamic cyclic response. Both ex vivo and in vivo samples displayed non-linear viscoelastic behavior with a significant increase in relaxation with applied strain. However, at all three strain magnitudes compared, ex vivo samples experienced a higher stress and greater relaxation than in vivo samples. Significant differences between model parameters also showed distinct relaxation behaviors, especially in non-linear relaxation modulus components associated with the short-term response (0.1-1 s). The results of this study underscore the necessity of utilizing material models developed from in vivo experimental data for studies of spinal cord injury, where the time-dependent properties are critical. The ability of each material model to accurately predict the dynamic cyclic response validates the presented methodology and supports the use of the in vivo model in future high-resolution finite element modeling efforts. Neural tissues (such as the brain and spinal cord) display time-dependent, or viscoelastic, mechanical behavior making it difficult to model how they respond to various loading conditions, including injury. Methods that aim to characterize the behavior of the spinal cord almost exclusively use ex vivo cadaveric or animal samples, despite evidence that time after death affects the behavior compared to that in a living animal (in vivo response). Therefore, this study directly compared the mechanical response of ex vivo and in vivo samples to quantify these differences for the first time. This will allow researchers to draw more accurate conclusions about spinal cord injuries based on ex vivo data (which are easier to obtain) and emphasizes the importance of future in vivo experimental animal work. Copyright © 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Understanding of flux-limited behaviors of heat transport in nonlinear regime

NASA Astrophysics Data System (ADS)

Guo, Yangyu; Jou, David; Wang, Moran

2016-01-01

The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.

Characterization of Time-Dependent Behavior of Ramming Paste Used in an Aluminum Electrolysis Cell

NASA Astrophysics Data System (ADS)

Orangi, Sakineh; Picard, Donald; Alamdari, Houshang; Ziegler, Donald; Fafard, Mario

2015-12-01

A new methodology was proposed for the characterization of time-dependent behavior of materials in order to develop a constitutive model. The material used for the characterization was ramming paste, a porous material used in an aluminum electrolysis cell, which is baked in place under varying loads induced by the thermal expansion of other components of the cell. In order to develop a constitutive model representing the paste mechanical behavior, it was necessary to get some insight into its behavior using samples which had been baked at different temperatures ranging from 200 to 1000 °C. Creep stages, effect of testing temperature on the creep, creep-recovery, as well as nonlinear creep were observed for designing a constitutive law. Uniaxial creep-recovery tests were carried out at two temperatures on the baked paste: ambient and higher. Results showed that the shape of creep curves was similar to a typical creep; recovery happened and the creep was shown to be nonlinear. Those experimental observations and the identification of nonlinear parameters of developed constitutive model demonstrated that the baked paste experiences nonlinear viscoelastic-viscoplastic behavior at different temperatures.

The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2004-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.

A phenomenological intra-laminar plasticity model for FRP composite materials

NASA Astrophysics Data System (ADS)

Zhou, Yinhua; Hou, Chi; Wang, Wenzhi; Zhao, Meiying; Wan, Xiaopeng

2015-07-01

The nonlinearity of fibre-reinforced polymer (FRP) composites have significant effects on the analysis of composite structures. This article proposes a phenomenological intralaminar plasticity model to represent the nonlinearity of FRP composite materials. Based on the model presented by Ladeveze et al., the plastic potential and hardening functions are improved to give a more rational description of phenomenological nonlinearity behavior. A four-parameter hardening model is built to capture important features of the hardening curve and consequently gives the good matching of the experiments. Within the frame of plasticity theory, the detailed constitutive model, the numerical algorithm and the derivation of the tangent stiffness matrix are presented in this study to improve model robustness. This phenomenological model achieved excellent agreement between the experimental and simulation results in element scale respectively for glass fibre-reinforced polymer (GFRP) and carbon fibre-reinforced polymer (CFRP). Moreover, the model is capable of simulating the nonlinear phenomenon of laminates, and good agreement is achieved in nearly all cases.

Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach

NASA Astrophysics Data System (ADS)

Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich

2018-04-01

Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.

Kuznetsov-Ma waves train generation in a left-handed material

NASA Astrophysics Data System (ADS)

Atangana, Jacques; Giscard Onana Essama, Bedel; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Crépin Kofane, Timoléon

2015-03-01

We analyze the behavior of an electromagnetic wave which propagates in a left-handed material. Second-order dispersion and cubic-quintic nonlinearities are considered. This behavior of an electromagnetic wave is modeled by a nonlinear Schrödinger equation which is solved by collective coordinates theory in order to characterize the light pulse intensity profile. More so, a specific frequency range has been outlined where electromagnetic wave behavior will be investigated. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton. When the quintic nonlinearity comes into play, it provokes strong and long internal perturbations which lead to Benjamin-Feir instability. This phenomenon, also called modulational instability, induces appearance of a Kuznetsov-Ma waves train. We numerically verify the validity of Kuznetsov-Ma theory by presenting physical conditions which lead to Kuznetsov-Ma waves train generation. Thereafter, some properties of such waves train are also verified.

MSC products for the simulation of tire behavior

NASA Technical Reports Server (NTRS)

Muskivitch, John C.

1995-01-01

The modeling of tires and the simulation of tire behavior are complex problems. The MacNeal-Schwendler Corporation (MSC) has a number of finite element analysis products that can be used to address the complexities of tire modeling and simulation. While there are many similarities between the products, each product has a number of capabilities that uniquely enable it to be used for a specific aspect of tire behavior. This paper discusses the following programs: (1) MSC/NASTRAN - general purpose finite element program for linear and nonlinear static and dynamic analysis; (2) MSC/ADAQUS - nonlinear statics and dynamics finite element program; (3) MSC/PATRAN AFEA (Advanced Finite Element Analysis) - general purpose finite element program with a subset of linear and nonlinear static and dynamic analysis capabilities with an integrated version of MSC/PATRAN for pre- and post-processing; and (4) MSC/DYTRAN - nonlinear explicit transient dynamics finite element program.

The role of nonlinear viscoelasticity on the functionality of laminating shortenings

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

Macias-Rodriguez, Braulio A.; Peyronel, Fernanda; Marangoni, Alejandro G.

The rheology of fats is essential for the development of homogeneous and continuous layered structures of doughs. Here, we define laminating shortenings in terms of rheological behavior displayed during linear-to-nonlinear shear deformations, investigated by large amplitude oscillatory shear rheology. Likewise, we associate the rheological behavior of the shortenings with structural length scales elucidated by ultra-small angle x-ray scattering and cryo-electron microscopy. Shortenings exhibited solid-like viscoelastic and viscoelastoplastic behaviors in the linear and nonlinear regimes respectively. In the nonlinear region, laminating shortenings dissipated more viscous energy (larger normalized dynamic viscosities) than a cake bakery shortening. The fat solid-like network of laminatingmore » shortening displayed a three-hierarchy structure and layered crystal aggregates, in comparison to two-hierarchy structure and spherical-like crystal aggregates of a cake shortening. We argue that the observed rheology, correlated to the structural network, is crucial for optimal laminating performance of shortenings.« less

Ratcheting in a nonlinear viscoelastic adhesive

NASA Astrophysics Data System (ADS)

Lemme, David; Smith, Lloyd

2017-11-01

Uniaxial time-dependent creep and cycled stress behavior of a standard and toughened film adhesive were studied experimentally. Both adhesives exhibited progressive accumulation of strain from an applied cycled stress. Creep tests were fit to a viscoelastic power law model at three different applied stresses which showed nonlinear response in both adhesives. A third order nonlinear power law model with a permanent strain component was used to describe the creep behavior of both adhesives and to predict creep recovery and the accumulation of strain due to cycled stress. Permanent strain was observed at high stress but only up to 3% of the maximum strain. Creep recovery was under predicted by the nonlinear model, while cycled stress showed less than 3% difference for the first cycle but then over predicted the response above 1000 cycles by 4-14% at high stress. The results demonstrate the complex response observed with structural adhesives, and the need for further analytical advancements to describe their behavior.

Nonlinear Characterization of Half and Full Wavelength Power Ultrasonic Devices

NASA Astrophysics Data System (ADS)

Mathieson, Andrew; Cerisola, Niccolò; Cardoni, Andrea

It is well known that power ultrasonic devices whilst driven under elevated excitation levels exhibit nonlinear behaviors. If no attempt is made to understand and subsequently control these behaviors, these devices can exhibit poor performance or even suffer premature failure. This paper presents an experimental method for the dynamic characterization of a commercial ultrasonic transducer for bone cutting applications (Piezosurgery® Device) operated together with a variety of rod horns that are tuned to operate in a longitudinal mode of vibration. Near resonance responses, excited via a burst sine sweep method were used to identify nonlinear responses exhibited by the devices, while experimental modal analysis was performed to identify the modal parameters of the longitudinal modes of vibration of the assemblies between 0-80 kHz. This study tries to provide an understanding of the effects that geometry and material choices may have on the nonlinear behavior of a tuned device.

Influence of mechanically-induced dilatation on the shape memory behavior of amorphous polymers at large deformation

NASA Astrophysics Data System (ADS)

Hanzon, Drew W.; Lu, Haibao; Yakacki, Christopher M.; Yu, Kai

2018-01-01

In this study, we explore the influence of mechanically-induced dilatation on the thermomechanical and shape memory behavior of amorphous shape memory polymers (SMPs) at large deformation. The uniaxial tension, glass transition, stress relaxation and free recovery behaviors are examined with different strain levels (up to 340% engineering strain). A multi-branched constitutive model that incorporates dilatational effects on the polymer relaxation time is established and applied to assist in discussions and understand the nonlinear viscoelastic behaviors of SMPs. It is shown that the volumetric dilatation results in an SMP network with lower viscosity, faster relaxation, and lower Tg. The influence of the dilatational effect on the thermomechanical behaviors is significant when the polymers are subject to large deformation or in a high viscosity state. The dilation also increases the free recovery rate of SMP at a given recovery temperature. Even though the tested SMPs are far beyond their linear viscoelastic region when a large programming strain is applied, the free recovery behavior still follows the time-temperature superposition (TTSP) if the dilatational effect is considered during the transformation of time scales; however, if the programming strain is different, TTSP fails in predicting the recovery behavior of SMPs because the network has different entropy state and driving force during shape recovery. Since most soft active polymers are subject to large deformation in practice, this study provides a theoretical basis to better understand their nonlinear viscoelastic behaviors, and optimize their performance in engineering applications.

An experimentally based nonlinear viscoelastic model of joint passive moment.

PubMed

Esteki, A; Mansour, J M

1996-04-01

Previous investigations have not converged on a generally accepted model of the dissipative part of joint passive moment. To provide a basis for developing a model, a series of measurements were performed to characterize the passive moment at the metacarpophalangeal joint of the index finger. Two measurement procedures were used, one in moment relaxation over a range of fixed joint angles and the other at a series of constant joint velocities. Fung's quasi-linear viscoelastic theory motivated the development of the passive moment model. Using this approach, it was not necessary to make restrictive assumptions regarding the viscoelastic behavior of the passive moment. The generality of the formulation allowed specific functions to be chosen based on experimental data rather than finding coefficients which attempted to fit a preselected model of the data. It was shown that a nonlinear viscoelastic model described the passive stiffness. No significant frictional effects were found. Of particular importance was the nonlinear behavior of the dissipative part of the passive moment which was modeled by joint speed raised to a power less than one. This result could explain the differing findings among previous investigations, and may have important implications for control of limb movement.

Physical Quality Indicators and Mechanical Behavior of Agricultural Soils of Argentina.

PubMed

Imhoff, Silvia; da Silva, Alvaro Pires; Ghiberto, Pablo J; Tormena, Cássio A; Pilatti, Miguel A; Libardi, Paulo L

2016-01-01

Mollisols of Santa Fe have different tilth and load support capacity. Despite the importance of these attributes to achieve a sustainable crop production, few information is available. The objectives of this study are i) to assess soil physical indicators related to plant growth and to soil mechanical behavior; and ii) to establish relationships to estimate the impact of soil loading on the soil quality to plant growth. The study was carried out on Argiudolls and Hapludolls of Santa Fe. Soil samples were collected to determine texture, organic matter content, bulk density, water retention curve, soil resistance to penetration, least limiting water range, critical bulk density for plant growth, compression index, pre-consolidation pressure and soil compressibility. Water retention curve and soil resistance to penetration were linearly and significantly related to clay and organic matter (R2 = 0.91 and R2 = 0.84). The pedotransfer functions of water retention curve and soil resistance to penetration allowed the estimation of the least limiting water range and critical bulk density for plant growth. A significant nonlinear relationship was found between critical bulk density for plant growth and clay content (R2 = 0.98). Compression index was significantly related to bulk density, water content, organic matter and clay plus silt content (R2 = 0.77). Pre-consolidation pressure was significantly related to organic matter, clay and water content (R2 = 0.77). Soil compressibility was significantly related to initial soil bulk density, clay and water content. A nonlinear and significantly pedotransfer function (R2 = 0.88) was developed to predict the maximum acceptable pressure to be applied during tillage operations by introducing critical bulk density for plant growth in the compression model. The developed pedotransfer function provides a useful tool to link the mechanical behavior and tilth of the soils studied.

Physical Quality Indicators and Mechanical Behavior of Agricultural Soils of Argentina

PubMed Central

Pires da Silva, Alvaro; Ghiberto, Pablo J.; Tormena, Cássio A.; Pilatti, Miguel A.; Libardi, Paulo L.

2016-01-01

Mollisols of Santa Fe have different tilth and load support capacity. Despite the importance of these attributes to achieve a sustainable crop production, few information is available. The objectives of this study are i) to assess soil physical indicators related to plant growth and to soil mechanical behavior; and ii) to establish relationships to estimate the impact of soil loading on the soil quality to plant growth. The study was carried out on Argiudolls and Hapludolls of Santa Fe. Soil samples were collected to determine texture, organic matter content, bulk density, water retention curve, soil resistance to penetration, least limiting water range, critical bulk density for plant growth, compression index, pre-consolidation pressure and soil compressibility. Water retention curve and soil resistance to penetration were linearly and significantly related to clay and organic matter (R2 = 0.91 and R2 = 0.84). The pedotransfer functions of water retention curve and soil resistance to penetration allowed the estimation of the least limiting water range and critical bulk density for plant growth. A significant nonlinear relationship was found between critical bulk density for plant growth and clay content (R2 = 0.98). Compression index was significantly related to bulk density, water content, organic matter and clay plus silt content (R2 = 0.77). Pre-consolidation pressure was significantly related to organic matter, clay and water content (R2 = 0.77). Soil compressibility was significantly related to initial soil bulk density, clay and water content. A nonlinear and significantly pedotransfer function (R2 = 0.88) was developed to predict the maximum acceptable pressure to be applied during tillage operations by introducing critical bulk density for plant growth in the compression model. The developed pedotransfer function provides a useful tool to link the mechanical behavior and tilth of the soils studied. PMID:27099925

Coulomb Blockade in a Two-Dimensional Conductive Polymer Monolayer.

PubMed

Akai-Kasaya, M; Okuaki, Y; Nagano, S; Mitani, T; Kuwahara, Y

2015-11-06

Electronic transport was investigated in poly(3-hexylthiophene-2,5-diyl) monolayers. At low temperatures, nonlinear behavior was observed in the current-voltage characteristics, and a nonzero threshold voltage appeared that increased with decreasing temperature. The current-voltage characteristics could be best fitted using a power law. These results suggest that the nonlinear conductivity can be explained using a Coulomb blockade (CB) mechanism. A model is proposed in which an isotropic extended charge state exists, as predicted by quantum calculations, and percolative charge transport occurs within an array of small conductive islands. Using quantitatively evaluated capacitance values for the islands, this model was found to be capable of explaining the observed experimental data. It is, therefore, suggested that percolative charge transport based on the CB effect is a significant factor giving rise to nonlinear conductivity in organic materials.

Experimental Nonlinear Dynamics and Snap-Through of Post-Buckled Thin Laminated Composite Plates

NASA Astrophysics Data System (ADS)

Kim, Han-Gyu

Modern aerospace systems are increasingly being designed with composite panels and plates to achieve light weight and high specific strength and stiffness. For constrained panels, thermally-induced axial loading may cause buckling of the structure, which can lead to nonlinear and potentially chaotic behavior. When post-buckled composite plates experience snap-through, they are subjected to large-amplitude deformations and in-plane compressive loading. These phenomena pose a potential threat to the structural integrity of composite structures. In this work, the nonlinear dynamic behavior of post-buckled composite plates was investigated experimentally and computationally. For the experimental work, an electrodynamic shaker was used to apply harmonic loads and the dynamic response of plate specimens was measured using a single-point displacement-sensing laser, a double-point laser vibrometer (velocity-sensing), and a set of digital image correlation cameras. Both chaotic and periodic steady-state snap-through behaviors were investigated. The experimental data were used to characterize snap-through behaviors of the post-buckled specimens and their boundaries in the harmonic forcing parameter space. The nonlinear behavior of post-buckled plates was modeled using the classical laminated plate theory (CLPT) and the von Karman strain-displacement relations. The static equilibrium paths of the post-buckled plates were analyzed using an arc-length method with a branch-switching technique. For the dynamic analysis, the nonlinear equations of motion were derived based on CLPT and the nonlinear finite element model of the equations was constructed using the Hermite cubic interpolation functions for both conforming and nonconforming elements. The numerical analyses were conducted using the model and were compared with the experimental data.

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations. Part 2; Global Asymptotic Behavior of Time Discretizations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1995-01-01

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

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

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.

2006-01-01

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

Chaotic behaviors of operational amplifiers.

PubMed

Yim, Geo-Su; Ryu, Jung-Wan; Park, Young-Jai; Rim, Sunghwan; Lee, Soo-Young; Kye, Won-Ho; Kim, Chil-Min

2004-04-01

We investigate nonlinear dynamical behaviors of operational amplifiers. When the output terminal of an operational amplifier is connected to the inverting input terminal, the circuit exhibits period-doubling bifurcation, chaos, and periodic windows, depending on the voltages of the positive and the negative power supplies. We study these nonlinear dynamical characteristics of this electronic circuit experimentally.

The elastic and inelastic behavior of woven graphite fabric reinforced polyimide composites

NASA Astrophysics Data System (ADS)

Searles, Kevin H.

In many aerospace and conventional engineering applications, load-bearing composite structures are designed with the intent of being subjected to uniaxial stresses that are predominantly tensile or compressive. However, it is likely that biaxial and possibly triaxial states of stress will exist throughout the in-service life of the structure or component. The existing paradigm suggests that unidirectional tape materials are superior under uniaxial conditions since the vast majority of fibers lie in-plane and can be aligned to the loading axis. This may be true, but not without detriment to impact performance, interlaminar strength, strain to failure and complexity of part geometry. In circumstances where a sufficient balance of these properties is required, composites based on woven fabric reinforcements become attractive choices. In this thesis, the micro- and mesoscale elastic behavior of composites based on 8HS woven graphite fabric architectures and polyimide matrices is studied analytically and numerically. An analytical model is proposed to predict the composite elastic constants and is verified using numerical strain energy methods of equivalence. The model shows good agreement with the experiments and numerical strain energy equivalence. Lamina stresses generated numerically from in-plane shear loading show substantial shear and transverse normal stress concentrations in the transverse undulated tow which potentially leads to intralaminar damage. The macroscale inelastic behavior of the same composites is also studied experimentally and numerically. On an experimental basis, the biaxial and modified biaxial Iosipescu test methods are employed to study the weaker-mode shear and biaxial failure properties at room and elevated temperatures. On a numerical basis, the macroscale inelastic shear behavior of the composites is studied. Structural nonlinearities and material nonlinearities are identified and resolved. In terms of specimen-to-fixture interactions, load eccentricities, geometric (large strains and rotations) nonlinearities and boundary contact (friction) nonlinearities are explored. In terms of material nonlinearities, anisotropic plasticity and progressive damage are explored. A progressive damage criterion is proposed which accounts for the elastic strain energy densities in three directions. Of the types of nonlinearities studied, the nonlinear shear stress-strain behavior of the composites is principally from progressive intralaminar damage. Structural nonlinearities and elastoplastic deformation appear to be inconsequential.

Nonlinear temperature dependence of glue-induced birefringence in polarization maintaining FBG sensors

NASA Astrophysics Data System (ADS)

Hopf, Barbara; Koch, Alexander W.; Roths, Johannes

2016-05-01

Glue-induced stresses decrease the accuracy of surface-mounted fiber Bragg gratings (FBG). Significant temperature dependent glue-induced birefringence was verified when a thermally cured epoxy-based bonding technique had been used. Determining the peak separation of two azimuthally aligned FBGs in PM fibers combined with a polarization resolved measurement set-up in a temperature range between -30°C and 150°C revealed high glue-induced stresses at low temperatures. Peak separations of about 60 pm and a nonlinear temperature dependence of the glue-induced birefringence due to stress relaxation processes and a visco-elastic behavior of the used adhesive have been shown.

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

Kamışlıoğlu, Miraç, E-mail: m.kamislioglu@gmail.com; Külahcı, Fatih, E-mail: fatihkulahci@firat.edu.tr

Nonlinear time series analysis techniques have large application areas on the geoscience and geophysics fields. Modern nonlinear methods are provided considerable evidence for explain seismicity phenomena. In this study nonlinear time series analysis, fractal analysis and spectral analysis have been carried out for researching the chaotic behaviors of release radon gas ({sup 222}Rn) concentration occurring during seismic events. Nonlinear time series analysis methods (Lyapunov exponent, Hurst phenomenon, correlation dimension and false nearest neighbor) were applied for East Anatolian Fault Zone (EAFZ) Turkey and its surroundings where there are about 35,136 the radon measurements for each region. In this paper weremore » investigated of {sup 222}Rn behavior which it’s used in earthquake prediction studies.« less

Nonlinear wavenumber shift of large amplitude Langmuir waves

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

Li, Dehui, E-mail: dhli@ipp.ac.cn; Wang, Shaojie

2016-07-15

Nonlinear particle-in-cell simulation is carried out to investigate the nonlinear behavior of the Langmuir wave launched with a fixed frequency in a uniform plasma. It is found that in the strong driving case, the launched wave propagates in a phase velocity larger than that predicted by the linear theory; there appears a nonlinear down-shift of wavenumber. The phase velocity of the nonlinear wave and the down-shift of the wavenumber are demonstrated to be determined by the velocity of nonlinearly accelerated resonant electrons.

Simple quasi-analytical holonomic homogenization model for the non-linear analysis of in-plane loaded masonry panels: Part 1, meso-scale

NASA Astrophysics Data System (ADS)

Milani, G.; Bertolesi, E.

2017-07-01

A simple quasi analytical holonomic homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented. The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and non-linear interfaces (mortar). A holonomic behavior with softening is assumed for mortar. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how homogenized stress-strain behavior can be evaluated semi-analytically.

Stress-enhanced gelation: a dynamic nonlinearity of elasticity.

PubMed

Yao, Norman Y; Broedersz, Chase P; Depken, Martin; Becker, Daniel J; Pollak, Martin R; Mackintosh, Frederick C; Weitz, David A

2013-01-04

A hallmark of biopolymer networks is their sensitivity to stress, reflected by pronounced nonlinear elastic stiffening. Here, we demonstrate a distinct dynamical nonlinearity in biopolymer networks consisting of filamentous actin cross-linked by α-actinin-4. Applied stress delays the onset of relaxation and flow, markedly enhancing gelation and extending the regime of solidlike behavior to much lower frequencies. We show that this macroscopic network response can be accounted for at the single molecule level by the increased binding affinity of the cross-linker under load, characteristic of catch-bond-like behavior.

Nonlinear analysis of pupillary dynamics.

PubMed

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. (c) autonomic stimulation is partially reflected in nonlinear dynamics.

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

PubMed

Harvey, Gerald; Gachagan, Anthony

2011-04-01

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

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

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

2002-01-01

This talk describes some of the building blocks 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.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.

2005-01-01

This chapter describes some of the building blocks 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.

Reproducing the nonlinear dynamic behavior of a structured beam with a generalized continuum model

NASA Astrophysics Data System (ADS)

Vila, J.; Fernández-Sáez, J.; Zaera, R.

2018-04-01

In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

NASA Technical Reports Server (NTRS)

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

2001-01-01

This chapter describes some of the building blocks 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.

Neuromechanical tuning of nonlinear postural control dynamics

NASA Astrophysics Data System (ADS)

Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.

2009-06-01

Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

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

2007-11-01

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

Optical rogue waves generation in a nonlinear metamaterial

NASA Astrophysics Data System (ADS)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY

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

Deng, L. H.; Xiang, Y. Y.; Dun, G. T.

The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaoticmore » attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.« less

Chameleon's behavior of modulable nonlinear electrical transmission line

NASA Astrophysics Data System (ADS)

Togueu Motcheyo, A. B.; Tchinang Tchameu, J. D.; Fewo, S. I.; Tchawoua, C.; Kofane, T. C.

2017-12-01

We show that modulable discrete nonlinear transmission line can adopt Chameleon's behavior due to the fact that, without changing its appearance structure, it can become alternatively purely right or left handed line which is different to the composite one. Using a quasidiscrete approximation, we derive a nonlinear Schrödinger equation, that predicts accurately the carrier frequency threshold from the linear analysis. It appears that the increasing of the linear capacitor in parallel in the series branch induced the selectivity of the filter in the right-handed region while it increases band pass filter in the left-handed region. Numerical simulations of the nonlinear model confirm the forward wave in the right handed line and the backward wave in the left handed one.

Controllable rogue waves in the nonautonomous nonlinear system with a linear potential

NASA Astrophysics Data System (ADS)

Dai, C. Q.; Zheng, C. L.; Zhu, H. P.

2012-04-01

Based on the similarity transformation connected the nonautonomous nonlinear Schrödinger equation with the autonomous nonlinear Schrödinger equation, we firstly derive self-similar rogue wave solutions (rational solutions) for the nonautonomous nonlinear system with a linear potential. Then, we investigate the controllable behaviors of one-rogue wave, two-rogue wave and rogue wave triplets in a soliton control system. Our results demonstrate that the propagation behaviors of rogue waves, including postpone, sustainment, recurrence and annihilation, can be manipulated by choosing the relation between the maximum value of the effective propagation distance Z m and the parameter Z 0. Moreover, the excitation time of controllable rogue waves is decided by the parameter T 0.

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

A Nonlinear Viscoelastic Model for Ceramics at High Temperatures

NASA Technical Reports Server (NTRS)

Powers, Lynn M.; Panoskaltsis, Vassilis P.; Gasparini, Dario A.; Choi, Sung R.

2002-01-01

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the nonlinear, asymmetric time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Element deletion has been implemented within ABAQUS. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. The analytical model is intended to be used to predict the creep rupture lives of ceramic parts in arbitrary stress conditions.

Nonlinear differential system applied of a mechanical plan model of the automotives used for the nonlinear stability analysis

NASA Astrophysics Data System (ADS)

Simniceanu, Loreta; Mihaela, Bogdan; Otat, Victor; Trotea, Mario

2017-10-01

This paper proposes a plan mechanical model for the vehicles with two axles, taking into account the lateral deflection of the tire. For this mechanical model are determined two mathematical models under the nonlinear differential equations systems form without taking into account the action of the driver and taking into account. The analysis of driver-vehicle system consists in the mathematical description of vehicle dynamics, coupled with the possibilities and limits of the human factor. Description seeks to emphasize the significant influence of the driver in handling and stability analyzes of vehicles and vehicle-driver system stability until the advent of skidding. These mathematical models are seen as very useful tools to analyzing the vehicles stability. The paper analyzes the influence of some parameters of the vehicle on its behavior in terms of stability of dynamic systems.

Nonlinear modeling and dynamic analysis of a hydro-turbine governing system in the process of sudden load increase transient

NASA Astrophysics Data System (ADS)

Li, Huanhuan; Chen, Diyi; Zhang, Hao; Wang, Feifei; Ba, Duoduo

2016-12-01

In order to study the nonlinear dynamic behaviors of a hydro-turbine governing system in the process of sudden load increase transient, we establish a novel nonlinear dynamic model of the hydro-turbine governing system which considers the elastic water-hammer model of the penstock and the second-order model of the generator. The six nonlinear dynamic transfer coefficients of the hydro-turbine are innovatively proposed by utilizing internal characteristics and analyzing the change laws of the characteristic parameters of the hydro-turbine governing system. Moreover, from the point of view of engineering, the nonlinear dynamic behaviors of the above system are exhaustively investigated based on bifurcation diagrams and time waveforms. More importantly, all of the above analyses supply theoretical basis for allowing a hydropower station to maintain a stable operation in the process of sudden load increase transient.

Three-photon absorption and nonlinear refraction of BaMgF4 in the ultraviolet region.

PubMed

Ma, Yanzhi; Chen, Junjie; Zheng, Yuanlin; Chen, Xianfeng

2012-08-01

The nonlinear refraction and nonlinear absorption phenomena are investigated in BaMgF(4) single crystal using the Z-scan technique in the ultraviolet region with a pulsed laser at 400 nm with 1 ps pulse duration. The remarkable nonlinear absorption behavior is identified to be three-photon absorption under the experimental conditions. In addition, both nonlinear refraction and nonlinear absorption have relatively large values and possess small anisotropy along three different crystallographic axes. The large values of nonlinear refractive index are demonstrated through the self-phase modulation effect.

Effect of Processing Conditions on the Anelastic Behavior of Plasma Sprayed Thermal Barrier Coatings

NASA Astrophysics Data System (ADS)

Viswanathan, Vaishak

2011-12-01

Plasma sprayed ceramic materials contain an assortment of micro-structural defects, including pores, cracks, and interfaces arising from the droplet based assemblage of the spray deposition technique. The defective architecture of the deposits introduces a novel "anelastic" response in the coatings comprising of their non-linear and hysteretic stress-strain relationship under mechanical loading. It has been established that this anelasticity can be attributed to the relative movement of the embedded defects under varying stresses. While the non-linear response of the coatings arises from the opening/closure of defects, hysteresis is produced by the frictional sliding among defect surfaces. Recent studies have indicated that anelastic behavior of coatings can be a unique descriptor of their mechanical behavior and related to the defect configuration. In this dissertation, a multi-variable study employing systematic processing strategies was conducted to augment the understanding on various aspects of the reported anelastic behavior. A bi-layer curvature measurement technique was adapted to measure the anelastic properties of plasma sprayed ceramic. The quantification of anelastic parameters was done using a non-linear model proposed by Nakamura et.al. An error analysis was conducted on the technique to know the available margins for both experimental as well as computational errors. The error analysis was extended to evaluate its sensitivity towards different coating microstructure. For this purpose, three coatings with significantly different microstructures were fabricated via tuning of process parameters. Later the three coatings were also subjected to different strain ranges systematically, in order to understand the origin and evolution of anelasticity on different microstructures. The last segment of this thesis attempts to capture the intricacies on the processing front and tries to evaluate and establish a correlation between them and the anelastic parameters.

