Mechanism of nonlinear flow pattern selection in moderately non-Boussinesq mixed convection.

PubMed

Suslov, Sergey A

2010-02-01

Nonlinear (non-Boussinesq) variations in fluid's density, viscosity, and thermal conductivity caused by a large temperature gradient in a flow domain lead to a wide variety of instability phenomena in mixed convection channel flow of a simple gas such as air. It is known that in strongly nonisothermal flows, the instabilities and the resulting flow patterns are caused by competing buoyancy and shear effects [see S. A. Suslov and S. Paolucci, J. Fluid Mech. 302, 91 (1995)]. However, as is the case in the Boussinesq limit of small temperature gradients, in moderately non-Boussinesq regimes, only a shear instability mechanism is active. Yet in contrast to Boussinesq flows, multiple instability modes are still detected. By reducing the system of full governing Navier-Stokes equations to a dynamical system of coupled Landau-type disturbance amplitude equations we compute a comprehensive parametric map of various shear-driven instabilities observed in a representative moderately non-Boussinesq regime. Subsequently, we analyze nonlinear interaction of unstable modes and reveal physical reasons for their appearance.

A variational assimilation method for satellite and conventional data: Development of basic model for diagnosis of cyclone systems

NASA Technical Reports Server (NTRS)

Achtemeier, G. L.; Ochs, H. T., III; Kidder, S. Q.; Scott, R. W.; Chen, J.; Isard, D.; Chance, B.

1986-01-01

A three-dimensional diagnostic model for the assimilation of satellite and conventional meteorological data is developed with the variational method of undetermined multipliers. Gridded fields of data from different type, quality, location, and measurement source are weighted according to measurement accuracy and merged using least squares criteria so that the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation are satisfied. The model is used to compare multivariate variational objective analyses with and without satellite data with initial analyses and the observations through criteria that were determined by the dynamical constraints, the observations, and pattern recognition. It is also shown that the diagnoses of local tendencies of the horizontal velocity components are in good comparison with the observed patterns and tendencies calculated with unadjusted data. In addition, it is found that the day-night difference in TOVS biases are statistically different (95% confidence) at most levels. Also developed is a hybrid nonlinear sigma vertical coordinate that eliminates hydrostatic truncation error in the middle and upper troposphere and reduces truncation error in the lower troposphere. Finally, it is found that the technique used to grid the initial data causes boundary effects to intrude into the interior of the analysis a distance equal to the average separation between observations.

Ultrasound coefficient of nonlinearity imaging.

PubMed

van Sloun, Ruud; Demi, Libertario; Shan, Caifeng; Mischi, Massimo

2015-07-01

Imaging the acoustical coefficient of nonlinearity, β, is of interest in several healthcare interventional applications. It is an important feature that can be used for discriminating tissues. In this paper, we propose a nonlinearity characterization method with the goal of locally estimating the coefficient of nonlinearity. The proposed method is based on a 1-D solution of the nonlinear lossy Westerfelt equation, thereby deriving a local relation between β and the pressure wave field. Based on several assumptions, a β imaging method is then presented that is based on the ratio between the harmonic and fundamental fields, thereby reducing the effect of spatial amplitude variations of the speckle pattern. By testing the method on simulated ultrasound pressure fields and an in vitro B-mode ultrasound acquisition, we show that the designed algorithm is able to estimate the coefficient of nonlinearity, and that the tissue types of interest are well discriminable. The proposed imaging method provides a new approach to β estimation, not requiring a special measurement setup or transducer, that seems particularly promising for in vivo imaging.

Free-vibration acoustic resonance of a nonlinear elastic bar

NASA Astrophysics Data System (ADS)

Tarumi, Ryuichi; Oshita, Yoshihito

2011-02-01

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

On the Limitations of Variational Bias Correction

NASA Technical Reports Server (NTRS)

Moradi, Isaac; Mccarty, Will; Gelaro, Ronald

2018-01-01

Satellite radiances are the largest dataset assimilated into Numerical Weather Prediction (NWP) models, however the data are subject to errors and uncertainties that need to be accounted for before assimilating into the NWP models. Variational bias correction uses the time series of observation minus background to estimate the observations bias. This technique does not distinguish between the background error, forward operator error, and observations error so that all these errors are summed up together and counted as observation error. We identify some sources of observations errors (e.g., antenna emissivity, non-linearity in the calibration, and antenna pattern) and show the limitations of variational bias corrections on estimating these errors.

Modeling of an intelligent pressure sensor using functional link artificial neural networks.