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

PubMed

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

2017-06-12

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

Evidences of grain boundary capacitance effect on the colossal dielectric permittivity in (Nb + In) co-doped TiO2 ceramics

PubMed Central

Li, Jinglei; Li, Fei; Li, Chao; Yang, Guang; Xu, Zhuo; Zhang, Shujun

2015-01-01

The (Nb + In) co-doped TiO2 ceramics were synthesized by conventional solid-state sintering (CSSS) and spark plasma sintering (SPS) methods. The phases and microstructures were studied by X-ray diffraction, Raman spectra, field-emission scanning electron microscopy and transmission electron microscopy, indicating that both samples were in pure rutile phase while showing significant difference in grain size. The dielectric and I–V behaviors of SPS and CSSS samples were investigated. Though both possess colossal permittivity (CP), the SPS samples exhibited much higher dielectric permittivity/loss factor and lower breakdown electric field when compared to their CSSS counterparts. To further explore the origin of CP in co-doped TiO2 ceramics, the I–V behavior was studied on single grain and grain boundary in CSSS sample. The nearly ohmic I–V behavior was observed in single grain, while GBs showed nonlinear behavior and much higher resistance. The higher dielectric permittivity and lower breakdown electric field in SPS samples, thus, were thought to be associated with the feature of SPS, by which reduced space charges and/or impurity segregation can be achieved at grain boundaries. The present results support that the grain boundary capacitance effect plays an important role in the CP and nonlinear I–V behavior of (Nb + In) co-doped TiO2 ceramics. PMID:25656713

Evidences of grain boundary capacitance effect on the colossal dielectric permittivity in (Nb + In) co-doped TiO2 ceramics

NASA Astrophysics Data System (ADS)

Li, Jinglei; Li, Fei; Li, Chao; Yang, Guang; Xu, Zhuo; Zhang, Shujun

2015-02-01

The (Nb + In) co-doped TiO2 ceramics were synthesized by conventional solid-state sintering (CSSS) and spark plasma sintering (SPS) methods. The phases and microstructures were studied by X-ray diffraction, Raman spectra, field-emission scanning electron microscopy and transmission electron microscopy, indicating that both samples were in pure rutile phase while showing significant difference in grain size. The dielectric and I-V behaviors of SPS and CSSS samples were investigated. Though both possess colossal permittivity (CP), the SPS samples exhibited much higher dielectric permittivity/loss factor and lower breakdown electric field when compared to their CSSS counterparts. To further explore the origin of CP in co-doped TiO2 ceramics, the I-V behavior was studied on single grain and grain boundary in CSSS sample. The nearly ohmic I-V behavior was observed in single grain, while GBs showed nonlinear behavior and much higher resistance. The higher dielectric permittivity and lower breakdown electric field in SPS samples, thus, were thought to be associated with the feature of SPS, by which reduced space charges and/or impurity segregation can be achieved at grain boundaries. The present results support that the grain boundary capacitance effect plays an important role in the CP and nonlinear I-V behavior of (Nb + In) co-doped TiO2 ceramics.

Evidences of grain boundary capacitance effect on the colossal dielectric permittivity in (Nb + In) co-doped TiO2 ceramics.

PubMed

Li, Jinglei; Li, Fei; Li, Chao; Yang, Guang; Xu, Zhuo; Zhang, Shujun

2015-02-06

The (Nb + In) co-doped TiO2 ceramics were synthesized by conventional solid-state sintering (CSSS) and spark plasma sintering (SPS) methods. The phases and microstructures were studied by X-ray diffraction, Raman spectra, field-emission scanning electron microscopy and transmission electron microscopy, indicating that both samples were in pure rutile phase while showing significant difference in grain size. The dielectric and I-V behaviors of SPS and CSSS samples were investigated. Though both possess colossal permittivity (CP), the SPS samples exhibited much higher dielectric permittivity/loss factor and lower breakdown electric field when compared to their CSSS counterparts. To further explore the origin of CP in co-doped TiO2 ceramics, the I-V behavior was studied on single grain and grain boundary in CSSS sample. The nearly ohmic I-V behavior was observed in single grain, while GBs showed nonlinear behavior and much higher resistance. The higher dielectric permittivity and lower breakdown electric field in SPS samples, thus, were thought to be associated with the feature of SPS, by which reduced space charges and/or impurity segregation can be achieved at grain boundaries. The present results support that the grain boundary capacitance effect plays an important role in the CP and nonlinear I-V behavior of (Nb + In) co-doped TiO2 ceramics.

Thermo-elastoviscoplastic snapthrough behavior of cylindrical panels

NASA Technical Reports Server (NTRS)

Song, Y.; Simitses, G. J.

1992-01-01

The thermo-elastoviscoplastic snapthrough behavior of simply supported cylindrical panels is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations which include both Bodner-Partom's and Walker's material models. A finite element approach is employed to predict the inelastic buckling behavior. Numerical examples are given to demonstrate the effects of several parameters which include the temperature, thickness and flatness of the panel. Comparisons of buckling responses between Bodner-Partom's model and Walker's model are given. The creep buckling behavior, as an example of time-dependent inelastic deformation, is also presented.

Nonlinear Analysis of Surface EMG Time Series of Back Muscles

NASA Astrophysics Data System (ADS)

Dolton, Donald C.; Zurcher, Ulrich; Kaufman, Miron; Sung, Paul

2004-10-01

A nonlinear analysis of surface electromyography time series of subjects with and without low back pain is presented. The mean-square displacement and entropy shows anomalous diffusive behavior on intermediate time range 10 ms < t < 1 s. This behavior implies the presence of correlations in the signal. We discuss the shape of the power spectrum of the signal.

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 transport.

A stochastic model for correlated protein motions

NASA Astrophysics Data System (ADS)

Karain, Wael I.; Qaraeen, Nael I.; Ajarmah, Basem

2006-06-01

A one-dimensional Langevin-type stochastic difference equation is used to find the deterministic and Gaussian contributions of time series representing the projections of a Bovine Pancreatic Trypsin Inhibitor (BPTI) protein molecular dynamics simulation along different eigenvector directions determined using principal component analysis. The deterministic part shows a distinct nonlinear behavior only for eigenvectors contributing significantly to the collective protein motion.

Sub transitional and supersonic travelling field response in nonlinear viscoelastic media

NASA Technical Reports Server (NTRS)

Padovan, Joe

1989-01-01

This paper considers the problem of traveling fields in nonlinearly elastic and viscoelastic media. By introducing the appropriate hierarchical partitioning, the governing equations of motion are shown to be a continuum analogy of Duffing's equation. Through the use of a constrained perturbation procedure, the response behavior is obtained in sub, transitional as well as supersonic ranges of disturbance speed. Due to the generality of the approach taken, the effects of damping can be handled. To quantify the effects of material nonlinearity, strain softening and hardening are considered. Such behavior is quantified in general example problems.

Effects of graphene quantum dots on linear and nonlinear optical behavior of malignant ovarian cells

NASA Astrophysics Data System (ADS)

Mohajer, Salman; Ara, Mohammad Hossein Majles; Serahatjoo, Leila

2016-07-01

We investigate linear and nonlinear optical properties of standard human ovarian cancer cells (cell line: A2780cp) in vitro. Cells were treated by graphene quantum dots (GQDs) with two special concentrations. Nontoxicity of GQDs was examined in standard biological viability tests. Cancerous cells were fixed on a glass slide; then, interaction of light with biofilms was studied in linear and nonlinear regimes. Absorption spectra of untreated biofilms and biofilms with two different concentrations of GQDs was studied by UV-visible spectrophotometer. Optical behavior of biofilms in a linear regime of intensity (with low-intensity laser exposure) was reported using a simple optical setup. After that, we compared the attenuation of light in biofilm of cancerous cells with and without GQDs. Nonlinear behavior of these biofilms was investigated by a Z-scan setup using a continued wave He-Ne laser. Results showed that GQDs decreased the extinction coefficient and changed the sign and exact value of the nonlinear refractive index of malignant ovarian cells noticeably. The nonlinear refractive index of studied cells with no GQDs treatment was in the order of 10-8 (cm2/w) with a positive sign. This quantity changed to the same order of magnitude with a negative sign after GQDs treatment. Thus, GQDs can be used for cancer diagnosis under laser irradiation.

No evidence of nonlinear effects of predator density, refuge availability, or body size of prey on prey mortality rates.

PubMed

Simkins, Richard M; Belk, Mark C

2017-08-01

Predator density, refuge availability, and body size of prey can all affect the mortality rate of prey. We assume that more predators will lead to an increase in prey mortality rate, but behavioral interactions between predators and prey, and availability of refuge, may lead to nonlinear effects of increased number of predators on prey mortality rates. We tested for nonlinear effects in prey mortality rates in a mesocosm experiment with different size classes of western mosquitofish ( Gambusia affinis ) as the prey, different numbers of green sunfish ( Lepomis cyanellus ) as the predators, and different levels of refuge. Predator number and size class of prey, but not refuge availability, had significant effects on the mortality rate of prey. Change in mortality rate of prey was linear and equal across the range of predator numbers. Each new predator increased the mortality rate by about 10% overall, and mortality rates were higher for smaller size classes. Predator-prey interactions at the individual level may not scale up to create nonlinearity in prey mortality rates with increasing predator density at the population level.

Nonlinear Alfvén wave propagating in ideal MHD plasmas

NASA Astrophysics Data System (ADS)

Zheng, Jugao; Chen, Yinhua; Yu, Mingyang

2016-01-01

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

Nonlinear Tracking Control of a Conductive Supercoiled Polymer Actuator.

PubMed

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

2018-04-01

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

Model of anisotropic nonlinearity in self-defocusing photorefractive media.

PubMed

Barsi, C; Fleischer, J W

2015-09-21

We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.

Breadth of Extracurricular Participation and Adolescent Adjustment Among African-American and European-American Youth

PubMed Central

Fredricks, Jennifer A.; Eccles, Jacquelynne S.

2012-01-01

We examined the linear and nonlinear relations between breadth of extracurricular participation in 11th grade and developmental outcomes at 11th grade and 1 year after high school in an economically diverse sample of African-American and European-American youth. In general, controlling for demographic factors, children's motivation, and the dependent variable measured 3 years earlier, breadth was positively associated with indicators of academic adjustment at 11th grade and at 1 year after high school. In addition, for the three academic outcomes (i.e., grades, educational expectations, and educational status) the nonlinear function was significant; at high levels of involvement the well-being of youth leveled off or declined slightly. In addition, breadth of participation at 11th grade predicted lower internalizing behavior, externalizing behavior, alcohol use, and marijuana use at 11th grade. Finally, the total number of extracurricular activities at 11th grade was associated with civic engagement 2 years later. PMID:22837637

Superior optical nonlinearity of an exceptional fluorescent stilbene dye

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

He, Tingchao; Division of Physics and Applied Physics, Centre for Disruptive Photonic Technologies; Sreejith, Sivaramapanicker

2015-03-16

Strong multiphoton absorption and harmonic generation in organic fluorescent chromophores are, respectively, significant in many fields of research. However, most of fluorescent chromophores fall short of the full potential due to the absence of the combination of such different nonlinear upconversion behaviors. Here, we demonstrate that an exceptional fluorescent stilbene dye could exhibit efficient two- and three-photon absorption under the excitation of femtosecond pulses in solution phase. Benefiting from its biocompatibility and strong excited state absorption behavior, in vitro two-photon bioimaging and superior optical limiting have been exploited, respectively. Simultaneously, the chromophore could generate efficient three-photon excited fluorescence and third-harmonicmore » generation (THG) when dispersed into PMMA film, circumventing the limitations of classical fluorescent chromophores. Such chromophore may find application in the production of coherent light sources of higher photon energy. Moreover, the combination of three-photon excited fluorescence and THG can be used in tandem to provide complementary information in biomedical studies.« less

Breadth of Extracurricular Participation and Adolescent Adjustment Among African-American and European-American Youth.

PubMed

Fredricks, Jennifer A; Eccles, Jacquelynne S

2010-06-01

We examined the linear and nonlinear relations between breadth of extracurricular participation in 11th grade and developmental outcomes at 11th grade and 1 year after high school in an economically diverse sample of African-American and European-American youth. In general, controlling for demographic factors, children's motivation, and the dependent variable measured 3 years earlier, breadth was positively associated with indicators of academic adjustment at 11th grade and at 1 year after high school. In addition, for the three academic outcomes (i.e., grades, educational expectations, and educational status) the nonlinear function was significant; at high levels of involvement the well-being of youth leveled off or declined slightly. In addition, breadth of participation at 11th grade predicted lower internalizing behavior, externalizing behavior, alcohol use, and marijuana use at 11th grade. Finally, the total number of extracurricular activities at 11th grade was associated with civic engagement 2 years later.

A nonlinear delayed model for the immune response in the presence of viral mutation

NASA Astrophysics Data System (ADS)

Messias, D.; Gleria, Iram; Albuquerque, S. S.; Canabarro, Askery; Stanley, H. E.

2018-02-01

We consider a delayed nonlinear model of the dynamics of the immune system against a viral infection that contains a wild-type virus and a mutant. We consider the finite response time of the immune system and find sustained oscillatory behavior as well as chaotic behavior triggered by the presence of delays. We present a numeric analysis and some analytical results.

Materials for Adaptive Structural Acoustic Control. Volume 2

DTIC Science & Technology

1994-04-11

Cross. Effects of Electrodes and Elecu’oding Methods on Fatigue Behavior in Ferroelectric Materials. Ferroelectrics: Proceedings of IMF8, Gaithersburg...describe the linear piezoelectric behavior of ferroelectric ceramics. We have generalized this model to describe the nonlinear effects resulting from...report some of the nonlinear effects under resonant conditions for a PZT-501A ceramic. Figure 8 shows the complex admittance circles at different

Study of a Steel’s Energy Absorption System for Heavy Quadricycles and Nonlinear Explicit Dynamic Analysis of its Behavior under Impact by FEM

PubMed Central

López Campos, José Ángel; Segade Robleda, Abraham; Vilán Vilán, José Antonio; García Nieto, Paulino José; Blanco Cordero, Javier

2015-01-01

Current knowledge of the behavior of heavy quadricycles under impact is still very poor. One of the most significant causes is the lack of energy absorption in the vehicle frame or its steel chassis structure. For this reason, special steels (with yield stresses equal to or greater than 350 MPa) are commonly used in the automotive industry due to their great strain hardening properties along the plastic zone, which allows good energy absorption under impact. This paper presents a proposal for a steel quadricycle energy absorption system which meets the percentages of energy absorption for conventional vehicles systems. This proposal is validated by explicit dynamics simulation, which will define the whole problem mathematically and verify behavior under impact at speeds of 40 km/h and 56 km/h using the finite element method (FEM). One of the main consequences of this study is that this FEM–based methodology can tackle high nonlinear problems like this one with success, avoiding the need to carry out experimental tests, with consequent economical savings since experimental tests are very expensive. Finally, the conclusions from this innovative research work are given. PMID:28793607

Study of a Steel's Energy Absorption System for Heavy Quadricycles and Nonlinear Explicit Dynamic Analysis of its Behavior under Impact by FEM.

PubMed

López Campos, José Ángel; Segade Robleda, Abraham; Vilán Vilán, José Antonio; García Nieto, Paulino José; Blanco Cordero, Javier

2015-10-10

Current knowledge of the behavior of heavy quadricycles under impact is still very poor. One of the most significant causes is the lack of energy absorption in the vehicle frame or its steel chassis structure. For this reason, special steels (with yield stresses equal to or greater than 350 MPa) are commonly used in the automotive industry due to their great strain hardening properties along the plastic zone, which allows good energy absorption under impact. This paper presents a proposal for a steel quadricycle energy absorption system which meets the percentages of energy absorption for conventional vehicles systems. This proposal is validated by explicit dynamics simulation, which will define the whole problem mathematically and verify behavior under impact at speeds of 40 km/h and 56 km/h using the finite element method (FEM). One of the main consequences of this study is that this FEM-based methodology can tackle high nonlinear problems like this one with success, avoiding the need to carry out experimental tests, with consequent economical savings since experimental tests are very expensive. Finally, the conclusions from this innovative research work are given.

Phase-space topography characterization of nonlinear ultrasound waveforms.

PubMed

Dehghan-Niri, Ehsan; Al-Beer, Helem

2018-03-01

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

Maximum Likelihood Analysis of Nonlinear Structural Equation Models with Dichotomous Variables

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2005-01-01

In this article, a maximum likelihood approach is developed to analyze structural equation models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the structural equation in the model is defined by a nonlinear function. The basic idea of the…

Experimental study of nonlinear ultrasonic behavior of soil materials during the compaction.

PubMed

Chen, Jun; Wang, Hao; Yao, Yangping

2016-07-01

In this paper, the nonlinear ultrasonic behavior of unconsolidated granular medium - soil during the compaction is experimentally studied. The second harmonic generation technique is adopted to investigate the change of microstructural void in materials during the compaction process of loose soils. The nonlinear parameter is measured with the change of two important environmental factors i.e. moisture content and impact energy of compaction. It is found the nonlinear parameter of soil material presents a similar variation pattern with the void ratio of soil samples, corresponding to the increased moisture content and impact energy. A same optimum moisture content is found by observing the variation of nonlinear parameter and void ratio with respect to moisture content. The results indicate that the unconsolidated soil is manipulated by a strong material nonlinearity during the compaction procedure. The developed experimental technique based on the second harmonic generation could be a fast and convenient testing method for the determination of optimum moisture content of soil materials, which is very useful for the better compaction effect of filled embankment for civil infrastructures in-situ. Copyright © 2016 Elsevier B.V. All rights reserved.

Dynamic control and information processing in chemical reaction systems by tuning self-organization behavior

NASA Astrophysics Data System (ADS)

Lebiedz, Dirk; Brandt-Pollmann, Ulrich

2004-09-01

Specific external control of chemical reaction systems and both dynamic control and signal processing as central functions in biochemical reaction systems are important issues of modern nonlinear science. For example nonlinear input-output behavior and its regulation are crucial for the maintainance of the life process that requires extensive communication between cells and their environment. An important question is how the dynamical behavior of biochemical systems is controlled and how they process information transmitted by incoming signals. But also from a general point of view external forcing of complex chemical reaction processes is important in many application areas ranging from chemical engineering to biomedicine. In order to study such control issues numerically, here, we choose a well characterized chemical system, the CO oxidation on Pt(110), which is interesting per se as an externally forced chemical oscillator model. We show numerically that tuning of temporal self-organization by input signals in this simple nonlinear chemical reaction exhibiting oscillatory behavior can in principle be exploited for both specific external control of dynamical system behavior and processing of complex information.

Nonlinear crack analysis with finite elements

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Saleme, E.; Pifko, A.; Levine, H. S.

1973-01-01

The application of finite element techniques to the analytic representation of the nonlinear behavior of arbitrary two-dimensional bodies containing cracks is discussed. Specific methods are proposed using which it should be possible to obtain information concerning: the description of the maximum, minimum, and residual near-tip stress and strain fields; the effects of crack closure on the near-tip behavior of stress and strain fields during cyclic loading into the plastic range; the stress-strain and displacement field behavior associated with a nonstationary crack; and the effects of large rotation near the crack tip.

Influences of hydraulic gradient, surface roughness, intersecting angle, and scale effect on nonlinear flow behavior at single fracture intersections

NASA Astrophysics Data System (ADS)

Li, Bo; Liu, Richeng; Jiang, Yujing

2016-07-01

Fluid flow tests were conducted on two crossed fracture models for which the geometries of fracture segments and intersections were measured by utilizing a visualization technique using a CCD (charged coupled device) camera. Numerical simulations by solving the Navier-Stokes equations were performed to characterize the fluid flow at fracture intersections. The roles of hydraulic gradient, surface roughness, intersecting angle, and scale effect in the nonlinear fluid flow behavior through single fracture intersections were investigated. The simulation results of flow rate agreed well with the experimental results for both models. The experimental and simulation results showed that with the increment of the hydraulic gradient, the ratio of the flow rate to the hydraulic gradient, Q/J, decreases and the relative difference of Q/J between the calculation results employing the Navier-Stokes equations and the cubic law, δ, increases. When taking into account the fracture surface roughness quantified by Z2 ranging 0-0.42 for J = 1, the value of δ would increase by 0-10.3%. The influences of the intersecting angle on the normalized flow rate that represents the ratio of the flow rate in a segment to the total flow rate, Ra, and the ratio of the hydraulic aperture to the mechanical aperture, e/E, are negligible when J < 10-3, whereas their values change significantly when J > 10-2. Based on the regression analysis on simulation results, a mathematical expression was proposed to quantify e/E, involving variables of J and Rr, where Rr is the radius of truncating circles centered at an intersection. For E/Rr > 10-2, e/E varies significantly and the scale of model has large impacts on the nonlinear flow behavior through intersections, while for E/Rr < 10-3, the scale effect is negligibly small. Finally, a necessary condition to apply the cubic law to fluid flow through fracture intersections is suggested as J < 10-3, E/Rr < 10-3, and Z2 = 0.

Study of critical behavior in concrete during curing by application of dynamic linear and nonlinear means.

PubMed

Lacouture, Jean-Christoph; Johnson, Paul A; Cohen-Tenoudji, Frederic

2003-03-01

The monitoring of both linear and nonlinear elastic properties of a high performance concrete during curing is presented by application of compressional and shear waves. To follow the linear elastic behavior, both compressional and shear waves are used in wide band pulse echo mode. Through the value of the complex reflection coefficient between the cell material (Lucite) and the concrete within the cell, the elastic moduli are calculated. Simultaneously, the transmission of a continuous compressional sine wave at progressively increasing drive levels permits us to calculate the nonlinear properties by extracting the harmonics amplitudes of the signal. Information regarding the chemical evolution of the concrete based upon the reaction of hydration of cement is obtained by monitoring the temperature inside the sample. These different types of measurements are linked together to interpret the critical behavior.

Nonlinear electromechanical modelling and dynamical behavior analysis of a satellite reaction wheel

NASA Astrophysics Data System (ADS)

Aghalari, Alireza; Shahravi, Morteza

2017-12-01

The present research addresses the satellite reaction wheel (RW) nonlinear electromechanical coupling dynamics including dynamic eccentricity of brushless dc (BLDC) motor and gyroscopic effects, as well as dry friction of shaft-bearing joints (relative small slip) and bearing friction. In contrast to other studies, the rotational velocity of the flywheel is considered to be controllable, so it is possible to study the reaction wheel dynamical behavior in acceleration stages. The RW is modeled as a three-phases BLDC motor as well as flywheel with unbalances on a rigid shaft and flexible bearings. Improved Lagrangian dynamics for electromechanical systems is used to obtain the mathematical model of the system. The developed model can properly describe electromechanical nonlinear coupled dynamical behavior of the satellite RW. Numerical simulations show the effectiveness of the presented approach.

Early-Stage Visual Processing and Cortical Amplification Deficits in Schizophrenia

PubMed Central

Butler, Pamela D.; Zemon, Vance; Schechter, Isaac; Saperstein, Alice M.; Hoptman, Matthew J.; Lim, Kelvin O.; Revheim, Nadine; Silipo, Gail; Javitt, Daniel C.

2005-01-01

Background Patients with schizophrenia show deficits in early-stage visual processing, potentially reflecting dysfunction of the magnocellular visual pathway. The magnocellular system operates normally in a nonlinear amplification mode mediated by glutamatergic (N-methyl-d-aspartate) receptors. Investigating magnocellular dysfunction in schizophrenia therefore permits evaluation of underlying etiologic hypotheses. Objectives To evaluate magnocellular dysfunction in schizophrenia, relative to known neurochemical and neuroanatomical substrates, and to examine relationships between electrophysiological and behavioral measures of visual pathway dysfunction and relationships with higher cognitive deficits. Design, Setting, and Participants Between-group study at an inpatient state psychiatric hospital and out-patient county psychiatric facilities. Thirty-three patients met DSM-IV criteria for schizophrenia or schizoaffective disorder, and 21 nonpsychiatric volunteers of similar ages composed the control group. Main Outcome Measures (1) Magnocellular and parvocellular evoked potentials, analyzed using nonlinear (Michaelis-Menten) and linear contrast gain approaches; (2) behavioral contrast sensitivity measures; (3) white matter integrity; (4) visual and nonvisual neuropsychological measures, and (5) clinical symptom and community functioning measures. Results Patients generated evoked potentials that were significantly reduced in response to magnocellular-biased, but not parvocellular-biased, stimuli (P=.001). Michaelis-Menten analyses demonstrated reduced contrast gain of the magnocellular system (P=.001). Patients showed decreased contrast sensitivity to magnocellular-biased stimuli (P<.001). Evoked potential deficits were significantly related to decreased white matter integrity in the optic radiations (P<.03). Evoked potential deficits predicted impaired contrast sensitivity (P=.002), which was in turn related to deficits in complex visual processing (P≤.04). Both evoked potential (P≤.04) and contrast sensitivity (P=.01) measures significantly predicted community functioning. Conclusions These findings confirm the existence of early-stage visual processing dysfunction in schizophrenia and provide the first evidence that such deficits are due to decreased nonlinear signal amplification, consistent with glutamatergic theories. Neuroimaging studies support the hypothesis of dysfunction within low-level visual pathways involving thalamocortical radiations. Deficits in early-stage visual processing significantly predict higher cognitive deficits. PMID:15867102

Temperature dependent nonlinear metal matrix laminae behavior

NASA Technical Reports Server (NTRS)

Barrett, D. J.; Buesking, K. W.

1986-01-01

An analytical method is described for computing the nonlinear thermal and mechanical response of laminated plates. The material model focuses upon the behavior of metal matrix materials by relating the nonlinear composite response to plasticity effects in the matrix. The foundation of the analysis is the unidirectional material model which is used to compute the instantaneous properties of the lamina based upon the properties of the fibers and matrix. The unidirectional model assumes that the fibers properties are constant with temperature and assumes that the matrix can be modelled as a temperature dependent, bilinear, kinematically hardening material. An incremental approach is used to compute average stresses in the fibers and matrix caused by arbitrary mechanical and thermal loads. The layer model is incorporated in an incremental laminated plate theory to compute the nonlinear response of laminated metal matrix composites of general orientation and stacking sequence. The report includes comparisons of the method with other analytical approaches and compares theoretical calculations with measured experimental material behavior. A section is included which describes the limitations of the material model.

Linear and Non-Linear Thermal Lens Signal of the Fifth C-H Vibrational Overtone of Naphthalene in Liquid Solutions of Hexane

NASA Astrophysics Data System (ADS)

Manzanares, Carlos; Diaz, Marlon; Barton, Ann; Nyaupane, Parashu R.

2017-06-01

The thermal lens technique is applied to vibrational overtone spectroscopy of solutions of naphthalene in n-hexane. The pump and probe thermal lens technique is found to be very sensitive for detecting samples of low composition (ppm) in transparent solvents. In this experiment two different probe lasers: one at 488 nm and another 568 nm were used. The C-H fifth vibrational overtone spectrum of benzene is detected at room temperature for different concentrations. A plot of normalized integrated intensity as a function of concentration of naphthalene in solution reveals a non-linear behavior at low concentrations when using the 488 nm probe and a linear behavior over the entire range of concentrations when using the 568 nm probe. The non-linearity cannot be explained assuming solvent enhancement at low concentrations. A two color absorption model that includes the simultaneous absorption of the pump and probe lasers could explain the enhanced magnitude and the non-linear behavior of the thermal lens signal. Other possible mechanisms will also be discussed.

Nonlinear system identification of smart structures under high impact loads

NASA Astrophysics Data System (ADS)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-05-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

Nonlinear Modeling of Joint Dominated Structures

NASA Technical Reports Server (NTRS)

Chapman, J. M.

1990-01-01

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

Modern aspects of nonlinear convection and magnetic field in flow of thixotropic nanofluid over a nonlinear stretching sheet with variable thickness

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Qayyum, Sajid; Alsaedi, Ahmed; Ahmad, Bashir

2018-05-01

Main objective of present analysis is to study the magnetohydrodynamic (MHD) nonlinear convective flow of thixotropic nanofluid. Flow is due to nonlinear stretching surface with variable thickness. Nonlinear thermal radiation and heat generation/absorption are utilized in the energy expression. Convective conditions and zero mass flux at sheet are considered. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Appropriate transformations are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been scrutinized through homotopic algorithm. Behavior of various sundry variables on velocity, temperature, nanoparticle concentration, skin friction coefficient and local Nusselt number are displayed through graphs. It is concluded that qualitative behaviors of temperature and thermal layer thickness are similar for radiation and temperature ratio variables. Moreover an enhancement in heat generation/absorption show rise to thermal field.

Effects of static tensile load on the thermal expansion of Gr/PI composite material

NASA Technical Reports Server (NTRS)

Farley, G. L.

1981-01-01

The effect of static tensile load on the thermal expansion of Gr/PI composite material was measured for seven different laminate configurations. A computer program was developed which implements laminate theory in a piecewise linear fashion to predict the coupled nonlinear thermomechanical behavior. Static tensile load significantly affected the thermal expansion characteristics of the laminates tested. This effect is attributed to a fiber instability micromechanical behavior of the constituent materials. Analytical results correlated reasonably well with free thermal expansion tests (no load applied to the specimen). However, correlation was poor for tests with an applied load.

Nonlinearities in Behavioral Macroeconomics.

PubMed

Gomes, Orlando

2017-07-01

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

Slave finite elements: The temporal element approach to nonlinear analysis

NASA Technical Reports Server (NTRS)

Gellin, S.

1984-01-01

A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.

Nonlinear Analytical Modeling of Interfacial Phenomenon and Nano-Size Microstructural Features to Better Correlate Nde Electronic Property Measurements to Material State

NASA Astrophysics Data System (ADS)

Roubidoux, J. A.; Jackson, J. E.; Lasseigne, A. N.; Mishra, B.; Olson, D. L.

2010-02-01

This paper correlates nonlinear material properties to nondestructive electronic measurements by using wave analysis techniques (e.g. Perturbation Methods) and incorporating higher-order phenomena. The correlations suggest that nondestructive electronic property measurements and practices can be used to assess thin films, surface layers, and other advanced materials that exhibit modified behaviors based on their space-charged interfacial behavior.

Study nonlinear dynamics of stratospheric ozone concentration at Pakistan Terrestrial region

NASA Astrophysics Data System (ADS)

Jan, Bulbul; Zai, Muhammad Ayub Khan Yousuf; Afradi, Faisal Khan; Aziz, Zohaib

2018-03-01

This study investigates the nonlinear dynamics of the stratospheric ozone layer at Pakistan atmospheric region. Ozone considered now the most important issue in the world because of its diverse effects on earth biosphere, including human health, ecosystem, marine life, agriculture yield and climate change. Therefore, this paper deals with total monthly time series data of stratospheric ozone over the Pakistan atmospheric region from 1970 to 2013. Two approaches, basic statistical analysis and Fractal dimension (D) have adapted to study the nature of nonlinear dynamics of stratospheric ozone level. Results obtained from this research have shown that the Hurst exponent values of both methods of fractal dimension revealed an anti-persistent behavior (negatively correlated), i.e. decreasing trend for all lags and Rescaled range analysis is more appropriate as compared to Detrended fluctuation analysis. For seasonal time series all month follows an anti-persistent behavior except in the month of November which shown persistence behavior i.e. time series is an independent and increasing trend. The normality test statistics also confirmed the nonlinear behavior of ozone and the rejection of hypothesis indicates the strong evidence of the complexity of data. This study will be useful to the researchers working in the same field in the future to verify the complex nature of stratospheric ozone.

Nonlinear optical studies of curcumin metal derivatives with cw laser

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

Henari, F. Z., E-mail: fzhenari@rcsi-mub.com; Cassidy, S.

2015-03-30

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10{sup −7} cm{sup 2}/W and negative nonlinear absorption of the order of 10{sup −6} cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition modelmore » with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.« less

Modelling nonlinearity in superconducting split ring resonator and its effects on metamaterial structures

NASA Astrophysics Data System (ADS)

Mazdouri, Behnam; Mohammad Hassan Javadzadeh, S.

2017-09-01

Superconducting materials are intrinsically nonlinear, because of nonlinear Meissner effect (NLME). Considering nonlinear behaviors, such as harmonic generation and intermodulation distortion (IMD) in superconducting structures, are very important. In this paper, we proposed distributed nonlinear circuit model for superconducting split ring resonators (SSRRs). This model can be analyzed by using Harmonic Balance method (HB) as a nonlinear solver. Thereafter, we considered a superconducting metamaterial filter which was based on split ring resonators and we calculated fundamental and third-order IMD signals. There are good agreement between nonlinear results from proposed model and measured ones. Additionally, based on the proposed nonlinear model and by using a novel method, we considered nonlinear effects on main parameters in the superconducting metamaterial structures such as phase constant (β) and attenuation factor (α).

A comparison of linear and non-linear data assimilation methods using the NEMO ocean model

NASA Astrophysics Data System (ADS)

Kirchgessner, Paul; Tödter, Julian; Nerger, Lars

2015-04-01

The assimilation behavior of the widely used LETKF is compared with the Equivalent Weight Particle Filter (EWPF) in a data assimilation application with an idealized configuration of the NEMO ocean model. The experiments show how the different filter methods behave when they are applied to a realistic ocean test case. The LETKF is an ensemble-based Kalman filter, which assumes Gaussian error distributions and hence implicitly requires model linearity. In contrast, the EWPF is a fully nonlinear data assimilation method that does not rely on a particular error distribution. The EWPF has been demonstrated to work well in highly nonlinear situations, like in a model solving a barotropic vorticity equation, but it is still unknown how the assimilation performance compares to ensemble Kalman filters in realistic situations. For the experiments, twin assimilation experiments with a square basin configuration of the NEMO model are performed. The configuration simulates a double gyre, which exhibits significant nonlinearity. The LETKF and EWPF are both implemented in PDAF (Parallel Data Assimilation Framework, http://pdaf.awi.de), which ensures identical experimental conditions for both filters. To account for the nonlinearity, the assimilation skill of the two methods is assessed by using different statistical metrics, like CRPS and Histograms.

Volatility of linear and nonlinear time series

NASA Astrophysics Data System (ADS)

Kalisky, Tomer; Ashkenazy, Yosef; Havlin, Shlomo

2005-07-01

Previous studies indicated that nonlinear properties of Gaussian distributed time series with long-range correlations, ui , can be detected and quantified by studying the correlations in the magnitude series ∣ui∣ , the “volatility.” However, the origin for this empirical observation still remains unclear and the exact relation between the correlations in ui and the correlations in ∣ui∣ is still unknown. Here we develop analytical relations between the scaling exponent of linear series ui and its magnitude series ∣ui∣ . Moreover, we find that nonlinear time series exhibit stronger (or the same) correlations in the magnitude time series compared with linear time series with the same two-point correlations. Based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series; the nonlinear multifractal time series is generated by multiplying a long-range correlated time series (that represents the magnitude series) with uncorrelated time series [that represents the sign series sgn(ui) ]. We apply our techniques on daily deep ocean temperature records from the equatorial Pacific, the region of the El-Ninõ phenomenon, and find: (i) long-range correlations from several days to several years with 1/f power spectrum, (ii) significant nonlinear behavior as expressed by long-range correlations of the volatility series, and (iii) broad multifractal spectrum.

Random forests in non-invasive sensorimotor rhythm brain-computer interfaces: a practical and convenient non-linear classifier.

PubMed

Steyrl, David; Scherer, Reinhold; Faller, Josef; Müller-Putz, Gernot R

2016-02-01

There is general agreement in the brain-computer interface (BCI) community that although non-linear classifiers can provide better results in some cases, linear classifiers are preferable. Particularly, as non-linear classifiers often involve a number of parameters that must be carefully chosen. However, new non-linear classifiers were developed over the last decade. One of them is the random forest (RF) classifier. Although popular in other fields of science, RFs are not common in BCI research. In this work, we address three open questions regarding RFs in sensorimotor rhythm (SMR) BCIs: parametrization, online applicability, and performance compared to regularized linear discriminant analysis (LDA). We found that the performance of RF is constant over a large range of parameter values. We demonstrate - for the first time - that RFs are applicable online in SMR-BCIs. Further, we show in an offline BCI simulation that RFs statistically significantly outperform regularized LDA by about 3%. These results confirm that RFs are practical and convenient non-linear classifiers for SMR-BCIs. Taking into account further properties of RFs, such as independence from feature distributions, maximum margin behavior, multiclass and advanced data mining capabilities, we argue that RFs should be taken into consideration for future BCIs.

Generation mechanism of nonlinear ultrasonic Lamb waves in thin plates with randomly distributed micro-cracks.

PubMed

Zhao, Youxuan; Li, Feilong; Cao, Peng; Liu, Yaolu; Zhang, Jianyu; Fu, Shaoyun; Zhang, Jun; Hu, Ning

2017-08-01

Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S 0 Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S 0 fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S 0 mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates. Copyright © 2017 Elsevier B.V. All rights reserved.

Fundamental Limits:. Developing New Tools for a Better Understanding of Second-Order Molecular Nonlinear Optics

NASA Astrophysics Data System (ADS)

Pérez-Moreno, Javier; Clays, Koen

The generalized Thomas-Kuhn sum rules are used to characterize the nonlinear optical response of organic chromophores in terms of fundamental parameters that can be measured experimentally. The nonlinear optical performance of organic molecules is evaluated from the combination of hyper-Rayleigh scattering measurements and the analysis in terms of the fundamental limits. Different strategies for the enhancement of nonlinear optical behavior at the molecular and supramolecular level are evaluated and new paradigms for the design of more efficient nonlinear optical molecules are proposed and investigated.

Multidirectional In Vivo Characterization of Skin Using Wiener Nonlinear Stochastic System Identification Techniques.

PubMed

Parker, Matthew D; Jones, Lynette A; Hunter, Ian W; Taberner, A J; Nash, M P; Nielsen, P M F

2017-01-01

A triaxial force-sensitive microrobot was developed to dynamically perturb skin in multiple deformation modes, in vivo. Wiener static nonlinear identification was used to extract the linear dynamics and static nonlinearity of the force-displacement behavior of skin. Stochastic input forces were applied to the volar forearm and thenar eminence of the hand, producing probe tip perturbations in indentation and tangential extension. Wiener static nonlinear approaches reproduced the resulting displacements with variances accounted for (VAF) ranging 94-97%, indicating a good fit to the data. These approaches provided VAF improvements of 0.1-3.4% over linear models. Thenar eminence stiffness measures were approximately twice those measured on the forearm. Damping was shown to be significantly higher on the palm, whereas the perturbed mass typically was lower. Coefficients of variation (CVs) for nonlinear parameters were assessed within and across individuals. Individual CVs ranged from 2% to 11% for indentation and from 2% to 19% for extension. Stochastic perturbations with incrementally increasing mean amplitudes were applied to the same test areas. Differences between full-scale and incremental reduced-scale perturbations were investigated. Different incremental preloading schemes were investigated. However, no significant difference in parameters was found between different incremental preloading schemes. Incremental schemes provided depth-dependent estimates of stiffness and damping, ranging from 300 N/m and 2 Ns/m, respectively, at the surface to 5 kN/m and 50 Ns/m at greater depths. The device and techniques used in this research have potential applications in areas, such as evaluating skincare products, assessing skin hydration, or analyzing wound healing.

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

NASA Technical Reports Server (NTRS)

Stein, M.; Stein, P. A.

1978-01-01

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results

NASA Technical Reports Server (NTRS)

Lee, Nam C.; Parks, George K.

1992-01-01

A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.

Predicting radiotherapy outcomes using statistical learning techniques

NASA Astrophysics Data System (ADS)

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

2009-09-01

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

Nonlinear dynamics in the study of birdsong

NASA Astrophysics Data System (ADS)

Mindlin, Gabriel B.

2017-09-01

Birdsong, a rich and complex behavior, is a stellar model to understand a variety of biological problems, from motor control to learning. It also enables us to study how behavior emerges when a nervous system, a biomechanical device and the environment interact. In this review, I will show that many questions in the field can benefit from the approach of nonlinear dynamics, and how birdsong can inspire new directions for research in dynamics.

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

NASA Technical Reports Server (NTRS)

Padovan, J.

1981-01-01

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

A universal approach to the study of nonlinear systems

NASA Astrophysics Data System (ADS)

Hwa, Rudolph C.

2004-07-01

A large variety of nonlinear systems have been treated by a common approach that emphasizes the fluctuation of spatial patterns. By using the same method of analysis it is possible to discuss the chaotic behaviors of quark jets and logistic map in the same language. Critical behaviors of quark-hadron phase transition in heavy-ion collisions and of photon production at the threshold of lasing can also be described by a common scaling behavior. The universal approach also makes possible an insight into the recently discovered phenomenon of wind reversal in cryogenic turbulence as a manifestation of self-organized criticality.

Renormalization-group theory for the eddy viscosity in subgrid modeling

NASA Technical Reports Server (NTRS)

Zhou, YE; Vahala, George; Hossain, Murshed

1988-01-01

Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

Modeling and experimental parametric study of a tri-leg compliant orthoplanar spring based multi-mode piezoelectric energy harvester

NASA Astrophysics Data System (ADS)

Dhote, Sharvari; Yang, Zhengbao; Zu, Jean

2018-01-01

This paper presents the modeling and experimental parametric study of a nonlinear multi-frequency broad bandwidth piezoelectric vibration-based energy harvester. The proposed harvester consists of a tri-leg compliant orthoplanar spring (COPS) and multiple masses with piezoelectric plates attached at three different locations. The vibration modes, resonant frequencies, and strain distributions are studied using the finite element analysis. The prototype is manufactured and experimentally investigated to study the effect of single as well as multiple light-weight masses on the bandwidth. The dynamic behavior of the harvester with a mass at the center is modeled numerically and characterized experimentally. The simulation and experimental results are in good agreement. A wide bandwidth with three close nonlinear vibration modes is observed during the experiments when four masses are added to the proposed harvester. The current generator with four masses shows a significant performance improvement with multiple nonlinear peaks under both forward and reverse frequency sweeps.

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Hyperextended Cosmological Perturbation Theory: Predicting Nonlinear Clustering Amplitudes

NASA Astrophysics Data System (ADS)

Scoccimarro, Román; Frieman, Joshua A.

1999-07-01

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

Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids.

PubMed

Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A

2003-06-01

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.

Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations

NASA Technical Reports Server (NTRS)

Padovan, J.; Lackney, J.

1986-01-01

The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

Interaction between Liénard and Ikeda dynamics in a nonlinear electro-optical oscillator with delayed bandpass feedback.

PubMed

Marquez, Bicky A; Larger, Laurent; Brunner, Daniel; Chembo, Yanne K; Jacquot, Maxime

2016-12-01

We report on experimental and theoretical analysis of the complex dynamics generated by a nonlinear time-delayed electro-optic bandpass oscillator. We investigate the interaction between the slow- and fast-scale dynamics of autonomous oscillations in the breather regime. We analyze in detail the coupling between the fast-scale behavior associated to a characteristic low-pass Ikeda behavior and the slow-scale dynamics associated to a Liénard limit-cycle. Finally, we show that when projected onto a two-dimensional phase space, the attractors corresponding to periodic and chaotic breathers display a spiral-like pattern, which strongly depends on the shape of the nonlinear function.

Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser

NASA Astrophysics Data System (ADS)

Liu, Meng; Li, Heng; Luo, Ai-Ping; Cui, Hu; Xu, Wen-Cheng; Luo, Zhi-Chao

2018-03-01

Ultrafast fiber lasers have been demonstrated to be great platforms for the investigation of soliton dynamics. The soliton molecules, as one of the most fascinating nonlinear phenomena, have been a hot topic in the field of nonlinear optics in recent years. Herein, we experimentally observed the real-time evolving behavior of soliton molecule in an ultrafast fiber laser by using the dispersive Fourier transformation technology. Several types of evolving soliton molecules were obtained in our experiments, such as soliton molecules with monotonically or chaotically evolving phase, flipping and hopping phase. These results would be helpful to the communities interested in soliton nonlinear dynamics as well as ultrafast laser technologies.

Modeling the thermotaxis behavior of C.elegans based on the artificial neural network.

PubMed

Li, Mingxu; Deng, Xin; Wang, Jin; Chen, Qiaosong; Tang, Yun

2016-07-03

ASBTRACT This research aims at modeling the thermotaxis behavior of C.elegans which is a kind of nematode with full clarified neuronal connections. Firstly, this work establishes the motion model which can perform the undulatory locomotion with turning behavior. Secondly, the thermotaxis behavior is modeled by nonlinear functions and the nonlinear functions are learned by artificial neural network. Once the artificial neural networks have been well trained, they can perform the desired thermotaxis behavior. Last, several testing simulations are carried out to verify the effectiveness of the model for thermotaxis behavior. This work also analyzes the different performances of the model under different environments. The testing results reveal the essence of the thermotaxis of C.elegans to some extent, and theoretically support the research on the navigation of the crawling robots.

Postbuckling delamination of a stiffened composite panel using finite element methods

NASA Technical Reports Server (NTRS)

Natsiavas, S.; Babcock, C. D.; Knauss, W. G.

1987-01-01

A combined numerical and experimental study is carried out for the postbuckling behavior of a stiffened composite panel. The panel is rectangular and is subjected to static in-plane compression on two opposite edges to the collapse level. Nonlinear (large deflection) plate theory is employed, together with an experimentally based failure criterion. It is found that the stiffened composite panel can exhibit significant postbuckling strength.

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

Hoehler, M; McCallen, D; Noble, C

The analysis, and subsequent retrofit, of concrete arch bridges during recent years has relied heavily on the use of computational simulation. For seismic analysis in particular, computer simulation, typically utilizing linear approximations of structural behavior, has become standard practice. This report presents the results of a comprehensive study of the significance of model sophistication (i.e. linear vs. nonlinear) and pertinent modeling assumptions on the dynamic response of concrete arch bridges. The study uses the Bixby Creek Bridge, located in California, as a case study. In addition to presenting general recommendations for analysis of this class of structures, this report providesmore » an independent evaluation of the proposed seismic retrofit for the Bixby Creek Bridge. Results from the study clearly illustrate a reduction of displacement drifts and redistribution of member forces brought on by the inclusion of material nonlinearity. The analyses demonstrate that accurate modeling of expansion joints, for the Bixby Creek Bridge in particular, is critical to achieve representative modal and transient behavior. The inclusion of near-field displacement pulses in ground motion records was shown to significantly increase demand on the relatively softer, longer period Bixby Creek Bridge arch. Stiffer, shorter period arches, however, are more likely susceptible to variable support motions arising from the canyon topography typical for this class of bridges.« less

Nonlinear identification of the total baroreflex arc: chronic hypertension model.

PubMed

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru; Mukkamala, Ramakrishna

2016-05-01

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). Its linear dynamic functioning has been shown to be preserved in spontaneously hypertensive rats (SHR). However, the system is known to exhibit nonlinear dynamic behaviors. The aim of this study was to establish nonlinear dynamic models of the total arc (and its subsystems) in hypertensive rats and to compare these models with previously published models for normotensive rats. Hypertensive rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned. The carotid sinus regions were isolated and attached to a servo-controlled piston pump. AP and sympathetic nerve activity were measured while CSP was controlled via the pump using Gaussian white noise stimulation. Second-order, nonlinear dynamics models were developed by application of nonparametric system identification to a portion of the measurements. The models of the total arc predicted AP 21-43% better (P < 0.005) than conventional linear dynamic models in response to a new portion of the CSP measurement. The linear and nonlinear terms of these validated models were compared with the corresponding terms of an analogous model for normotensive rats. The nonlinear gains for the hypertensive rats were significantly larger than those for the normotensive rats [-0.38 ± 0.04 (unitless) vs. -0.22 ± 0.03, P < 0.01], whereas the linear gains were similar. Hence, nonlinear dynamic functioning of the sympathetically mediated total arc may enhance baroreflex buffering of AP increases more in SHR than normotensive rats. Copyright © 2016 the American Physiological Society.

Experimental Investigations in Nonlinear Viscous Behavior of Subgrade Soils Under Traffic-Induced Loading

DOT National Transportation Integrated Search

1999-08-01

This paper concerns experimental investigations of nonlinear viscosity of : subgrade soils under vehicle-induced loading. Subgrade soil samples--collected : from the Soil/Aggregate Laboratory at the Geotechnical Exploration Division at : the Maryland...

Improving the sustainability of asphalt pavements through developing a predictive model with fundamental material properties.

DOT National Transportation Integrated Search

2009-08-01

This study presents the numerical implementation and validation of general constitutive relationships for describing the : nonlinear behavior of asphalt concrete mixes. These constitutive relationships incorporate nonlinear viscoelasticity and : visc...

Bifurcation Analysis of an Electrostatically Actuated Nano-Beam Based on Modified Couple Stress Theory

NASA Astrophysics Data System (ADS)

Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman

2017-12-01

In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.

Substrate clamping effects on irreversible domain wall dynamics in lead zirconate titanate thin films.

PubMed

Griggio, F; Jesse, S; Kumar, A; Ovchinnikov, O; Kim, H; Jackson, T N; Damjanovic, D; Kalinin, S V; Trolier-McKinstry, S

2012-04-13

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.

A study of hyperelastic models for predicting the mechanical behavior of extensor apparatus.

PubMed

Elyasi, Nahid; Taheri, Kimia Karimi; Narooei, Keivan; Taheri, Ali Karimi

2017-06-01

In this research, the nonlinear elastic behavior of human extensor apparatus was investigated. To this goal, firstly the best material parameters of hyperelastic strain energy density functions consisting of the Mooney-Rivlin, Ogden, invariants, and general exponential models were derived for the simple tension experimental data. Due to the significance of stress response in other deformation modes of nonlinear models, the calculated parameters were used to study the pure shear and balance biaxial tension behavior of the extensor apparatus. The results indicated that the Mooney-Rivlin model predicts an unstable behavior in the balance biaxial deformation of the extensor apparatus, while the Ogden order 1 represents a stable behavior, although the fitting of experimental data and theoretical model was not satisfactory. However, the Ogden order 6 model was unstable in the simple tension mode and the Ogden order 5 and general exponential models presented accurate and stable results. In order to reduce the material parameters, the invariants model with four material parameters was investigated and this model presented the minimum error and stable behavior in all deformation modes. The ABAQUS Explicit solver was coupled with the VUMAT subroutine code of the invariants model to simulate the mechanical behavior of the central and terminal slips of the extensor apparatus during the passive finger flexion, which is important in the prediction of boutonniere deformity and chronic mallet finger injuries, respectively. Also, to evaluate the adequacy of constitutive models in simulations, the results of the Ogden order 5 were presented. The difference between the predictions was attributed to the better fittings of the invariants model compared with the Ogden model.

Nonlinear modal resonances in low-gravity slosh-spacecraft systems

NASA Technical Reports Server (NTRS)

Peterson, Lee D.

1991-01-01

Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

Nonlinear effects on the natural modes of oscillation of a finite length inviscid fluid column, supplement 2

NASA Technical Reports Server (NTRS)

Lyell, M. J.; Zhang, L.

1994-01-01

The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.

Origin of nonlinear transport across the magnetically induced superconductor-metal-insulator transition in two dimensions.

PubMed

Seo, Y; Qin, Y; Vicente, C L; Choi, K S; Yoon, Jongsoo

2006-08-04

We have studied the effect of perpendicular magnetic fields and temperatures on nonlinear electronic transport in amorphous Ta superconducting thin films. The films exhibit a magnetic field-induced metallic behavior intervening the superconductor-insulator transition in the zero temperature limit. We show that the phase-identifying nonlinear transport in the superconducting and metallic phases arises from an intrinsic origin, not from an electron heating effect. The nonlinear transport is found to accompany an extraordinarily long voltage response time.

Theoretical and experimental characterization of the first hyperpolarizability

NASA Astrophysics Data System (ADS)

Perez-Moreno, Javier

We present a theoretical and experimental study of the molecular susceptibilities. The generalized Thomas-Kuhn sum rules are used to characterize the nonlinear response of organic chromophores in terms of fundamental parameters. The nonlinear optical performance of real molecules is evaluated from the calculation of the quantum limits and Hyper-Rayleigh scattering measurements. Different strategies for the enhancement of nonlinear behavior at the molecular and supramolecular level are evaluated and new paradigms for de design of more efficient nonlinear molecules are proposed.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

PubMed

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

2016-09-15

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

Self-Organized Lattices of Nonlinear Optochemical Waves in Photopolymerizable Fluids: The Spontaneous Emergence of 3-D Order in a Weakly Correlated System.

PubMed

Ponte, Matthew R; Hudson, Alexander D; Saravanamuttu, Kalaichelvi

2018-03-01

Many of the extraordinary three-dimensional architectures that pattern our physical world emerge from complex nonlinear systems or dynamic populations whose individual constituents are only weakly correlated to each other. Shoals of fish, murmuration behaviors in birds, congestion patterns in traffic, and even networks of social conventions are examples of spontaneous pattern formation, which cannot be predicted from the properties of individual elements alone. Pattern formation at a different scale has been observed or predicted in weakly correlated systems including superconductors, atomic gases near Bose Einstein condensation, and incoherent optical fields. Understanding pattern formation in nonlinear weakly correlated systems, which are often unified through mathematical expression, could pave intelligent self-organizing pathways to functional materials, architectures, and computing technologies. However, it is experimentally difficult to directly visualize the nonlinear dynamics of pattern formation in most populations-especially in three dimensions. Here, we describe the collective behavior of large populations of nonlinear optochemical waves, which are poorly correlated in both space and time. The optochemical waves-microscopic filaments of white light entrapped within polymer channels-originate from the modulation instability of incandescent light traveling in photopolymerizable fluids. By tracing the three-dimensional distribution of optical intensity in the nascent polymerizing system, we find that populations of randomly distributed, optochemical waves synergistically and collectively shift in space to form highly ordered lattices of specific symmetries. These, to our knowledge, are the first three-dimensionally periodic structures to emerge from a system of weakly correlated waves. Their spontaneous formation in an incoherent and effectively chaotic field is counterintuitive, but the apparent contradiction of known behaviors of light including the laws of optical interference can be explained through the soliton-like interactions of optochemical waves with nearest neighbors. Critically, this work casts fundamentally new insight into the collective behaviors of poorly correlated nonlinear waves in higher dimensions and provides a rare, accessible platform for further experimental studies of these previously unexplored behaviors. Furthermore, it defines a self-organization paradigm that, unlike conventional counterparts, could generate polymer microstructures with symmetries spanning all the Bravais lattices.

An equivalent frequency approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice

2018-05-01

Pre-tensioned cable braces are widely used as bracing systems in various structural typologies. This technology is fundamentally utilized for stiffening purposes in the case of steel and timber structures. The pre-stressing force imparted to the braces provides to the system a remarkable increment of stiffness. On the other hand, the pre-tensioning force in the braces must be properly calibrated in order to satisfactorily meet both serviceability and ultimate limit states. Dynamic properties of these systems are however affected by non-linear behavior due to potential slackening of the pre-tensioned brace. In the recent years the author has been working on a similar problem regarding the non-linear response of cables in cable-stayed bridges and braced structures. In the present paper a displacement-based approach is used to examine the non-linear behavior of a building system. The methodology operates through linearization and allows obtaining an equivalent linearized frequency to approximately characterize, mode by mode, the dynamic behavior of the system. The equivalent frequency depends on both the mechanical characteristics of the system, the pre-tensioning level assigned to the braces and a characteristic vibration amplitude. The proposed approach can be used as a simplified technique, capable of linearizing the response of structural systems, characterized by non-linearity induced by the slackening of pre-tensioned braces.

Nonlinear identification of the total baroreflex arc.

PubMed

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru; Mukkamala, Ramakrishna

2015-12-15

The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This "Uryson" model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure. Copyright © 2015 the American Physiological Society.

Nonlinear identification of the total baroreflex arc

PubMed Central

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru

2015-01-01

The total baroreflex arc [the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP)] is known to exhibit nonlinear behaviors. However, few studies have quantitatively characterized its nonlinear dynamics. The aim of this study was to develop a nonlinear model of the sympathetically mediated total arc without assuming any model form. Normal rats were studied under anesthesia. The vagal and aortic depressor nerves were sectioned, the carotid sinus regions were isolated and attached to a servo-controlled piston pump, and the AP and sympathetic nerve activity (SNA) were measured. CSP was perturbed using a Gaussian white noise signal. A second-order Volterra model was developed by applying nonparametric identification to the measurements. The second-order kernel was mainly diagonal, but the diagonal differed in shape from the first-order kernel. Hence, a reduced second-order model was similarly developed comprising a linear dynamic system in parallel with a squaring system in cascade with a slower linear dynamic system. This “Uryson” model predicted AP changes 12% better (P < 0.01) than a linear model in response to new Gaussian white noise CSP. The model also predicted nonlinear behaviors, including thresholding and mean responses to CSP changes about the mean. Models of the neural arc (the system relating CSP to SNA) and peripheral arc (the system relating SNA to AP) were likewise developed and tested. However, these models of subsystems of the total arc showed approximately linear behaviors. In conclusion, the validated nonlinear model of the total arc revealed that the system takes on an Uryson structure. PMID:26354845

The Influence of Road Bumps Characteristics on the Chaotic Vibration of a Nonlinear Full-Vehicle Model with Driver

NASA Astrophysics Data System (ADS)

Fakhraei, J.; Khanlo, H. M.; Ghayour, M.; Faramarzi, Kh.

In this paper, the chaotic behavior of a ground vehicle system with driver subjected to road disturbances is studied and the relationship between the nonlinear vibration of the vehicle and ride comfort is evaluated. The vehicle system is modeled as fully nonlinear with seven degrees of freedom and an additional degree of freedom for driver (8-DOF). The excitation force is the road irregularities that are assumed as road speed control bumps. The sinusoidal, consecutive half-sine and dented-rectangular waveforms are considered to simulate the road speed control bumps. The nonlinearities of the system are due to the nonlinear springs and dampers that are used in the suspension system and tires. The governing differential equations are extracted under Newton-Euler laws and solved via numerical methods. The chaotic behaviors were studied in more detail with special techniques such as bifurcation diagrams, phase plane portrait, Poincaré map and Lyapunov exponents. The ride comfort was evaluated as the RMS value of the vertical displacement of the vehicle body and driver. Firstly, the effect of amplitude (height) and frequency (vehicle’s speed) of these speed control bumps on chaotic vibrations of vehicle are studied. The obtained results show that various forms of vibrations, such as periodic, subharmonic and chaotic vibrations, can be detected in the system behavior with the change of the height and frequency of speed control bumps and present different types of strange attractors in the vehicle with and without driver. Then, the influence of nonlinear vibration on ride comfort and the relationship between chaotic vibrations of the vehicle and driving comfort are investigated. The results of analyzing the RMS diagrams reveal that the chaotic behaviors can directly affect the driving comfort and lead to the driver’s comfort being reduced. The obtained results can be used in the design of vehicle and road bumps pavement.

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

NASA Astrophysics Data System (ADS)

Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

2014-09-01

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion.

PubMed

Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

2014-09-01

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

Dissipative behavior of some fully non-linear KdV-type equations

NASA Astrophysics Data System (ADS)

Brenier, Yann; Levy, Doron

2000-03-01

The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

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

NASA Astrophysics Data System (ADS)

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

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

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

Modeling Plankton Aggregation and Transport by Nonlinear Internal Waves Propagating Onshore.

NASA Astrophysics Data System (ADS)

Garwood, J. C.; Musgrave, R. C.; Franks, P. J. S.

2016-02-01

Many coastal benthic species have planktonic larval forms. These larvae must return to suitable adult habitat to allow recruitment to the breeding population. To a large extent these larvae are at the mercy of the ambient currents. However, simple vertical swimming behaviors may significantly enhance onshore or offshore transport of these organisms in certain coastal flows. Here we use models to investigate the interaction of nonlinear internal waves (NLIW) and swimming behaviors in determining plankton aggregation and cross-shelf transport. In a 2D, non-hydrostatic MITgcm with particle tracking, NLIW are generated and propagate onshore into a region of sloping bottom topography. Lagrangian and swimming particles representing plankton are introduced in the flow field to quantify transport and dispersion. Characteristics of the environment (bottom slope and stratification), as well as of the particles (source, depth, and swimming vs. passive) were varied to identify scenarios that would maximize transport or accumulation. Our results will be used to design experiments using swarms of autonomous buoyancy-controlled drifters to quantify transport and accumulation in the field.

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

Chacon, Luis; Stanier, Adam John

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation.

PubMed

Shahid, Wajiha; Qiu, Zhen; Duan, Xiyu; Li, Haijun; Wang, Thomas D; Oldham, Kenn R

2014-12-01

High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror's nonlinear dynamics under such excitation is analyzed in a Hill's equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror's frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies.

Behavioral modeling and digital compensation of nonlinearity in DFB lasers for multi-band directly modulated radio-over-fiber systems

NASA Astrophysics Data System (ADS)

Li, Jianqiang; Yin, Chunjing; Chen, Hao; Yin, Feifei; Dai, Yitang; Xu, Kun

2014-11-01

The envisioned C-RAN concept in wireless communication sector replies on distributed antenna systems (DAS) which consist of a central unit (CU), multiple remote antenna units (RAUs) and the fronthaul links between them. As the legacy and emerging wireless communication standards will coexist for a long time, the fronthaul links are preferred to carry multi-band multi-standard wireless signals. Directly-modulated radio-over-fiber (ROF) links can serve as a lowcost option to make fronthaul connections conveying multi-band wireless signals. However, directly-modulated radioover- fiber (ROF) systems often suffer from inherent nonlinearities from directly-modulated lasers. Unlike ROF systems working at the single-band mode, the modulation nonlinearities in multi-band ROF systems can result in both in-band and cross-band nonlinear distortions. In order to address this issue, we have recently investigated the multi-band nonlinear behavior of directly-modulated DFB lasers based on multi-dimensional memory polynomial model. Based on this model, an efficient multi-dimensional baseband digital predistortion technique was developed and experimentally demonstrated for linearization of multi-band directly-modulated ROF systems.

A modified variational method for nonlinear vibration analysis of rotating beams including Coriolis effects

NASA Astrophysics Data System (ADS)

Tian, Jiajin; Su, Jinpeng; Zhou, Kai; Hua, Hongxing

2018-07-01

This paper presents a general formulation for nonlinear vibration analysis of rotating beams. A modified variational method combined with a multi-segment partitioning technique is employed to derive the free and transient vibration behaviors of the rotating beams. The strain energy and kinetic energy functional are formulated based on the order truncation principle of the fully geometrically nonlinear beam theory. The Coriolis effects as well as nonlinear effects due to the coupling of bending-stretching, bending-twist and twist-stretching are taken into account. The present method relaxes the need to explicitly meet the requirements of the boundary conditions for the admissible functions, and allows the use of any linearly independent, complete basis functions as admissible functions for rotating beams. Moreover, the method is readily used to deal with the nonlinear transient vibration problems for rotating beams subjected to dynamic loads. The accuracy, convergence and efficiency of the proposed method are examined by numerical examples. The influences of Coriolis and centrifugal forces on the vibration behaviors of the beams with various hub radiuses and slenderness ratios and rotating at different angular velocities are also investigated.

Fluctuation Reduction in a Si Micromechanical Resonator Tuned to Nonlinear Internal Resonance

NASA Astrophysics Data System (ADS)

Strachan, B. Scott; Czaplewski, David; Chen, Changyao; Dykman, Mark; Lopez, Daniel; Shaw, Steven

2015-03-01

We describe experimental and theoretical results on an unusual behavior of fluctuations when the system exhibits internal resonance. We study the fundamental flexural mode (FFM) of a Si microbeam. The FFM is electrically actuated and detected. It is resonantly nonlinearly coupled to another mode, which is not directly accessible and has a frequency nearly three times the FFM frequency. Both the FFM and the passive mode have long lifetimes. We find that the passive mode can be a ``sink'' for fluctuations of the FFM. This explains the recently observed dramatic decrease of these fluctuations at nonlinear resonance. The re-distribution of the vibration amplitudes and the fluctuations is reminiscent of what happens at level anti-crossing in quantum mechanics. However, here it is different because of interplay of the dependence of the vibration frequency of the FFM on its amplitude due to internal nonlinearity and the nonlinear resonance with the passive mode. We study both the response of the system to external resonant driving and also the behavior of the system in the presence of a feedback loop. The experimental and theoretical results are in good agreement.