PubMed

Patra, J C; van den Bos, A

2000-01-01

A capacitor pressure sensor (CPS) is modeled for accurate readout of applied pressure using a novel artificial neural network (ANN). The proposed functional link ANN (FLANN) is a computationally efficient nonlinear network and is capable of complex nonlinear mapping between its input and output pattern space. The nonlinearity is introduced into the FLANN by passing the input pattern through a functional expansion unit. Three different polynomials such as, Chebyschev, Legendre and power series have been employed in the FLANN. The FLANN offers computational advantage over a multilayer perceptron (MLP) for similar performance in modeling of the CPS. The prime aim of the present paper is to develop an intelligent model of the CPS involving less computational complexity, so that its implementation can be economical and robust. It is shown that, over a wide temperature variation ranging from -50 to 150 degrees C, the maximum error of estimation of pressure remains within +/- 3%. With the help of computer simulation, the performance of the three types of FLANN models has been compared to that of an MLP based model.

The Influence of Weather Variation, Urban Design and Built Environment on Objectively Measured Sedentary Behaviour in Children.

PubMed

Katapally, Tarun Reddy; Rainham, Daniel; Muhajarine, Nazeem

2016-01-01

With emerging evidence indicating that independent of physical activity, sedentary behaviour (SB) can be detrimental to health, researchers are increasingly aiming to understand the influence of multiple contexts such as urban design and built environment on SB. However, weather variation, a factor that continuously interacts with all other environmental variables, has been consistently underexplored. This study investigated the influence of diverse environmental exposures (including weather variation, urban design and built environment) on SB in children. This cross-sectional observational study is part of an active living research initiative set in the Canadian prairie city of Saskatoon. Saskatoon's neighbourhoods were classified based on urban street design into grid-pattern, fractured grid-pattern and curvilinear types of neighbourhoods. Diverse environmental exposures were measured including, neighbourhood built environment, and neighbourhood and household socioeconomic environment. Actical accelerometers were deployed between April and June 2010 (spring-summer) to derive SB of 331 10-14 year old children in 25 one week cycles. Each cycle of accelerometry was conducted on a different cohort of children within the total sample. Accelerometer data were matched with localized weather patterns derived from Environment Canada weather data. Multilevel modeling using Hierarchical Linear and Non-linear Modeling software was conducted by factoring in weather variation to depict the influence of diverse environmental exposures on SB. Both weather variation and urban design played a significant role in SB. After factoring in weather variation, it was observed that children living in grid-pattern neighbourhoods closer to the city centre (with higher diversity of destinations) were less likely to be sedentary. This study demonstrates a methodology that could be replicated to integrate geography-specific weather patterns with existing cross-sectional accelerometry data to understand the influence of urban design and built environment on SB in children.

Variation in vulnerability to extreme-temperature-related mortality in Japan: A 40-year time-series analysis.

PubMed

Onozuka, Daisuke; Hagihara, Akihito

2015-07-01

Although the impact of extreme heat and cold on mortality has been documented in recent years, few studies have investigated whether variation in susceptibility to extreme temperatures has changed in Japan. We used data on daily total mortality and mean temperatures in Fukuoka, Japan, for 1973-2012. We used time-series analysis to assess the effects of extreme hot and low temperatures on all-cause mortality, stratified by decade, gender, and age, adjusting for time trends. We used a multivariate meta-analysis with a distributed lag non-linear model to estimate pooled non-linear lag-response relationships associated with extreme temperatures on mortality. The relative risk of mortality increased during heat extremes in all decades, with a declining trend over time. The mortality risk was higher during cold extremes for the entire study period, with a dispersed pattern across decades. Meta-analysis showed that both heat and cold extremes increased the risk of mortality. Cold effects were delayed and lasted for several days, whereas heat effects appeared quickly and did not last long. Our study provides quantitative evidence that extreme heat and low temperatures were significantly and non-linearly associated with the increased risk of mortality with substantial variation. Our results suggest that timely preventative measures are important for extreme high temperatures, whereas several days' protection should be provided for extreme low temperatures. Copyright © 2015 Elsevier Inc. All rights reserved.

Nonlinear response of summer temperature to Holocene insolation forcing in Alaska.