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

Dynamics of Oscillating and Rotating Liquid Drop using Electrostatic Levitator

NASA Astrophysics Data System (ADS)

Matsumoto, Satoshi; Awazu, Shigeru; Abe, Yutaka; Watanabe, Tadashi; Nishinari, Katsuhiro; Yoda, Shinichi

2006-11-01

In order to understand the nonlinear behavior of liquid drop with oscillatory and/or rotational motions, an experimental study was performed. The electrostatic levitator was employed to achieve liquid drop formation on ground. A liquid drop with about 3 mm in diameter was levitated. The oscillation of mode n=2 along the vertical axis was induced by an external electrostatic force. The oscillatory motions were observed to clarify the nonlinearities of oscillatory behavior. A relationship between amplitude and frequency shift was made clear and the effect of frequency shift on amplitude agreed well with the theory. The frequency shift became larger with increasing the amplitude of oscillation. To confirm the nonlinear effects, we modeled the oscillation by employing the mass-spring-damper system included the nonlinear term. The result indicates that the large-amplitude oscillation includes the effect of nonlinear oscillation. The sound pressure was imposed to rotate the liquid drop along a vertical axis by using a pair of acoustic transducers. The drop transited to the two lobed shape due to centrifugal force when nondimensional angular velocity exceeded to 0.58.

Chaotic behavior of the coronary circulation.

PubMed

Trzeciakowski, Jerome; Chilian, William M

2008-05-01

The regulation of the coronary circulation is a complex paradigm in which many inputs that influence vasomotor tone have to be integrated to provide the coronary vasomotor adjustments to cardiac metabolism and to perfusion pressure. We hypothesized that the integration of many disparate signals that influence membrane potential of smooth muscle cells, calcium sensitivity of contractile filaments, receptor trafficking result in complex non-linear characteristics of coronary vasomotion. To test this hypothesis, we measured an index of vasomotion, flowmotion, the periodic fluctuations of flow that reflect dynamic changes in resistances in the microcirculation. Flowmotion was continuously measured in periods ranging from 15 to 40 min under baseline conditions, during antagonism of NO synthesis, and during combined purinergic and NOS antagonism in the beating heart of anesthetized open-chest dogs. Flowmotion was measured in arterioles ranging from 80 to 135 microm in diameter. The signals from the flowmotion measurements were used to derive quantitative indices of non-linear behavior: power spectra, chaotic attractors, correlation dimensions, and the sum of the Lyapunov exponents (Kolmogorov-Sinai entropy), which reflects the total chaos and unpredictability of flowmotion. Under basal conditions, the coronary circulation demonstrated chaotic non-linear behavior with a power spectra showing three principal frequencies in flowmotion. Blockade of nitric oxide synthase or antagonism of purinergic receptors did not affect the correlation dimensions, but significantly increased the Kolmogorov-Sinai entropy, altered the power spectra of flowmotion, and changed the nature of the chaotic attractor. These changes are consistent with the view that certain endogenous controls, nitric oxide and various purines (AMP, ADP, ATP, adenosine) make the coronary circulation more predictable, and that blockade of these controls makes the control of flow less predictable and more chaotic.

Static behavior and the effects of thermal cycling in hybrid laminates

NASA Technical Reports Server (NTRS)

Liber, T. M.; Daniel, I. M.; Chamis, C. C.

1977-01-01

Static stiffness, strength and ultimate strain after thermal cycling were investigated for graphite/Kevlar 49/epoxy and graphite/S-glass/epoxy angle-ply laminates. Tensile stress-strain curves to failure and uniaxial tensile properties were determined, and theoretical predictions of modulus, Poisson's ratio and ultimate strain, based on linear lamination theory, constituent ply properties and measured strength, were made. No significant influence on tensile stress properties due to stacking sequence variations was observed. In general, specimens containing two 0-degree Kevlar or S-glass plies were found to behave linearly to failure, while specimens containing 4 0-degree Kevlar or S-glass plies showed some nonlinear behavior.

Matrix dominated stress/strain behavior in polymeric composites: Effects of hold time, nonlinearity and rate dependency

NASA Technical Reports Server (NTRS)

Gates, Thomas S.

1992-01-01

In order to understand matrix dominated behavior in laminated polymer matrix composites, an elastic/viscoplastic constitutive model was developed and used to predict stress strain behavior of off-axis and angle-ply symmetric laminates under in-plane, tensile axial loading. The model was validated for short duration tests at elevated temperatures. Short term stress relaxation and short term creep, strain rate sensitivity, and material nonlinearity were accounted for. The testing times were extended for longer durations, and periods of creep and stress relaxation were used to investigate the ability of the model to account for long term behavior. The model generally underestimated the total change in strain and stress for both long term creep and long term relaxation respectively.

Dynamic assessment of nonlinear typical section aeroviscoelastic systems using fractional derivative-based viscoelastic model

NASA Astrophysics Data System (ADS)

Sales, T. P.; Marques, Flávio D.; Pereira, Daniel A.; Rade, Domingos A.

2018-06-01

Nonlinear aeroelastic systems are prone to the appearance of limit cycle oscillations, bifurcations, and chaos. Such problems are of increasing concern in aircraft design since there is the need to control nonlinear instabilities and improve safety margins, at the same time as aircraft are subjected to increasingly critical operational conditions. On the other hand, in spite of the fact that viscoelastic materials have already been successfully used for the attenuation of undesired vibrations in several types of mechanical systems, a small number of research works have addressed the feasibility of exploring the viscoelastic effect to improve the behavior of nonlinear aeroelastic systems. In this context, the objective of this work is to assess the influence of viscoelastic materials on the aeroelastic features of a three-degrees-of-freedom typical section with hardening structural nonlinearities. The equations of motion are derived accounting for the presence of viscoelastic materials introduced in the resilient elements associated to each degree-of-freedom. A constitutive law based on fractional derivatives is adopted, which allows the modeling of temperature-dependent viscoelastic behavior in time and frequency domains. The unsteady aerodynamic loading is calculated based on the classical linear potential theory for arbitrary airfoil motion. The aeroelastic behavior is investigated through time domain simulations, and subsequent frequency transformations, from which bifurcations are identified from diagrams of limit cycle oscillations amplitudes versus airspeed. The influence of the viscoelastic effect on the aeroelastic behavior, for different values of temperature, is also investigated. The numerical simulations show that viscoelastic damping can increase the flutter speed and reduce the amplitudes of limit cycle oscillations. These results prove the potential that viscoelastic materials have to increase aircraft components safety margins regarding aeroelastic stability.

An exact solution for the history-dependent material and delamination behavior of laminated plates subjected to cylindrical bending

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

Williams, Todd O

2009-01-01

The exact solution for the history-dependent behavior of laminated plates subjected to cylindrical bending is presented. The solution represents the extension of Pagano's solution to consider arbitrary types of constitutive behaviors for the individual lamina as well as arbitrary types of cohesive zones models for delamination behavior. Examples of the possible types of material behavior are plasticity, viscoelasticity, viscoplasticity, and damaging. Examples of possible CZMs that can be considered are linear, nonlinear hardening, as well as nonlinear with softening. The resulting solution is intended as a benchmark solution for considering the predictive capabilities of different plate theories. Initial results aremore » presented for several types of history-dependent material behaviors. It is shown that the plate response in the presence of history-dependent behaviors can differ dramatically from the elastic response. These results have strong implications for what constitutes an appropriate plate theory for modeling such behaviors.« less

Skeletal muscle tensile strain dependence: hyperviscoelastic nonlinearity

PubMed Central

Wheatley, Benjamin B; Morrow, Duane A; Odegard, Gregory M; Kaufman, Kenton R; Donahue, Tammy L Haut

2015-01-01

Introduction Computational modeling of skeletal muscle requires characterization at the tissue level. While most skeletal muscle studies focus on hyperelasticity, the goal of this study was to examine and model the nonlinear behavior of both time-independent and time-dependent properties of skeletal muscle as a function of strain. Materials and Methods Nine tibialis anterior muscles from New Zealand White rabbits were subject to five consecutive stress relaxation cycles of roughly 3% strain. Individual relaxation steps were fit with a three-term linear Prony series. Prony series coefficients and relaxation ratio were assessed for strain dependence using a general linear statistical model. A fully nonlinear constitutive model was employed to capture the strain dependence of both the viscoelastic and instantaneous components. Results Instantaneous modulus (p<0.0005) and mid-range relaxation (p<0.0005) increased significantly with strain level, while relaxation at longer time periods decreased with strain (p<0.0005). Time constants and overall relaxation ratio did not change with strain level (p>0.1). Additionally, the fully nonlinear hyperviscoelastic constitutive model provided an excellent fit to experimental data, while other models which included linear components failed to capture muscle function as accurately. Conclusions Material properties of skeletal muscle are strain-dependent at the tissue level. This strain dependence can be included in computational models of skeletal muscle performance with a fully nonlinear hyperviscoelastic model. PMID:26409235

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Transformation of nonlinear behaviors: from bright- to dark-gap soliton in a one-dimensional photonic crystal containing a nonlinear indefinite metamaterial defect.

PubMed

Zhang, Wei; Chen, Yuanyuan; Hou, Peng; Shi, Jielong; Wang, Qi

2010-12-01

Nonlinear propagation characteristics are investigated theoretically in a one-dimensional photonic band-gap structure doped with a nonlinear indefinite metamaterial defect for five distinct frequency intervals. It is found from the electric field distribution that there exists the bright gap solitonlike when the nonlinear indefinite metamaterial defect is a cut-off medium, while the dark gap solitonlike can appear in the nonlinear never cut-off defect layer. It is also found that there exists corresponding bistable lateral shift the properties of which are strongly dependent on the permittivity and permeability of nonlinear indefinite metamaterials. Moreover, in contrast to the switch-down threshold value, the switch-up threshold value is more sensitive to the incident frequency.

Elastic Nonlinear Response in Granular Media Under Resonance Conditions

NASA Astrophysics Data System (ADS)

Jia, X.; Johnson, P. A.

2004-12-01

We are studying the elastic linear and nonlinear behavior of granular media using dynamic wave methods. In the work presented here, our goal is to quantify the elastic nonlinear response by applying wave resonance. Resonance studies are desirable because they provide the means to easily study amplitude dependencies of elastic nonlinear behavior and thus to characterize the physical nature of the elastic nonlinearity. This work has implications for a variety of topics, in particular, the in situ nonlinear response of surface sediments. For this work we constructed an experimental cell in which high sensitivity dynamic resonance studies were conducted using granular media under controlled effective pressure. We limit our studies here to bulk modes but have the capability to employ shear waves as well. The granular media are composed of glass beads held under pressure by a piston, while applying resonance waves from transducers as both the excitation and the material probe. The container is closed with two fitted pistons and a normal load is applied to the granular sample across the top piston. Force and displacement are measured directly. Resonant frequency sweeps with frequencies corresponding to the fundamental bulk mode are applied to the longitudinal source transducer. The pore pressure in the system is 1 atm. The glass beads used in our experiments are of diameter 0.5 mm, randomly deposited in a duralumin cylinder of diameter 30 mm and height of 15 mm. This corresponds to a granular skeleton acoustic wave velocity of v ª 750m/s under 50 N of force [0.07 Mpa]. The loaded system gives fundamental mode resonances in the audio frequency band at half a wavelength where resonance frequency is effective-pressure dependent. The volume fraction of glass beads thus obtained is found to be 0.63 ± 0.01. Plane-wave generating and detecting transducers of diameter 30 mm are placed on axis at the top and bottom of the cylindrical container in direct contact with the glass beads. The wave signals are detected using a lock-in amplifier, and frequency and amplitude are recorded on computer. Drive frequency is swept from below to above the resonance mode. A typical frequency sweep is 3 kHz in width with a frequency sampling of 6 Hz. Frequency sweeps are applied at progressively increasing drive voltages to test for nonlinear-dynamical induced modulus softening. The resonance frequency at peak amplitude corresponds directly to modulus. We find significant elastic nonlinearity at all effective pressures, manifest by the fundamental-mode resonance curves decreasing progressively, at progressively increasing drive level. This is equivalent to progressive material softening with wave amplitude, meaning the wavespeed and modulus diminish. The wave dissipation simultaneously increases (Johnson and Sutin 2004). For example, at 0.11 Mpa effective pressure the observed change in resonance frequency of about 2.6% corresponds to a material bulk modulus decrease of about 5.2%. Strain amplitudes are 10-7-10-6. Thus, we would predict that surface sediments should have significant elastic nonlinear response beginning at about 10-6 strain amplitude. reference: Johnson, P. and A. Sutin, Slow dynamics in diverse solids, J. Acoust. Soc Am., in press (2004).

Scaling of chaos in strongly nonlinear lattices.

PubMed

Mulansky, Mario

2014-06-01

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

Nonlinear dynamics of a circular piezoelectric plate for vibratory energy harvesting

NASA Astrophysics Data System (ADS)

Yuan, Tian-Chen; Yang, Jian; Chen, Li-Qun

2018-06-01

Nonlinear behaviors are investigated for a vibration-based energy harvester. The harvester consists of a circular composite plate with the clamped boundary, a proof mass and two steel rings. The lumped parameter model of the harvester is established and the parameters are identified from the experiment. The measured nonlinear behaviors can be approximately described by the lumped model. Both the experimental and the numerical results demonstrate that the circular plate harvester has soft characteristics under low excitation and both hard characteristics and soft characteristics under high excitation. The experimental results show that the output voltage can achieve over 35 V (about 50 mW) and more than 14 Hz of bandwidth with 25 kΩ load resistance.

Designs for thermal harvesting with nonlinear coordinate transformation

NASA Astrophysics Data System (ADS)

Ji, Qingxiang; Fang, Guodong; Liang, Jun

2018-04-01

In this paper a thermal concentrating design method was proposed based on the concept of generating function without knowing the needed coordinate transformation beforehand. The thermal harvesting performance was quantitatively characterized by heat concentrating efficiency and external temperature perturbation. Nonlinear transformations of different forms were employed to design high order thermal concentrators, and corresponding harvesting performances were investigated by numerical simulations. The numerical results shows that the form of coordinate transformation directly influences the distributions of heat flows inside the concentrator, consequently, influences the thermal harvesting behaviors significantly. The concentrating performance can be actively controlled and optimized by changing the form of coordinate transformations. The analysis in this paper offers a beneficial method to flexibly tune the harvesting performance of the thermal concentrator according to the requirements of practical applications.

Nonequilibrium response of an electron-mediated charge density wave ordered material to a large dc electric field

NASA Astrophysics Data System (ADS)

Matveev, O. P.; Shvaika, A. M.; Devereaux, T. P.; Freericks, J. K.

2016-01-01

Using the Kadanoff-Baym-Keldysh formalism, we employ nonequilibrium dynamical mean-field theory to exactly solve for the nonlinear response of an electron-mediated charge-density-wave-ordered material. We examine both the dc current and the order parameter of the conduction electrons as the ordered system is driven by the electric field. Although the formalism we develop applies to all models, for concreteness, we examine the charge-density-wave phase of the Falicov-Kimball model, which displays a number of anomalous behaviors including the appearance of subgap density of states as the temperature increases. These subgap states should have a significant impact on transport properties, particularly the nonlinear response of the system to a large dc electric field.

Constitutive Modeling of Crosslinked Nanotube Materials

NASA Technical Reports Server (NTRS)

Odegard, G. M.; Frankland, S. J. V.; Herzog, M. N.; Gates, T. S.; Fay, C. C.

2004-01-01

A non-linear, continuum-based constitutive model is developed for carbon nanotube materials in which bundles of aligned carbon nanotubes have varying amounts of crosslinks between the nanotubes. The model accounts for the non-linear elastic constitutive behavior of the material in terms of strain, and is developed using a thermodynamic energy approach. The model is used to examine the effect of the crosslinking on the overall mechanical properties of variations of the crosslinked carbon nanotube material with varying degrees of crosslinking. It is shown that the presence of the crosslinks has significant effects on the mechanical properties of the carbon nanotube materials. An increase in the transverse shear properties is observed when the nanotubes are crosslinked. However, this increase is accompanied by a decrease in axial mechanical properties of the nanotube material upon crosslinking.

An Active Metamaterial Platform for Chiral Responsive Optoelectronics.

PubMed

Kang, Lei; Lan, Shoufeng; Cui, Yonghao; Rodrigues, Sean P; Liu, Yongmin; Werner, Douglas H; Cai, Wenshan

2015-08-05

Chiral-selective non-linear optics and optoelectronic signal generation are demonstrated in an electrically active photonic metamaterial. The metamaterial reveals significant chiroptical responses in both harmonic generation and the photon drag effect, correlated to the resonance behavior in the linear regime. The multifunctional chiral metamaterial with dual electrical and optical functionality enables transduction of chiroptical responses to electrical signals for integrated photonics. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Analysis of Particulate Composite Behavior Based on Nonlinear Elasticity and an Improved Mori-Tanaka Theory

DTIC Science & Technology

1998-09-01

to characterize the weakening constraint power of the matrix as opposed to earlier analyses that used an additional eigenstrain term. It also...matrix Poisson ratio was constant and the inclusions were rigid, he showed that the disturbed strain and the eigenstrain in the Eshelby method could...Eshelby, elastic properties, prediction, energy balance, mechanical behavior, eigenstrain , nonlinear dcd03e So7S&3 UNCLASSIFIED SECURITY CLASSIFICATION OF FORM (Highest classification of Title, Abstract, Keywords)

Theoretical study of a thermo-acousto-electric generator equipped with an electroacoustic feedback loop

NASA Astrophysics Data System (ADS)

Olivier, Come; Penelet, Guillaume; Poignand, Gaelle; Lotton, Pierrick

2015-10-01

A simplified model of a Stirling-type thermoacoustic engine coupled to a resonant mechanical system is presented. The acoustic network is presented as its temperature-dependent lumped element equivalent, and the nonlinear effects involved in such engines are accounted for in a nonlinear heat equation governing the temperature distribution through the thermoacoustic core. The low-order model is sufficient to capture the behavior of the engine, both in terms of stability and dynamic behavior.

Pharmacokinetics of amikacin in serum and in tissue contiguous with pressure sores in humans with spinal cord injury.

PubMed Central

Segal, J L; Brunnemann, S R; Eltorai, I M

1990-01-01

Pressure sores are a common occurrence in immobilized patients. They increase morbidity and mortality and impede rehabilitation. Antibiotics are routinely used to assist in effecting a cure when infection is present. Nevertheless, for patients with spinal cord injuries (SCI), strategies for effective therapy with antibiotics based on measurement of concentrations in tissue and pharmacokinetic behavior in extravascular spaces do not exist. By analyzing the concentration-time profile and protein binding of amikacin in the interstitial fluid (IF) in contact with pressure sores, we found that the disposition of amikacin in the tissue contiguous with pressure sores appears to be governed by simultaneous first-order and capacity-limited pharmacokinetic behavior. Amikacin disposition in IF proceeded without a simple relationship to amikacin concentrations in serum, and the time course in IF was not accurately simulated by linear models of amikacin pharmacokinetic behavior. Total amikacin clearance estimated from a pharmacokinetic model using simultaneous first-order and nonlinear intercompartmental transfer of amikacin was not significantly different from clearance calculated by us in a prior study of amikacin pharmacokinetic behavior in patients with SCI. In patients with SCI, optimal use of amikacin in the treatment of infected pressure sores is contingent upon accurate characterization of the pharmacokinetic behavior of this aminoglycoside in serum and in the IF in contact with these lesions. Only methods which quantitate amikacin concentration and protein binding in IF and incorporate a model that can simultaneously simulate nonlinear and linear disposition processes should be relied upon to influence therapeutic decision making. PMID:2386372

Unexpected mechanical properties of very dry Berea sandstone near 45°C

NASA Astrophysics Data System (ADS)

Miller, R. A.; Darling, T. W.; TenCate, J. A.; Johnson, P. A.

2011-12-01

An understanding of the nonlinear and hysteretic behavior of porous rocks is important for seismic studies and geologic carbon sequestration applications. However, the fundamental processes responsible for such behavior are poorly understood, including interactions involving adsorbed water and bulk carbon dioxide. Water has been shown to affect the nonlinear mechanical properties of porous rocks, both in high humidity conditions and in low pressure conditions where only a monolayer of water is present on rock grain surfaces [1, 2]. To study the impact of small quantities of adsorbed water on the nonlinear behavior of sandstone, we compare nonlinear resonant ultrasound spectroscopy (NRUS) and time-of-flight modulation (TOFM) measurements [3] on a Berea sandstone core before and after removing bulk water from the sample. Water is removed through extended exposure to ultra high vacuum (UHV) conditions. At the sample's driest state, we achieve a partial pressure of water below 10-8 Torr at room temperature. Periodic measurements record acoustic data as the rock is slowly heated from room temperature to 55°C in UHV. Measurements made after several months of exposure to UHV conditions show behavior we have not previously observed. We report an unexpected sharp increase in Q-1 above 45°C, suggesting we have reduced the concentration of water to a low enough level to affect the sample's mechanical properties. Nonlinear effects are still present when the sample is at its driest state below 45°C, in agreement with previous work [4], which indicates water is not the sole contributor to nonlinearity in porous rock. We are also studying the effect of adding carbon dioxide or argon gas to the dry specimen. We present our acoustic data and propose a model for the impact of adsorbed water on the attenuation of porous rock. [We gratefully acknowledge support from the Nevada Terawatt Facility at the University of Nevada, Reno, and from the Geosciences Research Program of the DOE Office of Basic Energy Sciences]. [1] B. R. Tittmann, L. Ahlberg, and J. Curnow, "Internal friction and velocity measurements," Proc. of 7th Lunar Science Conference , pp. 3123-3132, 1997. [2] K. E.-A. Van Den Abeele, J. Carmeliet, P. A. Johnson, and B. Zinszner, "Influence of water saturation on the nonlinear elastic mesoscopic response in Earth materials and the implications to the mechanism of nonlinearity," Journal of Geophysical Research 107, p. 2121, June 2002. [3] "Dynamic Measures of Elastic Nonlinear (Anelastic) Behavior: Dynamic Acousto-Elasticity Testing (DAET)," G. Renaud, P-Y Le Bas, J. A. TenCate, T. J. Ulrich, J. W. Carey, J. Han, T.W. Darling and P. A. Johnson, AGU Fall Meeting, Dec. 2011. [4] "Water and CO2 chemistry influences on the mechanical integrity of rocks," T.W. Darling, P-Y Le Bas, J. W. Carey, P. A. Johnson and R. A. Miller, AGU Fall Meeting, Dec. 2010.

Nonlinear Time Delayed Feedback Control of Aeroelastic Systems: A Functional Approach

NASA Technical Reports Server (NTRS)

Marzocca, Piergiovanni; Librescu, Liviu; Silva, Walter A.

2003-01-01

In addition to its intrinsic practical importance, nonlinear time delayed feedback control applied to lifting surfaces can result in interesting aeroelastic behaviors. In this paper, nonlinear aeroelastic response to external time-dependent loads and stability boundary for actively controlled lifting surfaces, in an incompressible flow field, are considered. The structural model and the unsteady aerodynamics are considered linear. The implications of the presence of time delays in the linear/nonlinear feedback control and of geometrical parameters on the aeroelasticity of lifting surfaces are analyzed and conclusions on their implications are highlighted.

Plasmon resonance enhancement of nonlinear properties of amino acids

NASA Astrophysics Data System (ADS)

de Araujo, Renato E.; Rativa, Diego; Gomes, Anderson S. L.

2007-02-01

Here we analyze the influence of 9 nm (mean diameter) silver particles on the nonlinear properties of intrinsic cell molecules. A novel high sensitivity thermal managed eclipse Z-scan technique with a femtosecond laser system was used to analyze the nonlinear susceptibility of water solution of fluorescent and non-fluorescent amino acids (Tryptophan, Tyrosine, Phenylalanine, Proline and Histidine) with different concentration of silver nanoparticles. The generalized Maxwell Garnett model is used to explain the behavior of the measured nonlinear refractive index with the change of the nanoparticles concentration in the sample.

A Novel Behavior of Pump Power in the Instability Induced Supercontinuum Generation of Saturable Nonlinear Media

NASA Astrophysics Data System (ADS)

Nithyanandan, K.; Porsezian, K.

2015-04-01

We investigate the modulational instability (MI) induced Supercontinuum generation (SCG) in exponential saturable nonlinearity. The pump power (P) is observed to behave in a unique way such that unlike the conventional Kerr case, the effective nonlinearity of saturable nonlinear system does not monotonously increases with an increase in power. The supercontinuum is observed at the shortest distance of propagation at power equal to the saturation power (Ps), whereas for all combinations of powers (P < Ps or P > Ps) spectral broadening occurs at longer distance.

Nonlinearities in the exchange rates returns and volatility

NASA Astrophysics Data System (ADS)

Díaz, Andrés Fernández; Grau-Carles, Pilar; Mangas, Lorenzo Escot

2002-12-01

Recent findings of nonlinearities in financial assets can be the product of contamination produced by shifts in the distribution of the data. Using the BDS and Kaplan tests it is shown that, some of the nonlinearities found in foreign exchange rate returns, can be the product of shifts in variance while other do not. Also, the behavior of the volatility is studied, showing that the ARFIMA modeling is able to capture long memory, but, depending on the proxy used for the volatility, is not always able to capture all the nonlinearities of the data

Some problems of nonlinear waves in solid propellant rocket motors

NASA Technical Reports Server (NTRS)

Culick, F. E. C.

1979-01-01

An approximate technique for analyzing nonlinear waves in solid propellant rocket motors is presented which inexpensively provides accurate results up to amplitudes of ten percent. The connection with linear stability analysis is shown. The method is extended to third order in the amplitude of wave motion in order to study nonlinear stability, or triggering. Application of the approximate method to the behavior of pulses is described.

Global Nonlinear Analysis of Piezoelectric Energy Harvesting from Ambient and Aeroelastic Vibrations

NASA Astrophysics Data System (ADS)

Abdelkefi, Abdessattar

Converting vibrations to a usable form of energy has been the topic of many recent investigations. The ultimate goal is to convert ambient or aeroelastic vibrations to operate low-power consumption devices, such as microelectromechanical systems, heath monitoring sensors, wireless sensors or replacing small batteries that have a finite life span or would require hard and expensive maintenance. The transduction mechanisms used for transforming vibrations to electric power include: electromagnetic, electrostatic, and piezoelectric mechanisms. Because it can be used to harvest energy over a wide range of frequencies and because of its ease of application, the piezoelectric option has attracted significant interest. In this work, we investigate the performance of different types of piezoelectric energy harvesters. The objective is to design and enhance the performance of these harvesters. To this end, distributed-parameter and phenomenological models of these harvesters are developed. Global analysis of these models is then performed using modern methods of nonlinear dynamics. In the first part of this Dissertation, global nonlinear distributed-parameter models for piezoelectric energy harvesters under direct and parametric excitations are developed. The method of multiple scales is then used to derive nonlinear forms of the governing equations and associated boundary conditions, which are used to evaluate their performance and determine the effects of the nonlinear piezoelectric coefficients on their behavior in terms of softening or hardening. In the second part, we assess the influence of the linear and nonlinear parameters on the dynamic behavior of a wing-based piezoaeroelastic energy harvester. The system is composed of a rigid airfoil that is constrained to pitch and plunge and supported by linear and nonlinear torsional and flexural springs with a piezoelectric coupling attached to the plunge degree of freedom. Linear analysis is performed to determine the effects of the linear spring coefficients and electrical load resistance on the flutter speed. Then, the normal form of the Hopf bifurcation ( utter) is derived to characterize the type of instability and determine the effects of the aerodynamic nonlinearities and the nonlinear coefficients of the springs on the system's stability near the bifurcation. This is useful to characterize the effects of different parameters on the system's output and ensure that subcritical or "catastrophic" bifurcation does not take place. Both linear and nonlinear analyses are then used to design and enhance the performance of these harvesters. In the last part, the concept of energy harvesting from vortex-induced vibrations of a circular cylinder is investigated. The power levels that can be generated from these vibrations and the variations of these levels with the freestream velocity are determined. A mathematical model that accounts for the coupled lift force, cylinder motion and generated voltage is presented. Linear analysis of the electromechanical model is performed to determine the effects of the electrical load resistance on the natural frequency of the rigid cylinder and the onset of the synchronization region. The impacts of the nonlinearities on the cylinder's response and energy harvesting are then investigated.

Correlation between piezoresponse nonlinearity and hysteresis in ferroelectric crystals at nanoscale

DOE PAGES

Kalinin, Sergei V.; Jesse, Stephen; Yang, Yaodong; ...

2016-04-27

Here, the nonlinear response of a ferroic to external fields has been studied for decades, garnering interest for both understanding fundamental physics, as well as technological applications such as memory devices. Yet, the behavior of ferroelectrics at mesoscopic regimes remains poorly understood, and the scale limits of theories developed for macroscopic regimes are not well tested experimentally. Here, we test the link between piezo-nonlinearity and local piezoelectric strain hysteresis, via AC-field dependent measurements in conjunction with first order reversal curve (FORC) measurements on (K,Na)NbO 3 crystals with band-excitation piezoelectric force microscopy. The correlation coefficient between nonlinearity amplitude and the FORCmore » of the polarization switching shows a clear decrease in correlation with increasing AC bias, suggesting the impact of domain wall clamping on the DC measurement case. Further, correlation of polynomial fitting terms from the nonlinear measurements with the hysteresis loop area reveals that the largest correlations are reserved for the quadratic terms, which is expected for irreversible domain wall motion contributions that impact both piezoelectric behavior as well as minor loop formation. These confirm the link between local piezoelectric nonlinearity, domain wall motion and minor loop formation, and suggest that existing theories (such as Preisach) are applicable at these length scales, with associated implications for future nanoscale devices.« less

Testing Born-Infeld electrodynamics in waveguides.

PubMed

Ferraro, Rafael

2007-12-07

Waveguides can be employed to test nonlinear effects in electrodynamics. We solve Born-Infeld equations for TE waves in a rectangular waveguide. We show that the energy velocity acquires a dependence on the amplitude, and harmonic components appear as a consequence of the nonlinear behavior.

Transient Non Lin Deformation in Fractured Rock

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

Sartori, Enrico

1998-10-14

MATLOC is a nonlinear, transient, two-dimensional (planer and axisymmetric), thermal stress, finite-element code designed to determine the deformation within a fractured rock mass. The mass is modeled as a nonlinear anistropic elastic material which can exhibit stress-dependent bi-linear locking behavior.

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

PubMed Central

Dostal, Petr

2015-01-01

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

Nonlinear frequency response based adaptive vibration controller design for a class of nonlinear systems

NASA Astrophysics Data System (ADS)

Thenozhi, Suresh; Tang, Yu

2018-01-01

Frequency response functions (FRF) are often used in the vibration controller design problems of mechanical systems. Unlike linear systems, the FRF derivation for nonlinear systems is not trivial due to their complex behaviors. To address this issue, the convergence property of nonlinear systems can be studied using convergence analysis. For a class of time-invariant nonlinear systems termed as convergent systems, the nonlinear FRF can be obtained. The present paper proposes a nonlinear FRF based adaptive vibration controller design for a mechanical system with cubic damping nonlinearity and a satellite system. Here the controller gains are tuned such that a desired closed-loop frequency response for a band of harmonic excitations is achieved. Unlike the system with cubic damping, the satellite system is not convergent, therefore an additional controller is utilized to achieve the convergence property. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller.

Dynamics of Numerics & Spurious Behaviors in CFD Computations. Revised

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sweby, Peter K.

1997-01-01

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Sorption/Desorption and Transport of Trichloroethene in Freshly-amended, Synthetically- aged, and Field-contaminated Aquifer Material

NASA Astrophysics Data System (ADS)

Johnson, G. R.; Norris, D. K.; Brusseau, M. L.

2008-12-01

This study investigates the effect of long-term contaminant aging on the sorption/desorption and transport of trichloroethene in a low organic-carbon content aquifer material collected from the source zone of a chlorinated-solvent contaminated federal Superfund site in Arizona. This was accomplished by comparing elution behavior for field-contaminated, synthetically-aged (contact times of approximately four years), and freshly-amended aquifer material. Elution of trichloroethene exhibited extensive low-concentration tailing, despite minimal retention of trichloroethene by the aquifer material. The observed nonideal behavior indicates significant mass-transfer constraints influenced trichloroethene transport in this aquifer material. The elution behavior of trichloroethene for the field-contaminated and aged treatments was essentially identical to that observed for the fresh treatments. In addition, the results of three independent mass- balance analyses, total mass eluted, solvent-extraction analysis of residual sorbed mass, and flow- interruption rebound, showed equivalent recoveries for the aged and fresh treatments. These results indicate that long-term contaminant aging did not significantly influence the transport and fate behavior of trichloroethene in this low organic-carbon aquifer material. The observed nonideal behavior of trichloroethene (i.e., nonlinear sorption and significantly rate-limited sorption/desorption) suggests physically condensed carbonaceous material, comprising 61% of this media's organic-carbon content, mediates the transport and fate behavior of trichloroethene in this low organic-carbon content aquifer material.

Nonlinear dynamics behavior analysis of the spatial configuration of a tendril-bearing plant

NASA Astrophysics Data System (ADS)

Feng, Jingjing; Zhang, Qichang; Wang, Wei; Hao, Shuying

2017-03-01

Tendril-bearing plants appear to have a spiraling shape when tendrils climb along a support during growth. The growth characteristics of a tendril-bearer can be simplified to a model of a thin elastic rod with a cylindrical constraint. In this paper, the connection between some typical configuration characteristics of tendrils and complex nonlinear dynamic behavior are qualitatively analyzed. The space configuration problem of tendrils can be explained through the study of the nonlinear dynamic behavior of the thin elastic rod system equation. In this study, the complex non-Z2 symmetric critical orbits in the system equation under critical parameters were presented. A new function transformation method that can effectively maintain the critical orbit properties was proposed, and a new nonlinear differential equations system containing complex nonlinear terms can been obtained to describe the cross section position and direction of a rod during climbing. Numerical simulation revealed that the new system can describe the configuration of a rod with reasonable accuracy. To adequately explain the growing regulation of the rod shape, the critical orbit and configuration of rod are connected in a direct way. The high precision analytical expressions of these complex non-Z2 symmetric critical orbits are obtained by introducing a suitable analytical method, and then these expressions are used to draw the corresponding three-dimensional configuration figures of an elastic thin rod. Combined with actual tendrils on a live plant, the space configuration of the winding knots of tendril is explained by the concept of heteroclinic orbit from the perspective of nonlinear dynamics, and correctness of the theoretical analysis was verified. This theoretical analysis method could also be effectively applied to other similar slender structures.

Study of EPDM/PP polymeric blends: mechanical behavior and effects of compatibilization

NASA Astrophysics Data System (ADS)

Bouchart, Vanessa; Bhatnagar, N.; Brieu, Mathias; Ghosh, A. K.; Kondo, Djimedo

2008-09-01

A blend of Ethylene Propylene Diene Monomer (EPDM) rubber reinforced by polypropylene (PP) particles has been processed and its hyperelastic behavior has been characterized under cyclic uni-axial tensile tests. The experimental results show a significant effect of the fraction of polypropylene particles (10%, 25% and 30% by weight). Moreover, from another series of tests conducted on materials containing compatibilizers at different mass concentration, it is observed that the introduction of a compatibilizer increases the rigidity of the blends and affects notably their macroscopic behavior. These observations are interpreted as a consequence of the modification at microlevel of adherence between particles and matrix phases. The use of a nonlinear micromechanical model allows us to confirm this interpretation. To cite this article: V. Bouchart et al., C. R. Mecanique 336 (2008).

Tracking Control of a Magnetic Shape Memory Actuator Using an Inverse Preisach Model with Modified Fuzzy Sliding Mode Control.

PubMed

Lin, Jhih-Hong; Chiang, Mao-Hsiung

2016-08-25

Magnetic shape memory (MSM) alloys are a new class of smart materials with extraordinary strains up to 12% and frequencies in the range of 1 to 2 kHz. The MSM actuator is a potential device which can achieve high performance electromagnetic actuation by using the properties of MSM alloys. However, significant non-linear hysteresis behavior is a significant barrier to control the MSM actuator. In this paper, the Preisach model was used, by capturing experiments from different input signals and output responses, to model the hysteresis of MSM actuator, and the inverse Preisach model, as a feedforward control, provided compensational signals to the MSM actuator to linearize the hysteresis non-linearity. The control strategy for path tracking combined the hysteresis compensator and the modified fuzzy sliding mode control (MFSMC) which served as a path controller. Based on the experimental results, it was verified that a tracking error in the order of micrometers was achieved.

Tracking Control of a Magnetic Shape Memory Actuator Using an Inverse Preisach Model with Modified Fuzzy Sliding Mode Control

PubMed Central

Lin, Jhih-Hong; Chiang, Mao-Hsiung

2016-01-01

Magnetic shape memory (MSM) alloys are a new class of smart materials with extraordinary strains up to 12% and frequencies in the range of 1 to 2 kHz. The MSM actuator is a potential device which can achieve high performance electromagnetic actuation by using the properties of MSM alloys. However, significant non-linear hysteresis behavior is a significant barrier to control the MSM actuator. In this paper, the Preisach model was used, by capturing experiments from different input signals and output responses, to model the hysteresis of MSM actuator, and the inverse Preisach model, as a feedforward control, provided compensational signals to the MSM actuator to linearize the hysteresis non-linearity. The control strategy for path tracking combined the hysteresis compensator and the modified fuzzy sliding mode control (MFSMC) which served as a path controller. Based on the experimental results, it was verified that a tracking error in the order of micrometers was achieved. PMID:27571081

Improving dynamic performances of PWM-driven servo-pneumatic systems via a novel pneumatic circuit.

PubMed

Taghizadeh, Mostafa; Ghaffari, Ali; Najafi, Farid

2009-10-01

In this paper, the effect of pneumatic circuit design on the input-output behavior of PWM-driven servo-pneumatic systems is investigated and their control performances are improved using linear controllers instead of complex and costly nonlinear ones. Generally, servo-pneumatic systems are well known for their nonlinear behavior. However, PWM-driven servo-pneumatic systems have the advantage of flexibility in the design of pneumatic circuits which affects the input-output linearity of the whole system. A simple pneumatic circuit with only one fast switching valve is designed which leads to a quasi-linear input-output relation. The quasi-linear behavior of the proposed circuit is verified both experimentally and by simulations. Closed loop position control experiments are then carried out using linear P- and PD-controllers. Since the output position is noisy and cannot be directly differentiated, a Kalman filter is designed to estimate the velocity of the cylinder. Highly improved tracking performances are obtained using these linear controllers, compared to previous works with nonlinear controllers.

Nonlinear Behavior of a Shim Coil in an LTS/HTS NMR Magnet With an HTS Insert Comprising Double-Pancake HTS-Tape Coils

PubMed Central

Hahn, Seung-yong; Ahn, Min Cheol; Bascuñán, Juan; Yao, Weijun; Iwasa, Yukikazu

2010-01-01

This paper reports results, experimental and analytical, of the nonlinear behavior of a shim coil in the presence of an HTS coil assembled with double-pancake (DP) HTS-tape coils. The experimental results are from: 1) operation of a 700 MHz LTS/HTS NMR magnet (LH700) consisting of a 600 MHz LTS NMR magnet (L600) equipped with superconducting shim coils and a 100 MHz DP-assembled HTS insert (H100) and; 2) an experiment with a room-temperature (RT) Z1 shim coil coupled to a 50 MHz DP-as-sembled HTS insert (H50). A field mapping theory with a harmonic analysis is applied to interpret both results. Based on experimental results and analyses, we conclude that the screening-current-induced field (SCF) generated by a DP-assembled HTS insert is primarily responsible for the nonlinear behavior, including strength degradation, of a shim coil. PMID:20383282

Spatiotemporal chaos in mixed linear-nonlinear two-dimensional coupled logistic map lattice

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; He, Yi; Wang, Xing-Yuan

2018-01-01

We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.

Modeling, numerical simulation, and nonlinear dynamic behavior analysis of PV microgrid-connected inverter with capacitance catastrophe

NASA Astrophysics Data System (ADS)

Li, Sichen; Liao, Zhixian; Luo, Xiaoshu; Wei, Duqu; Jiang, Pinqun; Jiang, Qinghong

2018-02-01

The value of the output capacitance (C) should be carefully considered when designing a photovoltaic (PV) inverter since it can cause distortion in the working state of the circuit, and the circuit produces nonlinear dynamic behavior. According to Kirchhoff’s laws and the characteristics of an ideal operational amplifier for a strict piecewise linear state equation, a circuit simulation model is constructed to study the system parameters (time, C) for the current passing through an inductor with an inductance of L and the voltage across the capacitor with a capacitance of C. The developed simulation model uses Runge-Kutta methods to solve the state equations. This study focuses on predicting the fault of the circuit from the two aspects of the harmonic distortion and simulation results. Moreover, the presented model is also used to research the working state of the system in the case of a load capacitance catastrophe. The nonlinear dynamic behaviors in the inverter are simulated and verified.

A nonlinear energy sink with an energy harvester: Harmonically forced responses

NASA Astrophysics Data System (ADS)

Kremer, Daniel; Liu, Kefu

2017-12-01

This study intends to achieve simultaneous vibration suppression and energy harvesting using a variant form of nonlinear energy sink (NES). The proposed apparatus is not a true NES as its spring is not essentially nonlinear. In a previous study [22] (Journal of Sound and Vibration, 333 (20) (2014)), it has been shown that the apparatus demonstrates the transient behaviors similar to those of the NES. As a sequel, the present paper focuses on harmonically forced responses of the system. First, the approximate solutions of steady state responses are derived. Using the approximate solutions, the steady state behaviors are investigated by using the numerical continuation method. This is followed by an experimental study. The study has shown that under harmonic excitation, the proposed apparatus functions similarly to the NES with the typical behaviors such as strongly modulated responses, amplitude jumping, excitation level dependence, etc. Overall, the apparatus meets the design objectives: the vibration suppression and energy harvesting in a broadband manner.

Nonlinear Surface Dilatational Rheology and Foaming Behavior of Protein and Protein Fibrillar Aggregates in the Presence of Natural Surfactant.

PubMed

Wan, Zhili; Yang, Xiaoquan; Sagis, Leonard M C

2016-04-19

The surface and foaming properties of native soy glycinin (11S) and its heat-induced fibrillar aggregates, in the presence of natural surfactant steviol glycoside (STE), were investigated and compared at pH 7.0 to determine the impact of protein structure modification on protein-surfactant interfacial interactions. The adsorption at, and nonlinear dilatational rheological behavior of, the air-water interface were studied by combining drop shape analysis tensiometry, ellipsometry, and large-amplitude oscillatory dilatational rheology. Lissajous plots of surface pressure versus deformation were used to analyze the surface rheological response in terms of interfacial microstructure. The heat treatment generates a mixture of long fibrils and unconverted peptides. The presence of small peptides in 11S fibril samples resulted in a faster adsorption kinetics than that of native 11S. The addition of STE affected the adsorption of 11S significantly, whereas no apparent effect on the adsorption of the 11S fibril-peptide system was observed. The rheological response of interfaces stabilized by 11S-STE mixtures also differed significantly from the response for 11S fibril-peptide-STE mixtures. For 11S, the STE reduces the degree of strain hardening in extension and increases strain hardening in compression, suggesting the interfacial structure may change from a surface gel to a mixed phase of protein patches and STE domains. The foams generated from the mixtures displayed comparable foam stability to that of pure 11S. For 11S fibril-peptide mixtures STE only significantly affects the response in extension, where the degree of strain softening is decreased compared to the pure fibril-peptide system. The foam stability of the fibril-peptide system was significantly reduced by STE. These findings indicate that fibrillization of globular proteins could be a potential strategy to modify the complex surface and foaming behaviors of protein-surfactant mixtures.

Metal matrix composite micromechanics: In-situ behavior influence on composite properties

NASA Technical Reports Server (NTRS)

Murthy, P. L. N.; Hopkins, D. A.; Chamis, C. C.

1989-01-01

Recent efforts in computational mechanics methods for simulating the nonlinear behavior of metal matrix composites have culminated in the implementation of the Metal Matrix Composite Analyzer (METCAN) computer code. In METCAN material nonlinearity is treated at the constituent (fiber, matrix, and interphase) level where the current material model describes a time-temperature-stress dependency of the constituent properties in a material behavior space. The composite properties are synthesized from the constituent instantaneous properties by virtue of composite micromechanics and macromechanics models. The behavior of metal matrix composites depends on fabrication process variables, in situ fiber and matrix properties, bonding between the fiber and matrix, and/or the properties of an interphase between the fiber and matrix. Specifically, the influence of in situ matrix strength and the interphase degradation on the unidirectional composite stress-strain behavior is examined. These types of studies provide insight into micromechanical behavior that may be helpful in resolving discrepancies between experimentally observed composite behavior and predicted response.

Vibrational dynamics of vocal folds using nonlinear normal modes.

PubMed

Pinheiro, Alan P; Kerschen, Gaëtan

2013-08-01

Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues. The results show very interesting and complex nonlinear phenomena including frequency-energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.

1992-01-01

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.

Nonlinear vibration and radiation from a panel with transition to chaos

NASA Technical Reports Server (NTRS)

Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.

1992-01-01

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-dependent Non-linear Bearing Stiffness

NASA Technical Reports Server (NTRS)

Fleming, David P.; Poplawski, J. V.

2002-01-01

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

Analysis of Vertebral Bone Strength, Fracture Pattern, and Fracture Location: A Validation Study Using a Computed Tomography-Based Nonlinear Finite Element Analysis

PubMed Central

Imai, Kazuhiro

2015-01-01

Finite element analysis (FEA) is an advanced computer technique of structural stress analysis developed in engineering mechanics. Because the compressive behavior of vertebral bone shows nonlinear behavior, a nonlinear FEA should be utilized to analyze the clinical vertebral fracture. In this article, a computed tomography-based nonlinear FEA (CT/FEA) to analyze the vertebral bone strength, fracture pattern, and fracture location is introduced. The accuracy of the CT/FEA was validated by performing experimental mechanical testing with human cadaveric specimens. Vertebral bone strength and the minimum principal strain at the vertebral surface were accurately analyzed using the CT/FEA. The experimental fracture pattern and fracture location were also accurately simulated. Optimization of the element size was performed by assessing the accuracy of the CT/FEA, and the optimum element size was assumed to be 2 mm. It is expected that the CT/FEA will be valuable in analyzing vertebral fracture risk and assessing therapeutic effects on osteoporosis. PMID:26029476

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

NASA Astrophysics Data System (ADS)

Kashyap, Rahul; Westley, Alexandra; Sen, Surajit

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

Analysis of Fiber Clustering in Composite Materials Using High-Fidelity Multiscale Micromechanics

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Aboudi, Jacob; Arnold, Steven M.

2015-01-01

A new multiscale micromechanical approach is developed for the prediction of the behavior of fiber reinforced composites in presence of fiber clustering. The developed method is based on a coupled two-scale implementation of the High-Fidelity Generalized Method of Cells theory, wherein both the local and global scales are represented using this micromechanical method. Concentration tensors and effective constitutive equations are established on both scales and linked to establish the required coupling, thus providing the local fields throughout the composite as well as the global properties and effective nonlinear response. Two nondimensional parameters, in conjunction with actual composite micrographs, are used to characterize the clustering of fibers in the composite. Based on the predicted local fields, initial yield and damage envelopes are generated for various clustering parameters for a polymer matrix composite with both carbon and glass fibers. Nonlinear epoxy matrix behavior is also considered, with results in the form of effective nonlinear response curves, with varying fiber clustering and for two sets of nonlinear matrix parameters.

Neural activation in the "reward circuit" shows a nonlinear response to facial attractiveness.

PubMed

Liang, Xiaoyun; Zebrowitz, Leslie A; Zhang, Yi

2010-01-01

Positive behavioral responses to attractive faces have led neuroscientists to investigate underlying neural mechanisms in a "reward circuit" that includes brain regions innervated by dopamine pathways. Using male faces ranging from attractive to extremely unattractive, disfigured ones, this study is the first to demonstrate heightened responses to both rewarding and aversive faces in numerous areas of this putative reward circuit. Parametric analyses employing orthogonal linear and nonlinear regressors revealed positive nonlinear effects in anterior cingulate cortex, lateral orbital frontal cortex (LOFC), striatum (nucleus accumbens, caudate, putamen), and ventral tegmental area, in addition to replicating previously documented linear effects in medial orbital frontal cortex (MOFC) and LOFC and nonlinear effects in amygdala and MOFC. The widespread nonlinear responses are consistent with single cell recordings in animals showing responses to both rewarding and aversive stimuli, and with some human fMRI investigations of non-face stimuli. They indicate that the reward circuit does not process face valence with any simple dissociation of function across structures. Perceiver gender modulated some responses to our male faces: Women showed stronger linear effects, and men showed stronger nonlinear effects, which may have functional implications. Our discovery of nonlinear responses to attractiveness throughout the reward circuit echoes the history of amygdala research: Early work indicated a linear response to threatening stimuli, including faces; later work also revealed a nonlinear response with heightened activation to affectively salient stimuli regardless of valence. The challenge remains to determine how such dual coding influences feelings, such as pleasure and pain, and guides goal-related behavioral responses, such as approach and avoidance.

Low-dimensional manifold of actin polymerization dynamics

NASA Astrophysics Data System (ADS)

Floyd, Carlos; Jarzynski, Christopher; Papoian, Garegin

2017-12-01

Actin filaments are critical components of the eukaryotic cytoskeleton, playing important roles in a number of cellular functions, such as cell migration, organelle transport, and mechanosensation. They are helical polymers with a well-defined polarity, composed of globular subunits that bind nucleotides in one of three hydrolysis states (ATP, ADP-Pi, or ADP). Mean-field models of the dynamics of actin polymerization have succeeded in, among other things, determining the nucleotide profile of an average filament and resolving the mechanisms of accessory proteins. However, these models require numerical solution of a high-dimensional system of nonlinear ordinary differential equations. By truncating a set of recursion equations, the Brooks-Carlsson (BC) model reduces dimensionality to 11, but it still remains nonlinear and does not admit an analytical solution, hence, significantly hindering understanding of its resulting dynamics. In this work, by taking advantage of the fast timescales of the hydrolysis states of the filament tips, we propose two model reduction schemes: the quasi steady-state approximation model is five-dimensional and nonlinear, whereas the constant tip (CT) model is five-dimensional and linear, resulting from the approximation that the tip states are not dynamic variables. We provide an exact solution of the CT model and use it to shed light on the dynamical behaviors of the full BC model, highlighting the relative ordering of the timescales of various collective processes, and explaining some unusual dependence of the steady-state behavior on initial conditions.

On the Nonlinear Behavior of a Glass-Ceramic Seal and its Application in Planar SOFC Systems

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

Nguyen, Ba Nghiep; Koeppel, Brian J.; Vetrano, John S.

2006-06-01

This paper studies the nonlinear behavior of a glass-ceramic seal used in planar solid oxide fuel cells (SOFCs). To this end, a viscoelastic damage model has been developed that can capture the nonlinear material response due to both progressive damage in the glass-ceramic material and viscous flow of the residual glass in this material. The model has been implemented in the MSC MARC finite element code, and its validation has been carried out using the experimental relaxation test data obtained for this material at 700oC, 750oC, and 800oC. Finally, it has been applied to the simulation of a SOFC stackmore » under thermal cycling conditions. The areas of potential damage have been predicted.« less

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Nonlinear dynamics of the magnetosphere and space weather

NASA Technical Reports Server (NTRS)

Sharma, A. Surjalal

1996-01-01

The solar wind-magnetosphere system exhibits coherence on the global scale and such behavior can arise from nonlinearity on the dynamics. The observational time series data were used together with phase space reconstruction techniques to analyze the magnetospheric dynamics. Analysis of the solar wind, auroral electrojet and Dst indices showed low dimensionality of the dynamics and accurate prediction can be made with an input/output model. The predictability of the magnetosphere in spite of the apparent complexity arises from its dynamical synchronism with the solar wind. The electrodynamic coupling between different regions of the magnetosphere yields its coherent, low dimensional behavior. The data from multiple satellites and ground stations can be used to develop a spatio-temporal model that identifies the coupling between different regions. These nonlinear dynamical models provide space weather forecasting capabilities.

Nonlinear absorption properties of ZnO and Al doped ZnO thin films under continuous and pulsed modes of operations

NASA Astrophysics Data System (ADS)

Sandeep, K. M.; Bhat, Shreesha; Dharmaprakash, S. M.

2018-06-01

In the present investigation, we present the variations in nonlinear optical (NLO) properties of undoped and Al doped ZnO (AZO) films under two different off-resonant regimes using continuous and pulsed mode lasers. Z-scan open aperture experiment is performed to quantify nonlinear absorption constant and imaginary component of third order susceptibility. Reverse saturable absorption (RSA) and saturable absorption (SA) behaviors are noticed in both undoped and AZO films under pulsed mode and continuous wavelength (CW) regime respectively. The RSA and SA behavior observed in the films are attributed to two photon absorption (TPA) and thermal lensing properties respectively. The thermal lensing is assisted by the thermo-optic effects within the films due to the continuous illumination of the laser.

A simple nonlinear model for the return to isotropy in turbulence

NASA Technical Reports Server (NTRS)

Sarkar, Sutanu; Speziale, Charles G.

1990-01-01

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable nontrivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable nontrivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

A megahertz-frequency tunable piecewise-linear electromechanical resonator realized via nonlinear feedback

NASA Astrophysics Data System (ADS)

Bajaj, Nikhil; Chiu, George T.-C.; Rhoads, Jeffrey F.

2018-07-01

Vibration-based sensing modalities traditionally have relied upon monitoring small shifts in natural frequency in order to detect structural changes (such as those in mass or stiffness). In contrast, bifurcation-based sensing schemes rely on the detection of a qualitative change in the behavior of a system as a parameter is varied. This can produce easy-to-detect changes in response amplitude with high sensitivity to structural change, but requires resonant devices with specific dynamic behavior which is not always easily reproduced. Desirable behavior for such devices can be produced reliably via nonlinear feedback circuitry, but has in past efforts been largely limited to sub-MHz operation, partially due to the time delay limitations present in certain nonlinear feedback circuits, such as multipliers. This work demonstrates the design and implementation of a piecewise-linear resonator realized via diode- and integrated circuit-based feedback electronics and a quartz crystal resonator. The proposed system is fabricated and characterized, and the creation and selective placement of the bifurcation points of the overall electromechanical system is demonstrated by tuning the circuit gains. The demonstrated circuit operates at 16 MHz. Preliminary modeling and analysis is presented that qualitatively agrees with the experimentally-observed behavior.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks

PubMed Central

Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed. PMID:28796797

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks.

PubMed

Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

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

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

Time-dependent behavior of passive skeletal muscle

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

Complex behavior in chains of nonlinear oscillators.

PubMed

Alonso, Leandro M

2017-06-01

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

Asymptotic behavior for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions

NASA Astrophysics Data System (ADS)

Katayama, Soichiro

We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In this paper, we will show that the global solution is asymptotically free in the energy sense, by obtaining the asymptotic pointwise behavior of the derivatives of the solution. Nonetheless we can also show that the pointwise behavior of the solution itself may be quite different from that of the free solution. In connection with the above results, a theorem is also developed to characterize asymptotically free solutions for wave equations in arbitrary space dimensions.

Thermal expansion behavior study of Co nanowire array with in situ x-ray diffraction and x-ray absorption fine structure techniques

NASA Astrophysics Data System (ADS)

Mo, Guang; Cai, Quan; Jiang, Longsheng; Wang, Wei; Zhang, Kunhao; Cheng, Weidong; Xing, Xueqing; Chen, Zhongjun; Wu, Zhonghua

2008-10-01

In situ x-ray diffraction and x-ray absorption fine structure techniques were used to study the structural change of ordered Co nanowire array with temperature. The results show that the Co nanowires are polycrystalline with hexagonal close packed structure without phase change up until 700 °C. A nonlinear thermal expansion behavior has been found and can be well described by a quadratic equation with the first-order thermal expansion coefficient of 4.3×10-6/°C and the second-order thermal expansion coefficient of 5.9×10-9/°C. The mechanism of this nonlinear thermal expansion behavior is discussed.

Cognitive mediators of treatment for social anxiety disorder: comparing acceptance and commitment therapy and cognitive-behavioral therapy.

PubMed

Niles, Andrea N; Burklund, Lisa J; Arch, Joanna J; Lieberman, Matthew D; Saxbe, Darby; Craske, Michelle G

2014-09-01

To assess the relationship between session-by-session mediators and treatment outcomes in traditional cognitive-behavioral therapy (CBT) and acceptance and commitment therapy (ACT) for social anxiety disorder. Session-by-session changes in negative cognitions (a theorized mediator of CBT) and experiential avoidance (a theorized mediator of ACT) were assessed in 50 adult outpatients randomized to CBT (n=25) or ACT (n=25) for DSM-IV social anxiety disorder. Multilevel modeling analyses revealed significant nonlinear decreases in the proposed mediators in both treatments, with ACT showing steeper decline than CBT at the beginning of treatment and CBT showing steeper decline than ACT at the end of treatment. Curvature (or the nonlinear effect) of experiential avoidance during treatment significantly mediated posttreatment social anxiety symptoms and anhedonic depression in ACT, but not in CBT, with steeper decline of the Acceptance and Action Questionnaire at the beginning of treatment predicting fewer symptoms in ACT only. Curvature of negative cognitions during both treatments predicted outcome, with steeper decline of negative cognitions at the beginning of treatment predicting lower posttreatment social anxiety and depressive symptoms. Rate of change in negative cognitions at the beginning of treatment is an important predictor of change across both ACT and CBT, whereas rate of change in experiential avoidance at the beginning of treatment is a mechanism specific to ACT. Copyright © 2014. Published by Elsevier Ltd.

Cognitive Mediators of Treatment for Social Anxiety Disorder: Comparing Acceptance and Commitment Therapy and Cognitive-Behavioral Therapy

PubMed Central

Niles, Andrea N.; Burklund, Lisa J.; Arch, Joanna J.; Lieberman, Matthew D.; Saxbe, Darby; Craske, Michelle G.

2016-01-01

Objective To assess the relationship between session-by-session mediators and treatment outcomes in traditional cognitive-behavioral therapy (CBT) and acceptance and commitment therapy (ACT) for social anxiety disorder. Method Session-by-session changes in negative cognitions (a theorized mediator of CBT) and experiential avoidance (a theorized mediator of ACT) were assessed in 50 adult outpatients randomized to CBT (n = 25) or ACT (n = 25) for DSM-IV social anxiety disorder. Results Multilevel modeling analyses revealed significant nonlinear decreases in the proposed mediators in both treatments, with ACT showing steeper decline than CBT at the beginning of treatment and CBT showing steeper decline than ACT at the end of treatment. Curvature (or the nonlinear effect) of experiential avoidance during treatment significantly mediated posttreatment social anxiety symptoms and anhedonic depression in ACT, but not in CBT, with steeper decline of the Acceptance and Action Questionnaire at the beginning of treatment predicting fewer symptoms in ACT only. Curvature of negative cognitions during both treatments predicted outcome, with steeper decline of negative cognitions at the beginning of treatment predicting lower posttreatment social anxiety and depressive symptoms. Conclusions Rate of change in negative cognitions at the beginning of treatment is an important predictor of change across both ACT and CBT, whereas rate of change in experiential avoidance at the beginning of treatment is a mechanism specific to ACT. PMID:25022777

Study on Nonlinear Lateral Parameter Bifurcation Characteristic of Soft Footbridge

NASA Astrophysics Data System (ADS)

Chen, Zhou; Deng, De-Yuan; Yan, Quan-Sheng; Lu, Jin-Zhong; Lu, Jian-Xin

2018-03-01

With the trend of large span in the development of footbridge, its nonlinear characteristic is more and more obvious. Bifurcation has a great influence on the nonstationary trivial solution and its boundary stability of nonlinear vibration. Based on the Millennium Bridge in London, this paper deduces its nonlinear transverse vibration equation. Also, the method of Galerkin and multi-scale method is used to obtain the judgment condition of nonstationary trivial stability. Based on the bifurcation theory, the influence of nonlinear behavior on nontrivial solution as well as its stability is studied in the paper under two situations, a 1 ‑ σ bifurcation and a 1 ‑ ζ2 bifurcation of parameter plane respectively.

A computational procedure to analyze metal matrix laminates with nonlinear lamination residual strains

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sullivan, T. L.

1974-01-01

An approximate computational procedure is described for the analysis of angleplied laminates with residual nonlinear strains. The procedure consists of a combination of linear composite mechanics and incremental linear laminate theory. The procedure accounts for initial nonlinear strains, unloading, and in-situ matrix orthotropic nonlinear behavior. The results obtained in applying the procedure to boron/aluminum angleplied laminates show that this is a convenient means to accurately predict the initial tangent properties of angleplied laminates in which the matrix has been strained nonlinearly by the lamination residual stresses. The procedure predicted initial tangent properties results which were in good agreement with measured data obtained from boron/aluminum angleplied laminates.

Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow

NASA Technical Reports Server (NTRS)

Choudhari, Meelan; Duck, Peter W.

1996-01-01

We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.

Nonlocal Sediment Transport on Steep Lateral Moraines, Eastern Sierra Nevada, California, USA

NASA Astrophysics Data System (ADS)

Doane, Tyler H.; Furbish, David Jon; Roering, Joshua J.; Schumer, Rina; Morgan, Daniel J.

2018-01-01

Recent work has highlighted the significance of long-distance particle motions in hillslope sediment transport. Such motions imply that the flux at a given hillslope position is appropriately described as a weighted function of surrounding conditions that influence motions reaching the given position. Although the idea of nonlocal sediment transport is well grounded in theory, limited field evidence has been provided. We test local and nonlocal formulations of the flux and compare their ability to reproduce land surface profiles of steep moraines in California. We show that nonlocal and nonlinear models better reproduce evolved land surface profiles, notably the amount of lowering and concavity near the moraine crest and the lengthening and straightening of the depositional apron. The analysis provides the first estimates of key parameters that set sediment entrainment rates and travel distances in nonlocal formulations and highlights the importance of correctly specifying the entrainment rate when modeling land surface evolution. Moraine evolution associated with nonlocal and nonlinear transport formulations, when described in terms of the evolution of the Fourier transform of the moraine surface, displays a distinct behavior involving growth of certain wave numbers, in contrast to the decay of all wave numbers associated with linear transport. Nonlinear and nonlocal formulations share key mathematical elements yielding a nonlinear relation between the flux and the land surface slope.

The Effects of Hydrogen Band EMIC Waves on Ring Current H+ Ions

NASA Astrophysics Data System (ADS)

Wang, Zhiqiang; Zhai, Hao; Gao, Zhuxiu

2017-12-01

Hydrogen band electromagnetic ion cyclotron (EMIC) waves have received much attention recently because they are found to frequently span larger spatial areas than the other band EMIC waves. Using test particle simulations, we study the nonlinear effects of hydrogen band EMIC waves on ring current H+ ions. A dimensionless parameter R is used to characterize the competition between wave-induced and adiabatic motions. The results indicate that there are three regimes of wave-particle interactions for typical 35 keV H+ ions at L = 5: diffusive (quasi-linear) behavior when αeq ≤ 35° (R ≥ 2.45), the nonlinear phase trapping when 35° < αeq < 50° (0.75 < R < 2.45), and both the nonlinear phase bunching and phase trapping when αeq ≥ 50° (R ≤ 0.75). The phase trapping can transport H+ ions toward large pitch angle, while the phase bunching has the opposite effect. The phase-trapped H+ ions can be significantly accelerated (from 35 keV to over 500 keV) in about 4 min and thus contribute to the formation of high energy components of ring current ions. The results suggest that the effect of hydrogen band EMIC waves is not ignorable in the nonlinear acceleration and resonance scattering of ring current H+ ions.

Nonlinearity and Strain-Rate Dependence in the Deformation Response of Polymer Matrix Composites Modeled

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

2000-01-01

There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.

CONSEQUENCES OF NON-LINEAR DENSITY EFFECTS ON BUOYANCY AND PLUME BEHAVIOR

EPA Science Inventory

Aquatic plumes, as turbulent streams, grow by entraining ambient water. Buoyant plumes rise and dense ones sink, but, non-linear kinetic effects can reverse the buoyant force in mid-phenomenon. The class of nascent-density plumes begin as buoyant, upwardly accelerating plumes tha...

The nonlinear bending response of thin-walled laminated composite cylinders

NASA Technical Reports Server (NTRS)

Fuchs, Hannes P.; Hyer, Michael W.

1992-01-01

The geometrically nonlinear Donnell shell theory is applied to the problem of stable bending of thin-walled circular cylinders. Responses are computed for cylinders with a radius-to-thickness ratio of 50 and length-to-radius ratios of 1 and 5. Four laminated composite cylinders and an aluminum cylinder are considered. Critical moment estimates are presented for short cylinders for which compression-type buckling behavior is important, and for very long cylinders for which the cross-section flattening, i.e., Brazier effect, is important. A finite element analysis is used to estimate the critical end rotation in addition to establishing the range of validity of the prebuckling analysis. The radial displacement response shows that the character of the boundary layer is significantly influenced by the geometric nonlinearities. Application of a first ply failure analysis using the maximum stress criterion suggests that in nearly all instances material failure occurs before buckling. Failure of the composite cylinders can be attributed to fiber breakage. Striking similarities are seen between the prebuckling displacements of the bending problem and axial compression problem for short cylinders.

Non-linear dielectric signatures of entropy changes in liquids subject to time dependent electric fields

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

Richert, Ranko

2016-03-21

A model of non-linear dielectric polarization is studied in which the field induced entropy change is the source of polarization dependent retardation time constants. Numerical solutions for the susceptibilities of the system are obtained for parameters that represent the dynamic and thermodynamic behavior of glycerol. The calculations for high amplitude sinusoidal fields show a significant enhancement of the steady state loss for frequencies below that of the low field loss peak. Also at relatively low frequencies, the third harmonic susceptibility spectrum shows a “hump,” i.e., a maximum, with an amplitude that increases with decreasing temperature. Both of these non-linear effectsmore » are consistent with experimental evidence. While such features have been used to conclude on a temperature dependent number of dynamically correlated particles, N{sub corr}, the present result demonstrates that the third harmonic susceptibility display a peak with an amplitude that tracks the variation of the activation energy in a model that does not involve dynamical correlations or spatial scales.« less

Nonlinear Spectral Singularity and Laser Output Intensity for the TE and TM Modes

NASA Astrophysics Data System (ADS)

Ghaemidizicheh, Hamed; Mostafazadeh, Ali

The nonlinear spectral singularity arising from a Kerr nonlinearity is explored in. This reference studies the effect of nonlinearity in Lasing condition and shows that Kerr nonlinearity with spectral singularity for a normally incident wave provides an explanation of lasing at gain coefficient g. Lasing occurs when it exceeds threshold gain g0. For oblique waves, Ref. looks at the behavior of threshold gain coefficient g0 which is given by the condition that there is a linear spectral singularity. We investigated imposing the condition of the existence of nonlinear spectral singularity in the TE / TM modes of a mirrorless slab of gain materials and studied the θ-dependence of intensity. Supported by TUBITAK Project No: 114F357 and by the Turkish Academy of Science (TUBA).

Effect of spectral sampling on the temporal coherence analysis of a broadband source in a SFG interferometer.

PubMed

Darré, Pascaline; Szemendera, Ludovic; Grossard, Ludovic; Delage, Laurent; Reynaud, François

2015-10-05

In the frame of sum frequency generation of a broadband infrared source, we aim to enlarge the converted bandwidth by using a pump frequency comb while keeping a high conversion efficiency. The nonlinear effects are simultaneously induced in the same nonlinear medium. In this paper, we investigate the spectral filtering effect on the temporal coherence behavior with a Mach-Zehnder interferometer using two pump lines. We show that joined effects of quasi-phase matching and spectral sampling lead to an original coherence behavior.

Analytical results for post-buckling behaviour of plates in compression and in shear

NASA Technical Reports Server (NTRS)

Stein, M.

1985-01-01

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Receptor theory and biological constraints on value.

PubMed

Berns, Gregory S; Capra, C Monica; Noussair, Charles

2007-05-01

Modern economic theories of value derive from expected utility theory. Behavioral evidence points strongly toward departures from linear value weighting, which has given rise to alternative formulations that include prospect theory and rank-dependent utility theory. Many of the nonlinear forms for value assumed by these theories can be derived from the assumption that value is signaled by neurotransmitters in the brain, which obey simple laws of molecular movement. From the laws of mass action and receptor occupancy, we show how behaviorally observed forms of nonlinear value functions can arise.

Design considerations for multi component molecular-polymeric nonlinear optical materials

NASA Astrophysics Data System (ADS)

Singer, K. D.; Kuzyk, M. G.; Fang, T.; Holland, W. R.; Cahill, P. A.

1990-08-01

We review our work on multi component polymeric nonlinear optical materials. These materials consist of nonlinear optical molecules incorporated in a polymeric host. A cross-linked triazine polymer incorporating a dicyanovinyl terminated azo dye was found to be relatively stable at 85 deg and possess an electro-optic coefficient of 11pm/V. We have also observed the zero dispersion condition in a new anomalous dispersion dye for phase matched second harmonic generation, and expect efficient conversion to the blue. A squarylium dye, ISQ, has been found to possess a large third order nonlinearity, and may display two-level behavior.

Optimal Scaling of HIV-Related Sexual Risk Behaviors in Ethnically Diverse Homosexually Active Men.

ERIC Educational Resources Information Center

Cochran, Susan D.; And Others

1995-01-01

Used homogeneity analysis and latent class analysis to analyze sexual behavior patterns in two samples of homosexually active men. Results support the existence of a single, nonlinear, latent dimension underlying male homosexual behaviors consistent with HIV-related risk taking, providing an efficient means to scale sexual behavior patterns. (RJM)

The effect of storage temperature on blue cheese mechanical properties.

PubMed

Joyner Melito, Helen S; Francis, Dorothy; Luzzi, Brooke; Johnson, John R

2018-06-01

Blue cheese is commonly aged for 60 days at 10°C after curing. However, some manufacturers store blue cheese at 4°C and the effect of lower storage temperature on blue cheese final properties is unknown. Thus, the objective of this study was to determine the effect of storage temperature and time on blue cheese mechanical behaviors. Blue cheeses were stored at 4 or 10°C for 77 days after production. Composition and small- and large-strain rheological behaviors were evaluated every 2 weeks of storage. Storage time had significant impact on blue cheese rheological behaviors; storage temperature did not. Large-strain compressive force and viscoelastic moduli decreased with storage time, and the extent of nonlinear viscoelastic behavior increased. These results indicated that sample microstructure likely weakened and was more easily deformed as storage time increased. Overall, blue cheese can be stored at 4-10°C without significant changes to its composition or mechanical behavior. The results of this work can be used by blue cheese manufacturers to better understand the impact of storage time and temperature on blue cheese end quality. Manufacturers can take advantage of the effects of storage time on blue cheese mechanical behaviors to determine how long to age blue cheese to achieve the desired texture. © 2017 Wiley Periodicals, Inc.

Interlaminar fracture of random short-fiber SMC composite

NASA Technical Reports Server (NTRS)

Wang, S. S.; Suemasu, H.; Zahlan, N. M.

1984-01-01

In the experimental phase of the present study of the interlaminar fracture behavior of a randomly oriented short fiber sheet molding compound (SMC) composite, the double cantilever beam fracture test is used to evaluate the mode I interlaminar fracture toughness of different composite thicknesses. In the analytical phase of this work, a geometrically nonlinear analysis is introduced in order to account for large deflections and nonlinear load deflection curves in the evaluation of interlaminar fracture toughness. For the SMC-R50 material studied, interlaminar toughness is an order of magnitude higher than that of unreinforced neat resin, due to unusual damage mechanisms ahead of the crack tip, together with significant fiber bridging across crack surfaces. Composite thickness effects on interlaminar fracture are noted to be appreciable, and a detailed discussion is given on the influence of SMC microstructure.

Large strain deformation behavior of polymeric gels in shear- and cavitation rheology

NASA Astrophysics Data System (ADS)

Hashemnejad, Seyed Meysam; Kundu, Santanu

Polymeric gels are used in many applications including in biomedical and in food industries. Investigation of mechanical responses of swollen polymer gels and linking that to the polymer chain dynamics are of significant interest. Here, large strain deformation behavior of two different gel systems and with different network architecture will be presented. We consider biologically relevant polysaccharide hydrogels, formed through ionic and covalent crosslinking, and physically associating triblock copolymer gels in a midblock selective solvent. Gels with similar low-strain shear modulus display distinctly different non-linear rheological behavior in large strain shear deformation. Both these gels display strain-stiffening behavior in shear-deformation prior to macroscopic fracture of the network, however, only the alginate gels display negative normal stress. The cavitation rheology data show that the critical pressure for cavitation is higher for alginate gels than that observed for triblock gels. These distinctly different large-strain deformation behavior has been related to the gel network structure, as alginate chains are much stiffer than the triblock polymer chains.

Application of Nonlinear Elastic Resonance Spectroscopy For Damage Detection In Concrete: An Interesting Story

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

Byers, Loren W.; Ten Cate, James A.; Johnson, Paul A.

2012-06-28

Nonlinear resonance ultrasound spectroscopy experiments conducted on concrete cores, one chemically and mechanically damaged by alkali-silica reactivity, and one undamaged, show that this material displays highly nonlinear wave behavior, similar to many other damaged materials. They find that the damaged sample responds more nonlinearly, manifested by a larger resonant peak and modulus shift as a function of strain amplitude. The nonlinear response indicates that there is a hysteretic influence in the stress-strain equation of state. Further, as in some other materials, slow dynamics are present. The nonlinear response they observe in concrete is an extremely sensitive indicator of damage. Ultimately,more » nonlinear wave methods applied to concrete may be used to guide mixing, curing, or other production techniques, in order to develop materials with particular desired qualities such as enhanced strength or chemical resistance, and to be used for damage inspection.« less

Modeling of stress/strain behavior of fiber-reinforced ceramic matrix composites including stress redistribution

NASA Technical Reports Server (NTRS)

Mital, Subodh K.; Murthy, Pappu L. N.; Chamis, Christos C.

1994-01-01

A computational simulation procedure is presented for nonlinear analyses which incorporates microstress redistribution due to progressive fracture in ceramic matrix composites. This procedure facilitates an accurate simulation of the stress-strain behavior of ceramic matrix composites up to failure. The nonlinearity in the material behavior is accounted for at the constituent (fiber/matrix/interphase) level. This computational procedure is a part of recent upgrades to CEMCAN (Ceramic Matrix Composite Analyzer) computer code. The fiber substructuring technique in CEMCAN is used to monitor the damage initiation and progression as the load increases. The room-temperature tensile stress-strain curves for SiC fiber reinforced reaction-bonded silicon nitride (RBSN) matrix unidirectional and angle-ply laminates are simulated and compared with experimentally observed stress-strain behavior. Comparison between the predicted stress/strain behavior and experimental stress/strain curves is good. Collectively the results demonstrate that CEMCAN computer code provides the user with an effective computational tool to simulate the behavior of ceramic matrix composites.

Control of interaction strength in a network of the true slime mold by a microfabricated structure.

PubMed

Takamatsu, A; Fujii, T; Endo, I

2000-02-01

The plasmodium of the true slime mold, Physarum polycephalum, which shows various nonlinear oscillatory phenomena, for example, in its thickness, protoplasmic streaming and concentration of intracellular chemicals, can be regarded as a collective of nonlinear oscillators. The plasmodial oscillators are interconnected by microscale tubes whose dimensions can be closely related to the strength of interaction between the oscillators. Investigation of the collective behavior of the oscillators under the conditions in which the interaction strength can be systematically controlled gives significant information on the characteristics of the system. In this study, we proposed a living model system of a coupled oscillator system in the Physarum plasmodium. We patterned the geometry and dimensions of the microscale tube structure in the plasmodium by a microfabricated structure (microstructure). As the first step, we constructed a two-oscillator system for the plasmodium that has two wells (oscillator part) and a channel (coupling part). We investigated the oscillation behavior by monitoring the thickness oscillation of the plasmodium in the microstructure with various channel widths. It was found that the oscillation behavior of two oscillators dynamically changed depending on the channel width. Based on the results of measurements of the tube dimensions and the velocity of the protoplasmic streaming in the tube, we discuss how the channel width relates to the interaction strength of the coupled oscillator system.

Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations

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

Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, FaMAF, Universidad Nacional de Cordoba, Instituto de Fisica Enrique Gaviola, IFEG, CONICET, Ciudad Universitaria

2010-02-15

For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, thoughmore » the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.« less

Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan; Lee, John C. K.

2003-01-01

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…

Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

ERIC Educational Resources Information Center

Stickel, Sue A.

The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

The "Chaos" Pattern in Piaget's Theory of Cognitive Development.

ERIC Educational Resources Information Center

Lindsay, Jean S.

Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive…

Robust Decision Making in a Nonlinear World

ERIC Educational Resources Information Center

Dougherty, Michael R.; Thomas, Rick P.

2012-01-01

The authors propose a general modeling framework called the general monotone model (GeMM), which allows one to model psychological phenomena that manifest as nonlinear relations in behavior data without the need for making (overly) precise assumptions about functional form. Using both simulated and real data, the authors illustrate that GeMM…

An Examination of the Utility of Non-Linear Dynamics Techniques for Analyzing Human Information Behaviors.

ERIC Educational Resources Information Center

Snyder, Herbert; Kurtze, Douglas

1992-01-01

Discusses the use of chaos, or nonlinear dynamics, for investigating computer-mediated communication. A comparison between real, human-generated data from a computer network and similarly constructed random-generated data is made, and mathematical procedures for determining chaos are described. (seven references) (LRW)

Chaos and insect ecology

Treesearch

Jesse A. Logan; Fred P. Hain

1990-01-01

Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...

Nonlinear finite element modeling of corrugated board

Treesearch

A. C. Gilchrist; J. C. Suhling; T. J. Urbanik

1999-01-01

In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...

Winning in Time: Enabling Naturalistic Decision Making in Command and Control

DTIC Science & Technology

2000-11-01

non-linear with non-linearity defined as a condition master chess player , the NBA basketball player , the in which a system disobeys principles of great...are made up of basic others identified in the successive sectors, are feedback structures which have known behavioral points of leverage for policy

Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems

NASA Astrophysics Data System (ADS)

Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao

Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.

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.

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

PubMed

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

2018-01-01

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

A nonlinear dynamics approach for incorporating wind-speed patterns into wind-power project evaluation.

PubMed

Huffaker, Ray; Bittelli, Marco

2015-01-01

Wind-energy production may be expanded beyond regions with high-average wind speeds (such as the Midwest U.S.A.) to sites with lower-average speeds (such as the Southeast U.S.A.) by locating favorable regional matches between natural wind-speed and energy-demand patterns. A critical component of wind-power evaluation is to incorporate wind-speed dynamics reflecting documented diurnal and seasonal behavioral patterns. Conventional probabilistic approaches remove patterns from wind-speed data. These patterns must be restored synthetically before they can be matched with energy-demand patterns. How to accurately restore wind-speed patterns is a vexing problem spurring an expanding line of papers. We propose a paradigm shift in wind power evaluation that employs signal-detection and nonlinear-dynamics techniques to empirically diagnose whether synthetic pattern restoration can be avoided altogether. If the complex behavior of observed wind-speed records is due to nonlinear, low-dimensional, and deterministic system dynamics, then nonlinear dynamics techniques can reconstruct wind-speed dynamics from observed wind-speed data without recourse to conventional probabilistic approaches. In the first study of its kind, we test a nonlinear dynamics approach in an application to Sugarland Wind-the first utility-scale wind project proposed in Florida, USA. We find empirical evidence of a low-dimensional and nonlinear wind-speed attractor characterized by strong temporal patterns that match up well with regular daily and seasonal electricity demand patterns.

Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

NASA Astrophysics Data System (ADS)

Rozdeba, Paul J.

The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

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

NASA Astrophysics Data System (ADS)

Xing, Yani; Wang, Jun

2018-02-01

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

Composite Beam Theory with Material Nonlinearities and Progressive Damage

NASA Astrophysics Data System (ADS)

Jiang, Fang

Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping functions, and the 3D spatial gradients of these warping functions. Asymptotic analysis of the extended Hamiltonian's principle suggests dropping the terms of axial gradients of the warping functions. As a result, the solid mechanics problem resolved into a 3D continuum is dimensionally reduced to a problem of solving the warping functions on a 2D cross-sectional field by minimizing the information loss. The present theory is implemented using the finite element method (FEM) in Variational Asymptotic Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model in the form of the Euler-Bernoulli beam theory. The deformation gradient tensor is directly used to enable the capability of dealing with finite deformation, various strain definitions, and several types of material constitutive laws regarding the nonlinear elasticity and progressive damage. Analytical and numerical examples are given for various problems including the trapeze effect, Poynting effect, Brazier effect, extension-bending coupling effect, and free edge damage. By comparison with the predictions from 3D finite element analyses (FEA), 2D FEA based on plane stress assumptions, and experimental data, the structural and material responses are proven to be rigorously captured by the present theory and the computational cost is significantly reduced. Due to the semi-analytical feature of the code developed, the unrealistic numerical issues widely seen in the conventional FEA with strain softening material behaviors are prevented by VABS. In light of these intrinsic features, the nonlinear elastic and inelastic 3D material models can be economically calibrated by data-matching the VABS predictions directly with the experimental measurements from slender coupons. Furthermore, the global behavior of slender composite structures in meters can also be effectively characterized by VABS without unnecessary loss of important information of its local laminae in micrometers.

Multiscale Roughness Influencing on Transport Behavior of Passive Solute through a Single Self-affine Fracture

NASA Astrophysics Data System (ADS)

Dou, Z.

2017-12-01

In this study, the influence of multi-scale roughness on transport behavior of the passive solute through the self-affine fracture was investigated. The single self-affine fracture was constructed by the successive random additions (SRA) and the fracture roughness was decomposed into two different scales (i.e. large-scale primary roughness and small-scale secondary roughness) by the Wavelet analysis technique. The fluid flow in fractures, which was characterized by the Forchheimer's law, showed the non-linear flow behaviors such as eddies and tortuous streamlines. The results indicated that the small-scale secondary roughness was primarily responsible for the non-linear flow behaviors. The direct simulations of asymptotic passive solute transport represented the Non-Fickian transport characteristics (i.e. early arrivals and long tails) in breakthrough curves (BTCs) and residence time distributions (RTDs) with and without consideration of the secondary roughness. Analysis of multiscale BTCs and RTDs showed that the small-scale secondary roughness played a significant role in enhancing the Non-Fickian transport characteristics. We found that removing small-scale secondary roughness led to the lengthening arrival and shortening tail. The peak concentration in BTCs decreased as the secondary roughness was removed, implying that the secondary could also enhance the solute dilution. The estimated BTCs by the Fickian advection-dispersion equation (ADE) yielded errors which decreased with the small-scale secondary roughness being removed. The mobile-immobile model (MIM) was alternatively implemented to characterize the Non-Fickian transport. We found that the MIM was more capable of estimating Non-Fickian BTCs. The small-scale secondary roughness resulted in the decreasing mobile domain fraction and the increasing mass exchange rate between immobile and mobile domains. The estimated parameters from the MIM could provide insight into the inherent mechanism of roughness-induced Non-Fickian transport behaviors.

Toward nonlinear magnonics: Intensity-dependent spin-wave switching in insulating side-coupled magnetic stripes

NASA Astrophysics Data System (ADS)

Sadovnikov, A. V.; Odintsov, S. A.; Beginin, E. N.; Sheshukova, S. E.; Sharaevskii, Yu. P.; Nikitov, S. A.

2017-10-01

We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.

Circadian rhythms and fractal fluctuations in forearm motion

NASA Astrophysics Data System (ADS)

Hu, Kun; Hilton, Michael F.

2005-03-01

Recent studies have shown that the circadian pacemaker --- an internal body clock located in the brain which is normally synchronized with the sleep/wake behavioral cycles --- influences key physiologic functions such as the body temperature, hormone secretion and heart rate. Surprisingly, no previous studies have investigated whether the circadian pacemaker impacts human motor activity --- a fundamental physiologic function. We investigate high-frequency actigraph recordings of forearm motion from a group of young and healthy subjects during a forced desynchrony protocol which allows to decouple the sleep/wake cycles from the endogenous circadian cycle while controlling scheduled behaviors. We investigate both static properties (mean value, standard deviation), dynamical characteristics (long-range correlations), and nonlinear features (magnitude and Fourier-phase correlations) in the fluctuations of forearm acceleration across different circadian phases. We demonstrate that while the static properties exhibit significant circadian rhythms with a broad peak in the afternoon, the dynamical and nonlinear characteristics remain invariant with circadian phase. This finding suggests an intrinsic multi-scale dynamic regulation of forearm motion the mechanism of which is not influenced by the circadian pacemaker, thus suggesting that increased cardiac risk in the early morning hours is not related to circadian-mediated influences on motor activity.

An inverse finite-element model of heel-pad indentation.

PubMed

Erdemir, Ahmet; Viveiros, Meredith L; Ulbrecht, Jan S; Cavanagh, Peter R

2006-01-01

A numerical-experimental approach has been developed to characterize heel-pad deformation at the material level. Left and right heels of 20 diabetic subjects and 20 nondiabetic subjects matched for age, gender and body mass index were indented using force-controlled ultrasound. Initial tissue thickness and deformation were measured using M-mode ultrasound; indentation forces were recorded simultaneously. An inverse finite-element analysis of the indentation protocol using axisymmetric models adjusted to reflect individual heel thickness was used to extract nonlinear material properties describing the hyperelastic behavior of each heel. Student's t-tests revealed that heel pads of diabetic subjects were not significantly different in initial thickness nor were they stiffer than those from nondiabetic subjects. Another heel-pad model with anatomically realistic surface representations of the calcaneus and soft tissue was developed to estimate peak pressure prediction errors when average rather than individualized material properties were used. Root-mean-square errors of up to 7% were calculated, indicating the importance of subject-specific modeling of the nonlinear elastic behavior of the heel pad. Indentation systems combined with the presented numerical approach can provide this information for further analysis of patient-specific foot pathologies and therapeutic footwear designs.

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

DOE PAGES

Chacon, Luis; Stanier, Adam John

2016-12-01

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation

PubMed Central

Shahid, Wajiha; Qiu, Zhen; Duan, Xiyu; Li, Haijun; Wang, Thomas D.; Oldham, Kenn R.

2014-01-01

High frequency large scanning angle electrostatically actuated microelectromechanical systems (MEMS) mirrors are used in a variety of applications involving fast optical scanning. A 1-D parametrically resonant torsional micromirror for use in biomedical imaging is analyzed here with respect to operation by duty-cycled square waves. Duty-cycled square wave excitation can have significant advantages for practical mirror regulation and/or control. The mirror’s nonlinear dynamics under such excitation is analyzed in a Hill’s equation form. This form is used to predict stability regions (the voltage-frequency relationship) of parametric resonance behavior over large scanning angles using iterative approximations for nonlinear capacitance behavior of the mirror. Numerical simulations are also performed to obtain the mirror’s frequency response over several voltages for various duty cycles. Frequency sweeps, stability results, and duty cycle trends from both analytical and simulation methods are compared with experimental results. Both analytical models and simulations show good agreement with experimental results over the range of duty cycled excitations tested. This paper discusses the implications of changing amplitude and phase with duty cycle for robust open-loop operation and future closed-loop operating strategies. PMID:25506188

Risk-sensitive reinforcement learning.

PubMed

Shen, Yun; Tobia, Michael J; Sommer, Tobias; Obermayer, Klaus

2014-07-01

We derive a family of risk-sensitive reinforcement learning methods for agents, who face sequential decision-making tasks in uncertain environments. By applying a utility function to the temporal difference (TD) error, nonlinear transformations are effectively applied not only to the received rewards but also to the true transition probabilities of the underlying Markov decision process. When appropriate utility functions are chosen, the agents' behaviors express key features of human behavior as predicted by prospect theory (Kahneman & Tversky, 1979 ), for example, different risk preferences for gains and losses, as well as the shape of subjective probability curves. We derive a risk-sensitive Q-learning algorithm, which is necessary for modeling human behavior when transition probabilities are unknown, and prove its convergence. As a proof of principle for the applicability of the new framework, we apply it to quantify human behavior in a sequential investment task. We find that the risk-sensitive variant provides a significantly better fit to the behavioral data and that it leads to an interpretation of the subject's responses that is indeed consistent with prospect theory. The analysis of simultaneously measured fMRI signals shows a significant correlation of the risk-sensitive TD error with BOLD signal change in the ventral striatum. In addition we find a significant correlation of the risk-sensitive Q-values with neural activity in the striatum, cingulate cortex, and insula that is not present if standard Q-values are used.

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

NASA Astrophysics Data System (ADS)

van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

2017-12-01

A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

Nonlinear hydrodynamic stability and transition; Proceedings of the IUTAM Symposium, Nice, France, Sept. 3-7, 1990

NASA Astrophysics Data System (ADS)

Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.

Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech

NASA Astrophysics Data System (ADS)

Erath, Byron D.; Zañartu, Matías; Peterson, Sean D.; Plesniak, Michael W.

2011-09-01

Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < ps < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.

A simple nonlinear model for the return to isotropy in turbulence

NASA Technical Reports Server (NTRS)

Sarkar, Sutanu; Speziale, Charles G.

1989-01-01

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable non-trivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable non-trivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Simple model of cable-stayed bridge deck subjected to static wind loading

NASA Astrophysics Data System (ADS)

Kang, Yi-Lung; Wang, Yang Cheng

1997-05-01

Cable-stayed bridges have been known since 18th century with aesthetics design. The structural system and the structural behavior are significantly different from those of continuous bridges. Compared to continuous bridge, cable- stayed bridges have more flexure bridge deck than those of continuous bridges.On the other hand, cable-stayed bridges have less stiffness to resist wind loading especially for lateral loads. The first considering of bridge engineering is safety. In 1940's, Tacoma Narrows Suspension Bridge destroyed by wind loading is a good example even though it is not a cable-stayed bridge. After the bridge was destroyed, a lot of research articles have been published regarding cable supported bridge subjected to wind loading. In recent days, high strength materials have been served. The bridge engineers use the advantages to expand the span length of cable-stayed bridges. Due to the span length increased and the use of high strength materials, cable- stayed bridges have more significant nonlinear behavior subjected to wind loading. In this paper, a slice bridge deck of cable-stayed bridge connected to internal support cables is considered. The deck has been considered to be subjected to lateral static wind loading. Since cables can not take compressive force, the deck has strongly nonlinear behavior even though the materials are linear elastic. Several primary load combinations have ben considered in this paper such as the bridge deck supposed to be moved horizontally without rotation or the bridge deck supposed to be moved horizontally with rotational deformation. The mathematical formulas and the numerical solutions are found and represented in graphical forms. The results can be provided to bridge designers and researchers for further study of this type of structure subjected to wind loading.

Inference of pain stimulus level from stereotypical behavioral response of C.elegans allows quantification of effects of anesthesia and mutation

NASA Astrophysics Data System (ADS)

Leung, Kawai; Mohammadi, Aylia; Ryu, William; Nemenman, Ilya

In animals, we must infer the pain level from experimental characterization of behavior. This is not trivial since behaviors are very complex and multidimensional. To establish C.elegans as a model for pain research, we propose for the first time a quantitative model that allows inference of a thermal nociceptive stimulus level from the behavior of an individual worm. We apply controlled levels of pain by locally heating worms with an infrared laser and capturing the subsequent behavior. We discover that the behavioral response is a product of stereotypical behavior and a nonlinear function of the strength of stimulus. The same stereotypical behavior is observed in normal, anesthetized and mutated worms. From this result we build a Bayesian model to infer the strength of laser stimulus from the behavior. This model allows us to measure the efficacy of anaesthetization and mutation by comparing the inferred strength of stimulus. Based on the measured nociceptive escape of over 200 worms, our model is able to significantly differentiate normal, anaesthetized and mutated worms with 40 worm samples. This work was partially supported by NSF Grant No. IOS/1208126 and HFSP Grant No. RGY0084/.

Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium.

PubMed

Petrov, E Yu; Kudrin, A V

2010-05-14

The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.

Lipschitz regularity results for nonlinear strictly elliptic equations and applications

NASA Astrophysics Data System (ADS)

Ley, Olivier; Nguyen, Vinh Duc

2017-10-01

Most of Lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.

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

NASA Technical Reports Server (NTRS)

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

1974-01-01

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

Ultralow-intensity magneto-optical and mechanical effects in metal nanocolloids.

PubMed

Moocarme, M; Domínguez-Juárez, J L; Vuong, L T

2014-03-12

Magneto-plasmonics is a designation generally associated with ferromagnetic-plasmonic materials because such optical responses from nonmagnetic materials alone are considered weak. Here, we show that there exists a switching transition between linear and nonlinear magneto-optical behaviors in noble-metal nanocolloids that is observable at ultralow illumination intensities and direct current magnetic fields. The response is attributed to polarization-dependent nonzero-time-averaged plasmonic loops, vortex power flows, and nanoparticle magnetization. This work identifies significant mechanical effects that subsequently exist via magnetic-dipole interactions.

Transient dynamics of a quantum-dot: From Kondo regime to mixed valence and to empty orbital regimes

NASA Astrophysics Data System (ADS)

Cheng, YongXi; Li, ZhenHua; Wei, JianHua; Nie, YiHang; Yan, YiJing

2018-04-01

Based on the hierarchical equations of motion approach, we study the time-dependent transport properties of a strongly correlated quantum dot system in the Kondo regime (KR), mixed valence regime (MVR), and empty orbital regime (EOR). We find that the transient current in KR shows the strongest nonlinear response and the most distinct oscillation behaviors. Both behaviors become weaker in MVR and diminish in EOR. To understand the physical insight, we examine also the corresponding dot occupancies and the spectral functions, with their dependence on the Coulomb interaction, temperature, and applied step bias voltage. The above nonlinear and oscillation behaviors could be understood as the interplay between dynamical Kondo resonance and single electron resonant-tunneling.

Nonlinear analysis of EEGs of patients with major depression during different emotional states.

PubMed

Akdemir Akar, Saime; Kara, Sadık; Agambayev, Sümeyra; Bilgiç, Vedat

2015-12-01

Although patients with major depressive disorder (MDD) have dysfunctions in cognitive behaviors and the regulation of emotions, the underlying brain dynamics of the pathophysiology are unclear. Therefore, nonlinear techniques can be used to understand the dynamic behavior of the EEG signals of MDD patients. To investigate and clarify the dynamics of MDD patients׳ brains during different emotional states, EEG recordings were analyzed using nonlinear techniques. The purpose of the present study was to assess whether there are different EEG complexities that discriminate between MDD patients and healthy controls during emotional processing. Therefore, nonlinear parameters, such as Katz fractal dimension (KFD), Higuchi fractal dimension (HFD), Shannon entropy (ShEn), Lempel-Ziv complexity (LZC) and Kolmogorov complexity (KC), were computed from the EEG signals of two groups under different experimental states: noise (negative emotional content) and music (positive emotional content) periods. First, higher complexity values were generated by MDD patients relative to controls. Significant differences were obtained in the frontal and parietal scalp locations using KFD (p<0.001), HFD (p<0.05), and LZC (p=0.05). Second, lower complexities were observed only in the controls when they were subjected to music compared to the resting baseline state in the frontal (p<0.05) and parietal (p=0.005) regions. In contrast, the LZC and KFD values of patients increased in the music period compared to the resting state in the frontal region (p<0.05). Third, the patients׳ brains had higher complexities when they were exposed to noise stimulus than did the controls׳ brains. Moreover, MDD patients׳ negative emotional bias was demonstrated by their higher brain complexities during the noise period than the music stimulus. Additionally, we found that the KFD, HFD and LZC values were more sensitive in discriminating between patients and controls than the ShEn and KC measures, according to the results of ANOVA and ROC calculations. It can be concluded that the nonlinear analysis may be a useful and discriminative tool in investigating the neuro-dynamic properties of the brain in patients with MDD during emotional stimulation. Copyright © 2015 Elsevier Ltd. All rights reserved.

A displacement-based approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice; Caracoglia, Luca

2017-04-01

Pre-tensioned-cable bracing systems are widely employed in structural engineering to limit lateral deflections and stabilize structures. A suitable configuration of the pre-tensioned-cable bracing systems in a structure is an important issue since the internal force distribution, emerging from the interaction with the existing structure, significantly affects the structural dynamic behavior. The design, however, is often based on the intuition and the previous experience of the engineer. In recent years, the authors have been investigating the non-linear dynamic response of cable systems, installed on cable-stayed bridges, and in particular the so-called "cable-cross-tie systems" forming a cable network. The bracing cables (cross-ties) can exhibit slackening or snapping. Therefore, a non-linear unilateral model, combined with the taut-cable theory, is required to simulate the incipient slackening conditions in the stays. Capitalizing from this work on non-linear cable dynamics, this paper proposes a new approach to analyze, in laterally- braced truss structures, the unilateral effects and dynamic response accounting for the loss in the pre-tensioning force imparted to the bracing cables. This effect leads to non-linear vibration of the structure. In this preliminary study, the free vibrations of the structure are investigated by using the "Equivalent Linearization Method". A performance coefficient, a real positive number between 0.5 and 1.0, is defined and employed to monitor the relative reduction in the apparent stiffness of the braces during structural vibration, "mode by mode". It is shown that the system can exhibit alternate unilateral behavior of the cross-braces. A reduction of the performance coefficient close to fifty percent is observed in the braces when the initial pre-tensioning force is small. On the other hand the performance coefficient tends to one in the case of a high level of pre-stress. It is concluded that the performance coefficient may possibly be used as an indicator for the design of the braces since a suitable selection of the initial pre-tensioning force can avoid slackening in the braces.

Enthalpy-entropy compensation for the solubility of drugs in solvent mixtures: paracetamol, acetanilide, and nalidixic acid in dioxane-water.

PubMed

Bustamante, P; Romero, S; Pena, A; Escalera, B; Reillo, A

1998-12-01

In earlier work, a nonlinear enthalpy-entropy compensation was observed for the solubility of phenacetin in dioxane-water mixtures. This effect had not been earlier reported for the solubility of drugs in solvent mixtures. To gain insight into the compensation effect, the behavior of the apparent thermodynamic magnitudes for the solubility of paracetamol, acetanilide, and nalidixic acid is studied in this work. The solubility of these drugs was measured at several temperatures in dioxane-water mixtures. DSC analysis was performed on the original powders and on the solid phases after equilibration with the solvent mixture. The thermal properties of the solid phases did not show significant changes. The three drugs display a solubility maximum against the cosolvent ratio. The solubility peaks of acetanilide and nalidixic acid shift to a more polar region at the higher temperatures. Nonlinear van't Hoff plots were observed for nalidixic acid whereas acetanilide and paracetamol show linear behavior at the temperature range studied. The apparent enthalpies of solution are endothermic going through a maximum at 50% dioxane. Two different mechanisms, entropy and enthalpy, are suggested to be the driving forces that increase the solubility of the three drugs. Solubility is entropy controlled at the water-rich region (0-50% dioxane) and enthalpy controlled at the dioxane-rich region (50-100% dioxane). The enthalpy-entropy compensation analysis also suggests that two different mechanisms, dependent on cosolvent ratio, are involved in the solubility enhancement of the three drugs. The plots of deltaH versus deltaG are nonlinear, and the slope changes from positive to negative above 50% dioxane. The compensation effect for the thermodynamic magnitudes of transfer from water to the aqueous mixtures can be described by a common empirical nonlinear relationship, with the exception of paracetamol, which follows a separate linear relationship at dioxane ratios above 50%. The results corroborate earlier findings with phenacetin. The similar pattern shown by the drugs studied suggests that the nonlinear enthalpy-entropy compensation effect may be characteristic of the solubility of semipolar drugs in dioxane-water mixtures.

Using nonlinear methods to quantify changes in infant limb movements and vocalizations.

PubMed

Abney, Drew H; Warlaumont, Anne S; Haussman, Anna; Ross, Jessica M; Wallot, Sebastian

2014-01-01

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior.

Using nonlinear methods to quantify changes in infant limb movements and vocalizations

PubMed Central

Abney, Drew H.; Warlaumont, Anne S.; Haussman, Anna; Ross, Jessica M.; Wallot, Sebastian

2014-01-01

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior. PMID:25161629

Chaotic behavior in the locomotion of Amoeba proteus.

PubMed

Miyoshi, H; Kagawa, Y; Tsuchiya, Y

2001-01-01

The locomotion of Amoeba proteus has been investigated by algorithms evaluating correlation dimension and Lyapunov spectrum developed in the field of nonlinear science. It is presumed by these parameters whether the random behavior of the system is stochastic or deterministic. For the analysis of the nonlinear parameters, n-dimensional time-delayed vectors have been reconstructed from a time series of periphery and area of A. proteus images captured with a charge-coupled-device camera, which characterize its random motion. The correlation dimension analyzed has shown the random motion of A. proteus is subjected only to 3-4 macrovariables, though the system is a complex system composed of many degrees of freedom. Furthermore, the analysis of the Lyapunov spectrum has shown its largest exponent takes positive values. These results indicate the random behavior of A. proteus is chaotic and deterministic motion on an attractor with low dimension. It may be important for the elucidation of the cell locomotion to take account of nonlinear interactions among a small number of dynamics such as the sol-gel transformation, the cytoplasmic streaming, and the relating chemical reaction occurring in the cell.

Synchronizing movements with the metronome: nonlinear error correction and unstable periodic orbits.

PubMed

Engbert, Ralf; Krampe, Ralf Th; Kurths, Jürgen; Kliegl, Reinhold

2002-02-01

The control of human hand movements is investigated in a simple synchronization task. We propose and analyze a stochastic model based on nonlinear error correction; a mechanism which implies the existence of unstable periodic orbits. This prediction is tested in an experiment with human subjects. We find that our experimental data are in good agreement with numerical simulations of our theoretical model. These results suggest that feedback control of the human motor systems shows nonlinear behavior. Copyright 2001 Elsevier Science (USA).

Nonlinear Optical Properties of Au-Nanoparticles Conjugated with Lipoic Acid in Water

NASA Astrophysics Data System (ADS)

Trejo-Durán, M.; Cornejo-Monroy, D.; Alvarado-Méndez, E.; Olivares-Vargas, A.; Castano, V. M.

2014-08-01

Gold nanoparticles were chemically conjugated with lipoic acid to control their optical properties. Z-scan and other optical techniques were used to characterize the non-linear behavior of the resulting nanostructured materials. The results show that the nonlinearity is of thermal origin, which can be controlled by the use of lipoic acid as well as other organic molecules conjugated onto metal nanoparticles. In particular, the presence of lipoic acid increases n_2 and dn/dT.

Nonlinear mechanical behavior of thermoplastic matrix materials for advanced composites

NASA Technical Reports Server (NTRS)

Arenz, R. J.; Landel, R. F.

1989-01-01

Two recent theories of nonlinear mechanical response are quantitatively compared and related to experimental data. Computer techniques are formulated to handle the numerical integration and iterative procedures needed to solve the associated sets of coupled nonlinear differential equations. Problems encountered during these formulations are discussed and some open questions described. Bearing in mind these cautions, the consequences of changing parameters that appear in the formulations on the resulting engineering properties are discussed. Hence, engineering approaches to the analysis of thermoplastic matrix material can be suggested.

A therapy inactivating the tumor angiogenic factors.

PubMed

Morales-Rodrigo, Cristian

2013-02-01

This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. The main feature of the model under consideration is a nonlinear flux production of tumor angiogenic factors at the boundary of the tumor. It is proved the global existence for the nonlinear system and the effect in the large time behavior of the system for high doses of the therapeutic agent.

Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Hajkhalili, S.; Sheykhi, A.

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born-Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein-Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as r →∞. The maximum value of the electric field increases with increasing the nonlinear parameter β or decreasing the dilaton coupling α and is shifted to the singularity in the absence of either dilaton field (α = 0) or nonlinear gauge field (β →∞).

Selected Problems in Nonlinear Dynamics and Sociophysics

NASA Astrophysics Data System (ADS)

Westley, Alexandra Renee

This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

Nonlinear Dynamics: Theoretical Perspectives and Application to Suicidology

ERIC Educational Resources Information Center

Schiepek, Gunter; Fartacek, Clemens; Sturm, Josef; Kralovec, Karl; Fartacek, Reinhold; Ploderl, Martin

2011-01-01

Despite decades of research, the prediction of suicidal behavior remains limited. As a result, searching for more specific risk factors and testing their predictive power are central in suicidology. This strategy may be of limited value because it assumes linearity to the suicidal process that is most likely nonlinear by nature and which can be…

Social Contagion, Adolescent Sexual Behavior, and Pregnancy: A Nonlinear Dynamic EMOSA Model.

ERIC Educational Resources Information Center

Rodgers, Joseph Lee; Rowe, David C.; Buster, Maury

1998-01-01

Expands an existing nonlinear dynamic epidemic model of onset of social activities (EMOSA), motivated by social contagion theory, to quantify the likelihood of pregnancy for adolescent girls of different sexuality statuses. Compares five sexuality/pregnancy models to explain variance in national prevalence curves. Finds that adolescent girls have…

Applications of Nonlinear Principal Components Analysis to Behavioral Data.

ERIC Educational Resources Information Center

Hicks, Marilyn Maginley

1981-01-01

An empirical investigation of the statistical procedure entitled nonlinear principal components analysis was conducted on a known equation and on measurement data in order to demonstrate the procedure and examine its potential usefulness. This method was suggested by R. Gnanadesikan and based on an early paper of Karl Pearson. (Author/AL)

On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum

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

Kengne, Jacques; Kenmogne, Fabien

2014-12-15

The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by usingmore » time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.« less

Developing an active artificial hair cell using nonlinear feedback control

NASA Astrophysics Data System (ADS)

Joyce, Bryan S.; Tarazaga, Pablo A.

2015-09-01

The hair cells in the mammalian cochlea convert sound-induced vibrations into electrical signals. These cells have inspired a variety of artificial hair cells (AHCs) to serve as biologically inspired sound, fluid flow, and acceleration sensors and could one day replace damaged hair cells in humans. Most of these AHCs rely on passive transduction of stimulus while it is known that the biological cochlea employs active processes to amplify sound-induced vibrations and improve sound detection. In this work, an active AHC mimics the active, nonlinear behavior of the cochlea. The AHC consists of a piezoelectric bimorph beam subjected to a base excitation. A feedback control law is used to reduce the linear damping of the beam and introduce a cubic damping term which gives the AHC the desired nonlinear behavior. Model and experimental results show the AHC amplifies the response due to small base accelerations, has a higher frequency sensitivity than the passive system, and exhibits a compressive nonlinearity like that of the mammalian cochlea. This bio-inspired accelerometer could lead to new sensors with lower thresholds of detection, improved frequency sensitivities, and wider dynamic ranges.

Nonlocal modeling and buckling features of cracked nanobeams with von Karman nonlinearity

NASA Astrophysics Data System (ADS)

Akbarzadeh Khorshidi, Majid; Shaat, Mohamed; Abdelkefi, Abdessattar; Shariati, Mahmoud

2017-01-01

Buckling and postbuckling behaviors of cracked nanobeams made of single-crystalline nanomaterials are investigated. The nonlocal elasticity theory is used to model the nonlocal interatomic effects on the beam's performance accounting for the beam's axial stretching via von Karman nonlinear theory. The crack is then represented as torsional spring where the crack severity factor is derived accounting for the nonlocal features of the beam. By converting the beam into an equivalent infinite long plate with an edge crack subjected to a tensile stress at the far field, the crack energy release rate, intensity factor, and severity factor are derived according to the nonlocal elasticity theory. An analytical solution for the buckling and the postbuckling responses of cracked nonlocal nanobeams accounting for the beam axial stretching according to von Karman nonlinear theory of kinematics is derived. The impacts of the nonlocal parameter on the critical buckling loads and the static nonlinear postbuckling responses of cracked nonlocal nanobeams are studied. The results indicate that the buckling and postbuckling behaviors of cracked nanobeams are strongly affected by the crack location, crack depth, nonlocal parameter, and length-to-thickness ratio.

Nonlinear aeroacoustic characterization of Helmholtz resonators with a local-linear neuro-fuzzy network model

NASA Astrophysics Data System (ADS)

Förner, K.; Polifke, W.

2017-10-01

The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.

Interrelation of creep and relaxation: a modeling approach for ligaments.

PubMed

Lakes, R S; Vanderby, R

1999-12-01

Experimental data (Thornton et al., 1997) show that relaxation proceeds more rapidly (a greater slope on a log-log scale) than creep in ligament, a fact not explained by linear viscoelasticity. An interrelation between creep and relaxation is therefore developed for ligaments based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R > or = 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity.

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

Seasonal prediction for hydro-meteorological variables in the Korean Peninsula: Links with atmospheric teleconnections

NASA Astrophysics Data System (ADS)

Yoon, S.

2016-12-01

This study analyzes nonlinear behavior links with atmospheric teleconnections between hydrologic variables and climate indices using statistical models over the Korean Peninsula (KP). The ocean-related major climate factors such as the El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mode in the Tropical Ocean (TO) region were used to analyze the atmospheric teleconnections by principal component analysis (PCA) and a singular spectrum analysis (SSA). The nonlinear lag time correlations between climate indices and hydrological variables are calculated by the Mutual Information (MI) techniques. Results show that teleconnection based nonlinear correlation coefficients (CCs) were higher than linear CCs, ENSO shows a few months of lag time correlation with IOD, which has a direct influence on rainfall and streamflow anomalies in the KP. The precipitation and streamflow in KP shows a significant increasing and decreasing tendency during warm pool (WP) and cold tongue (CT) El Niño decaying years, respectively, while the La Niña year shows slightly above normal conditions. IOD events show significantly decreasing and increasing long-term normal conditions during positive and negative years, respectively. A better understanding of the relationship between climate indices and streamflow can help policy makers prepare for possible options in river discharge pattern changes. Furthermore, these results provide useful information for water managers and end-users to support long-range water resources prediction and water-related management plan.

Suppressing Electron Turbulence and Triggering Internal Transport Barriers with Reversed Magnetic Shear in the National Spherical Torus Experiment

NASA Astrophysics Data System (ADS)

Peterson, Jayson Luc

2011-10-01

Observations in the National Spherical Torus Experiment (NSTX) have found electron temperature gradients that greatly exceed the linear threshold for the onset for electron temperature gradient-driven (ETG) turbulence. These discharges, deemed electron internal transport barriers (e-ITBs), coincide with a reversal in the shear of the magnetic field and with a reduction in electron-scale density fluctuations, qualitatively consistent with earlier gyrokinetic predictions. To investigate this phenomenon further, we numerically model electron turbulence in NSTX reversed-shear plasmas using the gyrokinetic turbulence code GYRO. These first-of-a-kind nonlinear gyrokinetic simulations of NSTX e-ITBs confirm that reversing the magnetic shear can allow the plasma to reach electron temperature gradients well beyond the critical gradient for the linear onset of instability. This effect is very strong, with the nonlinear threshold for significant transport approaching three times the linear critical gradient in some cases, in contrast with moderate shear cases, which can drive significant ETG turbulence at much lower gradients. In addition to the experimental implications of this upshifted nonlinear critical gradient, we explore the behavior of ETG turbulence during reversed shear discharges. This work is supported by the SciDAC Center for the Study of Plasma Microturbulence, DOE Contract DE-AC02-09CH11466, and used the resources of NCCS at ORNL and NERSC at LBNL. M. Ono et al., Nucl. Fusion 40, 557 (2000).

Thermal annealing and single-domain preparation in tetragonal Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 crystal for electro-optic and non-linear optical applications

NASA Astrophysics Data System (ADS)

Zhao, Ye; Wang, Sanhong; Fu, Xiaotian; Zhuang, Yongyong; Yang, Rui; Yang, Zhi; Li, Zhenrong; Xu, Zhuo; Wei, Xiaoyong

2018-02-01

The relaxor-PbTiO3 single crystal has attracted extensive attention in ultrasound transducers, sensors, actuators, and optoelectronics devices due to its excellent piezoelectric response and electro-optic properties. Preparation of a single-domain crystal as a critical process for application in electro-optic and non-linear optical devices suffers from serious and inevitable cracking. Therefore, a pre-poling thermal annealing process was suggested to release residual stress from crystal growth and the ferroelectric-paraelectric phase transition, which significantly reduced the chance of cracking. The effect of thermal annealing on dielectric properties, strain behavior, and domain structure were investigated. As a result, a significant increase of the dielectric constant near room temperature was obtained after annealing, which is close to the dielectric constant of the a-oriented domain. The annealed single crystal showed a lower and sharper strain peak at the coercive electric field compared with the unannealed sample, and the 90° domain walls completely vanished, which was verified by optical microscopy. The crack-free single-domain crystal showed excellent optical quality, with high transmittance of approximately 70% in the visible and near-infrared regions, which indicates that this crystal is a promising candidate for applications in electro-optic and non-linear optical devices.

Nonlinear characterization of elasticity using quantitative optical coherence elastography.

PubMed

Qiu, Yi; Zaki, Farzana R; Chandra, Namas; Chester, Shawn A; Liu, Xuan

2016-11-01

Optical coherence elastography (OCE) has been used to perform mechanical characterization on biological tissue at the microscopic scale. In this work, we used quantitative optical coherence elastography (qOCE), a novel technology we recently developed, to study the nonlinear elastic behavior of biological tissue. The qOCE system had a fiber-optic probe to exert a compressive force to deform tissue under the tip of the probe. Using the space-division multiplexed optical coherence tomography (OCT) signal detected by a spectral domain OCT engine, we were able to simultaneously quantify the probe deformation that was proportional to the force applied, and to quantify the tissue deformation. In other words, our qOCE system allowed us to establish the relationship between mechanical stimulus and tissue response to characterize the stiffness of biological tissue. Most biological tissues have nonlinear elastic behavior, and the apparent stress-strain relationship characterized by our qOCE system was nonlinear an extended range of strain, for a tissue-mimicking phantom as well as biological tissues. Our experimental results suggested that the quantification of force in OCE was critical for accurate characterization of tissue mechanical properties and the qOCE technique was capable of differentiating biological tissues based on the elasticity of tissue that is generally nonlinear.

Model-on-Demand Predictive Control for Nonlinear Hybrid Systems With Application to Adaptive Behavioral Interventions

PubMed Central

Nandola, Naresh N.; Rivera, Daniel E.

2011-01-01

This paper presents a data-centric modeling and predictive control approach for nonlinear hybrid systems. System identification of hybrid systems represents a challenging problem because model parameters depend on the mode or operating point of the system. The proposed algorithm applies Model-on-Demand (MoD) estimation to generate a local linear approximation of the nonlinear hybrid system at each time step, using a small subset of data selected by an adaptive bandwidth selector. The appeal of the MoD approach lies in the fact that model parameters are estimated based on a current operating point; hence estimation of locations or modes governed by autonomous discrete events is achieved automatically. The local MoD model is then converted into a mixed logical dynamical (MLD) system representation which can be used directly in a model predictive control (MPC) law for hybrid systems using multiple-degree-of-freedom tuning. The effectiveness of the proposed MoD predictive control algorithm for nonlinear hybrid systems is demonstrated on a hypothetical adaptive behavioral intervention problem inspired by Fast Track, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children. Simulation results demonstrate that the proposed algorithm can be useful for adaptive intervention problems exhibiting both nonlinear and hybrid character. PMID:21874087

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

Kalinin, Sergei V.; Jesse, Stephen; Yang, Yaodong

Here, the nonlinear response of a ferroic to external fields has been studied for decades, garnering interest for both understanding fundamental physics, as well as technological applications such as memory devices. Yet, the behavior of ferroelectrics at mesoscopic regimes remains poorly understood, and the scale limits of theories developed for macroscopic regimes are not well tested experimentally. Here, we test the link between piezo-nonlinearity and local piezoelectric strain hysteresis, via AC-field dependent measurements in conjunction with first order reversal curve (FORC) measurements on (K,Na)NbO 3 crystals with band-excitation piezoelectric force microscopy. The correlation coefficient between nonlinearity amplitude and the FORCmore » of the polarization switching shows a clear decrease in correlation with increasing AC bias, suggesting the impact of domain wall clamping on the DC measurement case. Further, correlation of polynomial fitting terms from the nonlinear measurements with the hysteresis loop area reveals that the largest correlations are reserved for the quadratic terms, which is expected for irreversible domain wall motion contributions that impact both piezoelectric behavior as well as minor loop formation. These confirm the link between local piezoelectric nonlinearity, domain wall motion and minor loop formation, and suggest that existing theories (such as Preisach) are applicable at these length scales, with associated implications for future nanoscale devices.« less

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

PubMed Central

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

2018-01-01

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

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

PubMed

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

2018-01-01

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

Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.; Hodges, Dewey H.

1987-01-01

The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.

On Poisson's ratio for metal matrix composite laminates. [aluminum boron composites

NASA Technical Reports Server (NTRS)

Herakovich, C. T.; Shuart, M. J.

1978-01-01

The definition of Poisson's ratio for nonlinear behavior of metal matrix composite laminates is discussed and experimental results for tensile and compressive loading of five different boron-aluminum laminates are presented. It is shown that there may be considerable difference in the value of Poisson's ratio as defined by a total strain or an incremental strain definition. It is argued that the incremental definition is more appropriate for nonlinear material behavior. Results from a (0) laminate indicate that the incremental definition provides a precursor to failure which is not evident if the total strain definition is used.

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

NASA Astrophysics Data System (ADS)

Zverev, V. V.; Rubinstein, B. Ya.

1991-04-01

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.

Electrodynamic soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in nonlinear acoustic landmine detection

NASA Astrophysics Data System (ADS)

Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.

2015-10-01

An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit significant curvature when the soil particle velocity is relatively higher. An oscillator with hysteresis modeled by a distribution of parallel spring elements each with a different threshold slip condition seems to describe fairly linear backbone curve behavior [W. D. Iwan, Transactions of the ASME, J. of Applied Mech., 33,(1966), 893-900], while a single bilinear hysteresis element describes the backbone curvature results in the experiments reported here [T. K. Caughey, Transactions of the ASME, J. of Applied Mech., 27, (1960), 640-643]. When "off target" resonances have a different backbone curvature than "on the mine" backbone curves, then false alarms may be eliminated due to resonances from the natural soil layering. See [R. A. Guyer, J. TenCate, and P. Johnson, "Hysteresis and the Dynamic Elasticity of Consolidated Granular Materials," Phys. Rev. Lett., 82, 16 (1999), 3280-3283] for recent models of nonlinear mesoscopic behavior.

Commentary.

ERIC Educational Resources Information Center

Burgess, Robert L.; Molenaar, Peter C. M.

1995-01-01

Supports Gottlieb's conclusion that developmental behavior genetics is unsuitable for analyzing developmental coactional processes because it does not concern itself with mechanisms through which genotypes are transformed into phenotypes. But maintains that modern behavior genetics provides an indispensable tool to analyze nonlinear epigenetic…

Yield stress materials in soft condensed matter

NASA Astrophysics Data System (ADS)

Bonn, Daniel; Denn, Morton M.; Berthier, Ludovic; Divoux, Thibaut; Manneville, Sébastien

2017-07-01

A comprehensive review is presented of the physical behavior of yield stress materials in soft condensed matter, which encompasses a broad range of materials from colloidal assemblies and gels to emulsions and non-Brownian suspensions. All these disordered materials display a nonlinear flow behavior in response to external mechanical forces due to the existence of a finite force threshold for flow to occur: the yield stress. Both the physical origin and rheological consequences associated with this nonlinear behavior are discussed and an overview is given of experimental techniques available to measure the yield stress. Recent progress is discussed concerning a microscopic theoretical description of the flow dynamics of yield stress materials, emphasizing, in particular, the role played by relaxation time scales, the interplay between shear flow and aging behavior, the existence of inhomogeneous shear flows and shear bands, wall slip, and nonlocal effects in confined geometries.

Holographic insulator/superconductor transition with exponential nonlinear electrodynamics probed by entanglement entropy

NASA Astrophysics Data System (ADS)

Yao, Weiping; Yang, Chaohui; Jing, Jiliang

2018-05-01

From the viewpoint of holography, we study the behaviors of the entanglement entropy in insulator/superconductor transition with exponential nonlinear electrodynamics (ENE). We find that the entanglement entropy is a good probe to the properties of the holographic phase transition. Both in the half space and the belt space, the non-monotonic behavior of the entanglement entropy in superconducting phase versus the chemical potential is general in this model. Furthermore, the behavior of the entanglement entropy for the strip geometry shows that the confinement/deconfinement phase transition appears in both insulator and superconductor phases. And the critical width of the confinement/deconfinement phase transition depends on the chemical potential and the exponential coupling term. More interestingly, the behaviors of the entanglement entropy in their corresponding insulator phases are independent of the exponential coupling factor but depends on the width of the subsystem A.

Nonlinear Impact of Temperature on Mortality in France

NASA Astrophysics Data System (ADS)

Zhang, A. T.

2016-12-01

Anthropogenic climate change is posing unprecedented challenges to human welfare, yet there is much uncertainty about the cost of its impact. Accurate quantification of the social cost of carbon is crucial for designing effective climate policies that reduce emissions and mitigate the adverse impact of global warming, and human health is an important component of the calculation. Despite a growing body of literature documenting the relationship between temperature and mortality in the U.S., similar results using nationwide data have not been clearly established in other countries. Using random monthly variations in temperature for over a decade, this paper finds a statistically significant nonlinear relationship between monthly mortality rate and daily temperature in France between 1998 and 2012. Extremely hot days are associated with significantly higher mortality rates: One additional day with a mean temperature above 30°C, relative to a day in the 12°C to 15°C range, leads to 10 extra all-age, all-gender monthly deaths per 100,000. The effect of cold temperatures is milder: An extremely cold day with an average temperature from -9 °C to -6 °C increases all-age, all-gender mortality rate by about 1.2 per 100,000 each month. There is also notable heterogeneity in the observed nonlinear relationship across age groups and gender, in which males and the elderly are generally more susceptible to extreme temperatures than females and the young. This highlights that children and youth may be well protected through adaptive behaviors, such as spending more time indoors in temperature-controlled rooms and staying hydrated. Compared to studies done in the U.S., extremely hot days >30°C leads to considerably more deaths in France. Preliminary evidence suggests that there has been very limited adaptation despite two prominent heat waves in 2003 and 2006, although further analysis of electricity consumption and air conditioning usage is needed to ascertain the extent to which protective behavior mitigates mortality risks from temperature extremes.

Analysis of Pull-In Instability of Geometrically Nonlinear Microbeam Using Radial Basis Artificial Neural Network Based on Couple Stress Theory

PubMed Central

Heidari, Mohammad; Heidari, Ali; Homaei, Hadi

2014-01-01

The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS. PMID:24860602

Nonlinear longitudinal resonance interaction of energetic charged particles and VLF waves in the magnetosphere

NASA Technical Reports Server (NTRS)

Tkalcevic, S.

1982-01-01

The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.

Piezoelectric Power Requirements for Active Vibration Control

NASA Technical Reports Server (NTRS)

Brennan, Matthew C.; McGowan, Anna-Maria Rivas

1997-01-01

This paper presents a method for predicting the power consumption of piezoelectric actuators utilized for active vibration control. Analytical developments and experimental tests show that the maximum power required to control a structure using surface-bonded piezoelectric actuators is independent of the dynamics between the piezoelectric actuator and the host structure. The results demonstrate that for a perfectly-controlled system, the power consumption is a function of the quantity and type of piezoelectric actuators and the voltage and frequency of the control law output signal. Furthermore, as control effectiveness decreases, the power consumption of the piezoelectric actuators decreases. In addition, experimental results revealed a non-linear behavior in the material properties of piezoelectric actuators. The material non- linearity displayed a significant increase in capacitance with an increase in excitation voltage. Tests show that if the non-linearity of the capacitance was accounted for, a conservative estimate of the power can easily be determined.

A Nonlinear Dynamics Approach for Incorporating Wind-Speed Patterns into Wind-Power Project Evaluation

PubMed Central

Huffaker, Ray; Bittelli, Marco

2015-01-01

Wind-energy production may be expanded beyond regions with high-average wind speeds (such as the Midwest U.S.A.) to sites with lower-average speeds (such as the Southeast U.S.A.) by locating favorable regional matches between natural wind-speed and energy-demand patterns. A critical component of wind-power evaluation is to incorporate wind-speed dynamics reflecting documented diurnal and seasonal behavioral patterns. Conventional probabilistic approaches remove patterns from wind-speed data. These patterns must be restored synthetically before they can be matched with energy-demand patterns. How to accurately restore wind-speed patterns is a vexing problem spurring an expanding line of papers. We propose a paradigm shift in wind power evaluation that employs signal-detection and nonlinear-dynamics techniques to empirically diagnose whether synthetic pattern restoration can be avoided altogether. If the complex behavior of observed wind-speed records is due to nonlinear, low-dimensional, and deterministic system dynamics, then nonlinear dynamics techniques can reconstruct wind-speed dynamics from observed wind-speed data without recourse to conventional probabilistic approaches. In the first study of its kind, we test a nonlinear dynamics approach in an application to Sugarland Wind—the first utility-scale wind project proposed in Florida, USA. We find empirical evidence of a low-dimensional and nonlinear wind-speed attractor characterized by strong temporal patterns that match up well with regular daily and seasonal electricity demand patterns. PMID:25617767

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.

Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials.

PubMed

Li, Li; Yu, Fajun

2017-09-06

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.

Tuning the nonlinear response of (6,5)-enriched single-wall carbon nanotubes dispersions

NASA Astrophysics Data System (ADS)

Aréstegui, O. S.; Silva, E. C. O.; Baggio, A. L.; Gontijo, R. N.; Hickmann, J. M.; Fantini, C.; Alencar, M. A. R. C.; Fonseca, E. J. S.

2017-04-01

Ultrafast nonlinear optical properties of (6,5)-enriched single-wall carbon nanotubes (SWCNTs) dispersions are investigated using the thermally managed Z-scan technique. As the (6,5) SWCNTs presented a strong resonance in the range of 895-1048 nm, the nonlinear refractive index (n2) and the absorption coefficients (β) measurements were performed tuning the laser exactly around absorption peak of the (6,5) SWCNTs. It is observed that the nonlinear response is very sensitive to the wavelength and the spectral behavior of n2 is strongly correlated to the tubes one-photon absorption band, presenting also a peak when the laser photon energy is near the tube resonance energy. This result suggests that a suitable selection of nanotubes types may provide optimized nonlinear optical responses in distinct regions of the electromagnetic spectrum. Analysis of the figures of merit indicated that this material is promising for ultrafast nonlinear optical applications under near infrared excitation.

Ultra-fast dynamics in the nonlinear optical response of silver nanoprism ordered arrays.

PubMed

Sánchez-Esquivel, Héctor; Raygoza-Sanchez, Karen Y; Rangel-Rojo, Raúl; Kalinic, Boris; Michieli, Niccolò; Cesca, Tiziana; Mattei, Giovanni

2018-03-15

In this work we present the study of the ultra-fast dynamics of the nonlinear optical response of a honeycomb array of silver triangular nanoprisms, performed using a femtosecond pulsed laser tuned with the dipolar surface plasmon resonance of the nanoarray. Nonlinear absorption and refraction, and their time-dependence, were explored using the z-scan and time-resolved excite-probe techniques. Nonlinear absorption is shown to change sign with the input irradiance and the behavior was explained on the basis of a three-level model. The response time was determined to be in the picosecond regime. A technique based on a variable frequency chopper was also used in order to discriminate the thermal and electronic contributions to the nonlinearity, which were found to have opposite signs. All these findings propel the investigated nanoprism arrays as good candidates for applications in advanced ultra-fast nonlinear nanophotonic devices.

Optical Quasi-Soliton Solutions for the Cubic-Quintic Nonlinear SCHRÖDINGER Equation with Variable Coefficients

NASA Astrophysics Data System (ADS)

Yang, Qin; Zhang, Jie-Fang

Optical quasi-soliton solutions for the cubic-quintic nonlinear Schrödinger equation (CQNLSE) with variable coefficients are considered. Based on the extended tanh-function method, we not only successfully obtained bright and dark quasi-soliton solutions, but also obtained the kink quasi-soliton solutions under certain parametric conditions. We conclude that the quasi-solitons induced by the combined effects of the group velocity dispersion (GVD) distribution, the nonlinearity distribution, higher-order nonlinearity distribution, and the amplification or absorption coefficient are quite different from those of the solitons induced only by the combined effects of the GVD, the nonlinearity distribution, and the amplification or absorption coefficient without considering the higher-order nonlinearity distribution (i.e. α(z)=0). Furthermore, we choose appropriate optical fiber parameters D(z) and R(z) to control the velocity of quasi-soliton and time shift, and discuss the evolution behavior of the special quasi-soliton.

Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.

Nonlinear softening of unconsolidated granular earth materials

NASA Astrophysics Data System (ADS)

Lieou, Charles K. C.; Daub, Eric G.; Guyer, Robert A.; Johnson, Paul A.

2017-09-01

Unconsolidated granular earth materials exhibit softening behavior due to external perturbations such as seismic waves, namely, the wave speed and elastic modulus decrease upon increasing the strain amplitude above dynamics strains of about 10-6 under near-surface conditions. In this letter, we describe a theoretical model for such behavior. The model is based on the idea that shear transformation zones—clusters of grains that are loose and susceptible to contact changes, particle displacement, and rearrangement—are responsible for plastic deformation and softening of the material. We apply the theory to experiments on simulated fault gouge composed of glass beads and demonstrate that the theory predicts nonlinear resonance shifts, reduction of the P wave modulus, and attenuation, in agreement with experiments. The theory thus offers insights on the nature of nonlinear elastic properties of a granular medium and potentially into phenomena such as triggering on earthquake faults.

Non-linear heterogeneous FE approach for FRP strengthened masonry arches

NASA Astrophysics Data System (ADS)

Bertolesi, Elisa; Milani, Gabriele; Fedele, Roberto

2015-12-01

A fast and reliable non-linear heterogeneous FE approach specifically conceived for the analysis of FRP-reinforced masonry arches is presented. The approach proposed relies into the reduction of mortar joints to interfaces exhibiting a non-linear holonomic behavior, with a discretization of bricks by means of four-noded elastic elements. The FRP reinforcement is modeled by means of truss elements with elastic-brittle behavior, where the peak tensile strength is estimated by means of a consolidated approach provided by the Italian guidelines CNR-DT200 on masonry strengthening with fiber materials, where the delamination of the strip from the support is taken into account. The model is validated against some recent experimental results relying into circular masonry arches reinforced at both the intrados and the extrados. Some sensitivity analyses are conducted varying the peak tensile strength of the trusses representing the FRP reinforcement.

Mechanical-magnetic-electric coupled behaviors for stress-driven Terfenol-D energy harvester

NASA Astrophysics Data System (ADS)

Cao, Shuying; Zheng, Jiaju; Wang, Bowen; Pan, Ruzheng; Zhao, Ran; Weng, Ling; Sun, Ying; Liu, Chengcheng

2017-05-01

The stress-driven Terfernol-D energy harvester exhibits the nonlinear mechanical-magnetic-electric coupled (MMEC) behaviors and the eddy current effects. To analyze and design the device, it is necessary to establish an accurate model of the device. Based on the effective magnetic field expression, the constitutive equations with eddy currents and variable coefficients, and the dynamic equations, a nonlinear dynamic MMEC model for the device is founded. Comparisons between the measured and calculated results show that the model can describe the nonlinear coupled curves of magnetization versus stress and strain versus stress under different bias fields, and can provide the reasonable data trends of piezomagnetic coefficients, Young's modulus and relative permeability for Terfenol-D. Moreover, the calculated power results show that the model can determine the optimal bias conditions, optimal resistance, suitable proof mass, suitable slices for the maximum energy extraction of the device under broad stress amplitude and broad frequency.

Fuzzy control of a fluidized bed dryer

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

Taprantzis, A.V.; Siettos, C.I.; Bafas, G.V.

1997-05-01

Fluidized bed dryers are utilized in almost every area of drying applications and therefore improved control strategies are always of great interest. The nonlinear character of the process, exhibited in the mathematical model and the open loop analysis, implies that a fuzzy logic controller is appropriate because, in contrast with conventional control schemes, fuzzy control inherently compensates for process nonlinearities and exhibits more robust behavior. In this study, a fuzzy logic controller is proposed; its design is based on a heuristic approach and its performance is compared against a conventional PI controller for a variety of responses. It is shownmore » that the fuzzy controller exhibits a remarkable dynamic behavior, equivalent if not better than the PI controller, for a wide range of disturbances. In addition, the proposed fuzzy controller seems to be less sensitive to the nonlinearities of the process, achieves energy savings and enables MIMO control.« less

Modeling and analysis of Galfenol cantilever vibration energy harvester with nonlinear magnetic force

NASA Astrophysics Data System (ADS)

Cao, Shuying; Sun, Shuaishuai; Zheng, Jiaju; Wang, Bowen; Wan, Lili; Pan, Ruzheng; Zhao, Ran; Zhang, Changgeng

2018-05-01

Galfenol traditional cantilever energy harvesters (TCEHs) have bigger electrical output only at resonance and exhibit nonlinear mechanical-magnetic-electric coupled (NMMEC) behaviors. To increase low-frequency broadband performances of a TCEH, an improved CEH (ICEH) with magnetic repulsive force is studied. Based on the magnetic dipole model, the nonlinear model of material, the Faraday law and the dynamic principle, a lumped parameter NMMEC model of the devices is established. Comparisons between the calculated and measured results show that the proposed model can provide reasonable data trends of TCEH under acceleration, bias field and different loads. Simulated results show that ICEH exhibits low-frequency resonant, hard spring and bistable behaviors, thus can harvest more low-frequency broadband vibration energy than TCEH, and can elicit snap-through and generate higher voltage even under weak noise. The proposed structure and model are useful for improving performances of the devices.

Neuronal models in infinite-dimensional spaces and their finite-dimensional projections: Part II.

PubMed

Brzychczy, S; Leszczyński, H; Poznanski, R R

2012-09-01

Application of comparison theorem is used to examine the validitiy of the "lumped parameter assumption" in describing the behavior of solutions of the continuous cable equation U(t) = DU(xx)+f(U) with the discrete cable equation dV(n)/dt = d*(V(n+1) - 2V(n) + V(n-1)) + f(V(n)), where f is a nonlinear functional describing the internal diffusion of electrical potential in single neurons. While the discrete cable equation looks like a finite difference approximation of the continuous cable equation, solutions of the two reveal significantly different behavior which imply that the compartmental models (spiking neurons) are poor quantifiers of neurons, contrary to what is commonly accepted in computational neuroscience.

The lead-lag relationships between spot and futures prices of natural gas

NASA Astrophysics Data System (ADS)

Zhang, Yahui; Liu, Li

2018-01-01

The lead-lag relationships between spot and futures markets are of great interest for academics. Previous studies neglect the possibility of nonlinear behaviors which may be caused by asymmetry or persistence. To fill this gap, this paper uses the MF-DCCA method and the linear and nonlinear causality tests to explore the causal relationships between natural gas spot and futures prices in the New York Mercantile Exchange. We find that spot and futures prices are positive cross-correlated, the natural gas futures can linearly Granger cause spot price, and there are bidirectional nonlinear causality relationships between natural gas spot and futures prices. Further, we explore the sources of nonlinear causality relationships, and find that the volatility spillover can partly explain the nonlinear causality and affect their cross-correlations.

Generation of Caustics and Rogue Waves from Nonlinear Instability.

PubMed

Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W

2017-11-17

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Generation of Caustics and Rogue Waves from Nonlinear Instability

NASA Astrophysics Data System (ADS)

Safari, Akbar; Fickler, Robert; Padgett, Miles J.; Boyd, Robert W.

2017-11-01

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Exact solutions for the source-excited cylindrical electromagnetic waves in a nonlinear nondispersive medium.

PubMed

Es'kin, V A; Kudrin, A V; Petrov, E Yu

2011-06-01

The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.

Non-linear mechanical behavior of a sintered material for braking application using digital image correlation

NASA Astrophysics Data System (ADS)

Mann, Ruddy; Magnier, Vincent; Serrano-Munoz, Itziar; Brunel, Jean-Francois; Brunel, Florent; Dufrenoy, Philippe; Henrion, Michele

2017-12-01

Friction materials for braking applications are complex composites made of many components to ensure the various performances required (friction coefficient level, low wear, mechanical strength, thermal resistance, etc.). The material is developed empirically by a trial and error approach. With the solicitation, the material evolves and probably also its properties. In the literature, the mechanical behavior of such materials is generally considered as linear elastic and independent of the loading history. This paper describes a methodology to characterize the mechanical behavior of such a heterogeneous material in order to investigate its non-linear mechanical behavior. Results from mechanical tests are implemented into material laws for numerical simulations. Thanks to the instrumentation, some links with the microstructure can also be proposed. The material is made of a metallic matrix embedding graphite and ceramic particles and is manufactured by sintering. It is used for dry friction applications such as high-energy brake for trains, cars and motorcycles. Compression tests are done with digital image correlation to measure full-filled displacement. It allows to calculate strain fields with enough resolution to identify the material heterogeneity and the role of some of the components of the formulation. A behavior model of the material with plasticity and damage is proposed to simulate the non-linear mechanical behavior and is implemented in an FEM code. Results of mechanical test simulations are compared with two types of experiments showing good agreement. This method thus makes it possible to determine mechanical properties at a virgin state but is extensible for characterizing a material having been submitted to braking solicitations.

Loudspeakers: Modeling and control

NASA Astrophysics Data System (ADS)

Al-Ali, Khalid Mohammad

This thesis documented a comprehensive study of loudspeaker modeling and control. A lumped-parameter model for a voice-coil loudspeaker in a vented enclosure was presented that derived from a consideration of physical principles. In addition, a low-frequency (20 Hz to 100 Hz), feedback control method designed to improve the nonlinear performance of the loudspeaker and a suitable performance measure for use in design and evaluation were proposed. Data from experiments performed on a variety of actual loudspeakers confirmed the practicality of the theory developed in this work. The lumped-parameter loudspeaker model, although simple, captured much of the nonlinear behavior of the loudspeaker. In addition, the model formulation allowed a straightforward application of modern control system methods and lent itself well to modern parametric identification techniques. The nonlinear performance of the loudspeaker system was evaluated using a suitable distortion measure that was proposed and compared with other distortion measures currently used in practice. Furthermore, the linearizing effect of feedback using a linear controller (both static and dynamic) was studied on a class of nonlinear systems. The results illustrated that the distortion reduction was potentially significant and a useful upper bound on the closed-loop distortion was found based on the sensitivity function of the system's linearization. A feedback scheme based on robust control theory was chosen for application to the loudspeaker system. Using the pressure output of the loudspeaker system for feedback, the technique offered significant advantages over those previously attempted. Illustrative examples were presented that proved the applicability of the theory developed in this dissertation to a variety of loudspeaker systems. The examples included a vented loudspeaker model and actual loudspeakers enclosed in both vented and sealed configurations. In each example, predictable and measurable distortion reduction at the output of the closed-loop system was recorded.

New directions in photonics simulation: Lanczos recursion and finite-difference time-domain

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

Hawkins, R.J.; McLeod, R.R.; Kallman, J.S.

1992-06-01

Computational Integrated Photonics (CIP) is the area of computational physics that treats the propagation of light in optical fibers and in integrated optical circuits. The purpose of integrated photonics simulation is to develop the computational tools that will support the design of photonic and optoelectronic integrated devices. CIP has, in general, two thrusts: (1) predictive models of photonic device behavior that can be used reliably to enhance significantly the speed with which designs axe optimized for development applications, and (2) to further our ability to describe the linear and nonlinear processes that occur - and can be exploited - inmore » real photonic devices. Experimental integrated optics has been around for over a decade with much of the work during this period. centered on proof-of-principle devices that could be described using simple analytic and numerical models. Recent advances in material growths, photolithography, and device complexity have conspired to reduce significantly the number of devices that can be designed with simple models and to increase dramatically the interest in CIP. In the area of device design, CIP is viewed as critical to understanding device behavior and to optimization. In the area of propagation physics, CIP is an important tool in the study of nonlinear processes in integrated optical devices and fibers. In this talk I will discuss two of the new directions we have been investigating in CIP: Lanczos recursion and finite-difference time-domain.« less

FRF decoupling of nonlinear systems

NASA Astrophysics Data System (ADS)

Kalaycıoğlu, Taner; Özgüven, H. Nevzat

2018-03-01

Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model with Fixed Covariates

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan

2005-01-01

In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects…

Predicting the flexure response of wood-plastic composites from uni-axial and shear data using a finite-element model

Treesearch

Scott E. Hamel; John C. Hermanson; Steven M. Cramer

2014-01-01

Wood-plastic composites (WPCs), commonly used in residential decks and railings, exhibit mechanical behavior that is bimodal, anisotropic, and nonlinear viscoelastic. They exhibit different stress-strain responses to tension and compression, both of which are nonlinear. Their mechanical properties vary with respect to extrusion direction, their deformation under...

Prediction of Battery Life and Behavior from Analysis of Voltage Data

NASA Technical Reports Server (NTRS)

Mcdermott, P. P.

1984-01-01

A method for simulating charge and discharge characteristics of secondary batteries is discussed. The analysis utilizes a nonlinear regression technique where empirical data is computer fitted with a five coefficient nonlinear equation. The equations for charge and discharge voltage are identical except for a change of sign before the second and third terms.

Nonlinear mesomechanics of composites with periodic microstructure

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Jordan, Eric H.; Freed, Alan D.

1989-01-01

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

A finite element evaluation of mechanical function for 3 distal extension partial dental prosthesis designs with a 3-dimensional nonlinear method for modeling soft tissue.

PubMed

Nakamura, Yoshinori; Kanbara, Ryo; Ochiai, Kent T; Tanaka, Yoshinobu

2014-10-01

The mechanical evaluation of the function of partial removable dental prostheses with 3-dimensional finite element modeling requires the accurate assessment and incorporation of soft tissue behavior. The differential behaviors of the residual ridge mucosa and periodontal ligament tissues have been shown to exhibit nonlinear displacement. The mathematic incorporation of known values simulating nonlinear soft tissue behavior has not been investigated previously via 3-dimensional finite element modeling evaluation to demonstrate the effect of prosthesis design on the supporting tissues. The purpose of this comparative study was to evaluate the functional differences of 3 different partial removable dental prosthesis designs with 3-dimensional finite element analysis modeling and a simulated patient model incorporating known viscoelastic, nonlinear soft tissue properties. Three different designs of distal extension removable partial dental prostheses were analyzed. The stress distributions to the supporting abutments and soft tissue displacements of the designs tested were calculated and mechanically compared. Among the 3 dental designs evaluated, the RPI prosthesis demonstrated the lowest stress concentrations on the tissue supporting the tooth abutment and also provided wide mucosa-borne areas of support, thereby demonstrating a mechanical advantage and efficacy over the other designs evaluated. The data and results obtained from this study confirmed that the functional behavior of partial dental prostheses with supporting abutments and soft tissues are consistent with the conventional theories of design and clinical experience. The validity and usefulness of this testing method for future applications and testing protocols are shown. Copyright © 2014 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Bond, Vanessa L.

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

Nonlinear bleaching, absorption, and scattering of 532-nm-irradiated plasmonic nanoparticles

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

Liberman, V.; Sworin, M.; Kingsborough, R. P.

2013-02-07

Single-pulse irradiation of Au and Ag suspensions of nanospheres and nanodisks with 532-nm 4-ns pulses has identified complex optical nonlinearities while minimizing material damage. For all materials tested, we observe competition between saturable absorption (SA) and reverse SA (RSA), with RSA behavior dominating for intensities above {approx}50 MW/cm{sup 2}. Due to reduced laser damage in single-pulse experiments, the observed intrinsic nonlinear absorption coefficients are the highest reported to date for Au nanoparticles. We find size dependence to the nonlinear absorption enhancement for Au nanoparticles, peaking in magnitude for 80-nm nanospheres and falling off at larger sizes. The nonlinear absorption coefficientsmore » for Au and Ag spheres are comparable in magnitude. On the other hand, the nonlinear absorption for Ag disks, when corrected for volume fraction, is several times higher. These trends in nonlinear absorption are correlated to local electric field enhancement through quasi-static mean-field theory. Through variable size aperture measurements, we also separate nonlinear scattering from nonlinear absorption. For all materials tested, we find that nonlinear scattering is highly directional and that its magnitude is comparable to that of nonlinear absorption. These results indicate methods to improve the efficacy of plasmonic nanoparticles as optical limiters in pulsed laser systems.« less

Towards improved NDE and SHM methodologies incorporating nonlinear structural features

NASA Astrophysics Data System (ADS)

Chillara, Vamshi Krishna

Ultrasound is widely employed in Nondestructive Evaluation (NDE) and Structural Health Monitoring (SHM) applications to detect and characterize damage/defects in materials. In particular, ultrasonic guided waves are considered a foremost candidate for in-situ monitoring applications. Conventional ultrasonic techniques rely on changes/discontinuities in linear elastic material properties, namely the Young's modulus and shear modulus to detect damage. On the other hand, nonlinear ultrasonic techniques that rely on micro-scale nonlinear material/structural behavior are proven to be sensitive to damage induced microstructural changes that precede macro-scale damage and are hence capable of early damage detection. The goal of this thesis is to investigate the capabilities of nonlinear guided waves --- a fusion of nonlinear ultrasonic techniques with the guided wave methodologies for early damage detection. To that end, the thesis focuses on two important aspects of the problem: 1. Wavemechanics - deals with ultrasonic guided wave propagation in nonlinear waveguides; 2. Micromechanics - deals with correlating ultrasonic response with micro-scale nonlinear material behavior. For the development of efficient NDE and SHM methodologies that incorporate nonlinear structural features, a detailed understanding of the above aspects is indispensable. In this thesis, the wavemechanics aspect of the problem is dealt with from both theoretical and numerical standpoints. A generalized theoretical framework is developed to study higher harmonic guided waves in plates. This was employed to study second harmonic guided waves in pipes using a large-radius asymptotic approximation. Second harmonic guided waves in plates are studied from a numerical standpoint. Theoretical predictions are validated and some key aspects of higher harmonic generation in waveguides are outlined. Finally, second harmonic guided waves in plates with inhomogeneous and localized nonlinearities are studied and some important aspects of guided wave mode selection are addressed. The other part of the work focused on developing a micromechanics based understanding of ultrasonic higher harmonic generation. Three important aspects of micro-scale material behavior, namely tension-compression asymmetry, shearnormal coupling and deformation induced asymmetry are identified and their role in ultrasonic higher harmonic generation is discussed. Tension-compression asymmetry is identified to cause second (even) harmonic generation in materials. Then, shearnormal coupling is identified to cause generation of secondary waves of different polarity than the primary waves. In addition, deformation induced anisotropy due to the presence of residual stress/strain and its contribution to ultrasonic higher harmonic generation is qualitatively discussed. Also, the tension-compression asymmetry in the material is quantified using an energy based measure. The above measure is employed to develop a homogenization based approach amenable to multi-scale analysis to correlate microstructure with ultrasonic higher harmonic generation. Finally, experimental investigations concerning third harmonic SH wave generation in plates are carried out and the effect of load and temperature changes on nonlinear ultrasonic measurements are discussed in the context of SHM. It was found that while nonlinear ultrasound is sensitive to micro-scale damage, the relative nonlinearity parameter may not always be the best measure to quantify the nonlinearity as it is subject to spurious effects from changes in environmental factors such as loads and temperature.

Nonlinear effective permittivity of field grading composite dielectrics

NASA Astrophysics Data System (ADS)

Yang, Xiao; Zhao, Xiaolei; Li, Qi; Hu, Jun; He, Jinliang

2018-02-01

Field grading composite dielectrics with good nonlinear electrical properties can function as smart materials for electrical field control in a high-voltage apparatus. Besides the well-documented nonlinear conducting behavior, the field-dependent effective permittivity of field grading composites were also reported; however, in-depth research on the mechanism and influencing factors of this nonlinear permittivity are absent. This paper theoretically discusses the origin of the nonlinear effective permittivity, and the mechanism is illustrated through the waveform analysis of the nonlinear response of ZnO microvaristor/silicone rubber composites under a pure AC field. The field-dependent effective permittivity and loss property of the ZnO composites are measured by a dielectric spectrometer in both DC and AC fields under different frequencies. Through comparison of measurement results and theoretical models, the influence of the filler concentration, frequency, and time domain characteristics of the applied field on the nonlinear permittivity of the field grading composites are well explained. This paper provides insight into the nonlinear permittivity of field grading composites, and will be helpful for further tuning the performance of field grading composites.

A comparative analysis of alternative approaches for quantifying nonlinear dynamics in cardiovascular system.

PubMed

Chen, Yun; Yang, Hui

2013-01-01

Heart rate variability (HRV) analysis has emerged as an important research topic to evaluate autonomic cardiac function. However, traditional time and frequency-domain analysis characterizes and quantify only linear and stationary phenomena. In the present investigation, we made a comparative analysis of three alternative approaches (i.e., wavelet multifractal analysis, Lyapunov exponents and multiscale entropy analysis) for quantifying nonlinear dynamics in heart rate time series. Note that these extracted nonlinear features provide information about nonlinear scaling behaviors and the complexity of cardiac systems. To evaluate the performance, we used 24-hour HRV recordings from 54 healthy subjects and 29 heart failure patients, available in PhysioNet. Three nonlinear methods are evaluated not only individually but also in combination using three classification algorithms, i.e., linear discriminate analysis, quadratic discriminate analysis and k-nearest neighbors. Experimental results show that three nonlinear methods capture nonlinear dynamics from different perspectives and the combined feature set achieves the best performance, i.e., sensitivity 97.7% and specificity 91.5%. Collectively, nonlinear HRV features are shown to have the promise to identify the disorders in autonomic cardiovascular function.

Modeling of dispersion and nonlinear characteristics of tapered photonic crystal fibers for applications in nonlinear optics

NASA Astrophysics Data System (ADS)

Pakarzadeh, H.; Rezaei, S. M.

2016-01-01

In this article, we investigate for the first time the dispersion and the nonlinear characteristics of the tapered photonic crystal fibers (PCFs) as a function of length z, via solving the eigenvalue equation of the guided mode using the finite-difference frequency-domain method. Since the structural parameters such as the air-hole diameter and the pitch of the microstructured cladding change along the tapered PCFs, dispersion and nonlinear properties change with the length as well. Therefore, it is important to know the exact behavior of such fiber parameters along z which is necessary for nonlinear optics applications. We simulate the z dependency of the zero-dispersion wavelength, dispersion slope, effective mode area, nonlinear parameter, and the confinement loss along the tapered PCFs and propose useful relations for describing dispersion and nonlinear parameters. The results of this article, which are in a very good agreement with the available experimental data, are important for simulating pulse propagation as well as investigating nonlinear effects such as supercontinuum generation and parametric amplification in tapered PCFs.

An Ultrasonic Technique to Determine the Residual Strength of Adhesive Bonds

NASA Technical Reports Server (NTRS)

Achenbach, J. D.; Tang, Z.

1999-01-01

In this work, ultrasonic techniques to nondestructively evaluate adhesive bond degradation have been studied. The key to the present approach is the introduction of an external factor which pulls the adhesive bond in the nonlinear range, simultaneously with the application of an ultrasonic technique. With the aid of an external static tensile loading, a superimposed longitudinal wave has.been used to obtain the slopes of the stress-strain curve of an adhesive bond at a series of load levels. The critical load, at which a reduction of the slope is detected by the superimposed longitudinal wave, is an indication of the onset of nonlinear behavior of the adhesive bond, and therefore of bond degradation. This approach has been applied to the detection of adhesive bond degradation induced by cyclic fatigue loading. Analogously to the longitudinal wave case, a superimposed shear wave has been used to obtain the effective shear modulus of adhesive layers at different shear load levels. The onset of the nonlinear behavior of an adhesive bond under shear loading has been detected by the use of a superimposed shear wave. Experiments show that a longitudinal wave can also detect the nonlinear behavior when an adhesive bond is subjected to shear loading. An optimal combination of ultrasonic testing and mechanical loading methods for the detection of degradation related nonlinear behavior of adhesive bonds has been discussed. For the purpose of a practical application, an ultrasonic technique that uses a temperature increase as an alternative to static loading has also been investigated. A general strain-temperature correspondence principle that relates a mechanical strain to a temperature has been presented. Explicit strain-temperature correspondence relations for both the tension and shear cases have been derived. An important parameter which quantifies the relation between the wave velocity and temperature has been defined. This parameter, which is indicative of adhesive bond nonlinearity and which can be conveniently obtained by an ultrasonic measurement, has been used as an indication of adhesive bond degradation. Experimental results have shown that the temperature increase method is a convenient and productive alternative to static loading. A technique which uses the reflected waveform data to obtain the fundamental ultrasonic parameters (transit time, reflection coefficient and attenuation coefficient) of an adhesive bond has also been presented.

Phonon-assisted nonlinear optical processes in ultrashort-pulse pumped optical parametric amplifiers

NASA Astrophysics Data System (ADS)

Isaienko, Oleksandr; Robel, István

2016-03-01

Optically active phonon modes in ferroelectrics such as potassium titanyl phosphate (KTP) and potassium titanyl arsenate (KTA) in the ~7-20 THz range play an important role in applications of these materials in Raman lasing and terahertz wave generation. Previous studies with picosecond pulse excitation demonstrated that the interaction of pump pulses with phonons can lead to efficient stimulated Raman scattering (SRS) accompanying optical parametric oscillation or amplification processes (OPO/OPA), and to efficient polariton-phonon scattering. In this work, we investigate the behavior of infrared OPAs employing KTP or KTA crystals when pumped with ~800-nm ultrashort pulses of duration comparable to the oscillation period of the optical phonons. We demonstrate that under conditions of coherent impulsive Raman excitation of the phonons, when the effective χ(2) nonlinearity cannot be considered instantaneous, the parametrically amplified waves (most notably, signal) undergo significant spectral modulations leading to an overall redshift of the OPA output. The pump intensity dependence of the redshifted OPA output, the temporal evolution of the parametric gain, as well as the pump spectral modulations suggest the presence of coupling between the nonlinear optical polarizations PNL of the impulsively excited phonons and those of parametrically amplified waves.

Electromagnetic-continuum-induced nonlinearity

NASA Astrophysics Data System (ADS)

Matsko, Andrey B.; Vyatchanin, Sergey P.

2018-05-01

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

Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling

NASA Astrophysics Data System (ADS)

Dumeige, Yannick; Féron, Patrice

2011-10-01

Coupled nonlinear resonators have potential applications for the integration of multistable photonic devices. The dynamic properties of two coupled-mode nonlinear microcavities made of Kerr material are studied by linear stability analysis. Using a suitable combination of the modal coupling rate and the frequency detuning, it is possible to obtain configurations where a hysteresis loop is included inside other bistable cycles. We show that a single resonator with two modes both linearly and nonlinearly coupled via the cross-Kerr effect can have a multistable behavior. This could be implemented in semiconductor nonlinear whispering-gallery-mode microresonators under modal coupling for all optical signal processing or ternary optical logic applications.

Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

NASA Astrophysics Data System (ADS)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

Influence of heating rate on the condensational instability. [in outer layers of solar atmosphere

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Mariska, J. T.

1988-01-01

Analysis and numerical simulation are used to determine the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. It is found that linear stability depends strongly on the heating rate. The results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube are presented. Different heating rates lead to quite different nonlinear evolutions, as evidenced by the behavior of the global internal energy.

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

NASA Astrophysics Data System (ADS)

Övgün, A.

2017-02-01

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.

Pupil movements to light and accommodative stimulation - A comparative study.

NASA Technical Reports Server (NTRS)

Semmlow, J.; Stark, L.

1973-01-01

Isolation and definition of specific response components in pupil reflexes through comparison of the dynamic features of light-induced and accommodation-induced pupil movements. A quantitative analysis of the behavior of the complex nonlinear pupil responses reveals the presence of two independent nonlinear characteristics: a range-dependent gain and a direction dependence or movement asymmetry. These nonlinear properties are attributed to motor processes because they are observable in pupil responses to both light and accommodation stimuli. The possible mechanisms and consequences of these pupil response characteristics are quantitatively defined and discussed.

Electro-osmosis of non-Newtonian fluids in porous media using lattice Poisson-Boltzmann method.

PubMed

Chen, Simeng; He, Xinting; Bertola, Volfango; Wang, Moran

2014-12-15

Electro-osmosis in porous media has many important applications in various areas such as oil and gas exploitation and biomedical detection. Very often, fluids relevant to these applications are non-Newtonian because of the shear-rate dependent viscosity. The purpose of this study was to investigate the behaviors and physical mechanism of electro-osmosis of non-Newtonian fluids in porous media. Model porous microstructures (granular, fibrous, and network) were created by a random generation-growth method. The nonlinear governing equations of electro-kinetic transport for a power-law fluid were solved by the lattice Poisson-Boltzmann method (LPBM). The model results indicate that: (i) the electro-osmosis of non-Newtonian fluids exhibits distinct nonlinear behaviors compared to that of Newtonian fluids; (ii) when the bulk ion concentration or zeta potential is high enough, shear-thinning fluids exhibit higher electro-osmotic permeability, while shear-thickening fluids lead to the higher electro-osmotic permeability for very low bulk ion concentration or zeta potential; (iii) the effect of the porous medium structure depends significantly on the constitutive parameters: for fluids with large constitutive coefficients strongly dependent on the power-law index, the network structure shows the highest electro-osmotic permeability while the granular structure exhibits the lowest permeability on the entire range of power law indices considered; when the dependence of the constitutive coefficient on the power law index is weaker, different behaviors can be observed especially in case of strong shear thinning. Copyright © 2014 Elsevier Inc. All rights reserved.