PubMed

Clegg, Benjamin F; Kelly, Ryan; Clarke, Gina H; Walker, Ian R; Hu, Feng Sheng

2011-11-29

Regional climate responses to large-scale forcings, such as precessional changes in solar irradiation and increases in anthropogenic greenhouse gases, may be nonlinear as a result of complex interactions among earth system components. Such nonlinear behaviors constitute a major source of climate "surprises" with important socioeconomic and ecological implications. Paleorecords are key for elucidating patterns and mechanisms of nonlinear responses to radiative forcing, but their utility has been greatly limited by the paucity of quantitative temperature reconstructions. Here we present Holocene July temperature reconstructions on the basis of midge analysis of sediment cores from three Alaskan lakes. Results show that summer temperatures during 10,000-5,500 calibrated years (cal) B.P. were generally lower than modern and that peak summer temperatures around 5,000 were followed by a decreasing trend toward the present. These patterns stand in stark contrast with the trend of precessional insolation, which decreased by ∼10% from 10,000 y ago to the present. Cool summers before 5,500 cal B.P. coincided with extensive summer ice cover in the western Arctic Ocean, persistence of a positive phase of the Arctic Oscillation, predominantly La Niña-like conditions, and variation in the position of the Alaskan treeline. These results illustrate nonlinear responses of summer temperatures to Holocene insolation radiative forcing in the Alaskan sub-Arctic, possibly because of state changes in the Arctic Oscillation and El Niño-Southern Oscillation and associated land-atmosphere-ocean feedbacks.

Nonlinear response of summer temperature to Holocene insolation forcing in Alaska

PubMed Central

Clegg, Benjamin F.; Kelly, Ryan; Clarke, Gina H.; Walker, Ian R.; Hu, Feng Sheng

2011-01-01

Regional climate responses to large-scale forcings, such as precessional changes in solar irradiation and increases in anthropogenic greenhouse gases, may be nonlinear as a result of complex interactions among earth system components. Such nonlinear behaviors constitute a major source of climate “surprises” with important socioeconomic and ecological implications. Paleorecords are key for elucidating patterns and mechanisms of nonlinear responses to radiative forcing, but their utility has been greatly limited by the paucity of quantitative temperature reconstructions. Here we present Holocene July temperature reconstructions on the basis of midge analysis of sediment cores from three Alaskan lakes. Results show that summer temperatures during 10,000–5,500 calibrated years (cal) B.P. were generally lower than modern and that peak summer temperatures around 5,000 were followed by a decreasing trend toward the present. These patterns stand in stark contrast with the trend of precessional insolation, which decreased by ∼10% from 10,000 y ago to the present. Cool summers before 5,500 cal B.P. coincided with extensive summer ice cover in the western Arctic Ocean, persistence of a positive phase of the Arctic Oscillation, predominantly La Niña-like conditions, and variation in the position of the Alaskan treeline. These results illustrate nonlinear responses of summer temperatures to Holocene insolation radiative forcing in the Alaskan sub-Arctic, possibly because of state changes in the Arctic Oscillation and El Niño-Southern Oscillation and associated land–atmosphere–ocean feedbacks. PMID:22084085

Study on the influence of supplying compressed air channels and evicting channels on pneumatical oscillation systems for vibromooshing

NASA Astrophysics Data System (ADS)

Glăvan, D. O.; Radu, I.; Babanatsas, T.; Babanatis Merce, R. M.; Kiss, I.; Gaspar, M. C.

2018-01-01

The paper presents a pneumatic system with two oscillating masses. The system is composed of a cylinder (framework) with mass m1, which has a piston with mass m2 inside. The cylinder (framework system) has one supplying channel for compressed air and one evicting channel for each work chamber (left and right of the piston). Functionality of the piston position comparatively with the cylinder (framework) is possible through the supplying or evicting of compressed air. The variable force that keeps the movement depends on variation of the pressure that is changing depending on the piston position according to the cylinder (framework) and to the section form that is supplying and evicting channels with compressed air. The paper presents the physical model/pattern, the mathematical model/pattern (differential equations) and numerical solution of the differential equations in hypothesis with the section form of supplying and evicting channels with compressed air is rectangular (variation linear) or circular (variation nonlinear).

Nonlinear waves in viscoelastic magnetized complex astroplasmas with polarized dust-charge variations

NASA Astrophysics Data System (ADS)

Das, Papari; Karmakar, Pralay Kumar

2018-01-01

A nonextensive nonthermal magnetized viscoelastic astrofluid, compositionally containing nonthermal electrons and ions together with massive polarized dust micro-spherical grains of variable electric charge, is allowed to endure weakly nonlinear perturbation around its equilibrium. The nonextensivity originating from the large-scale non-local effects is included via the Tsallis thermo-statistical distribution laws describing the lighter species. Assuming the equilibrium as a homogeneous hydrostatic one, the dust polarization effects are incorporated via the conventional homogeneous polarization force law. The perturbed fluid model evolves as a unique conjugate pair of coupled extended Korteweg-de Vries (e-KdV) equations. A constructed numerical tapestry shows the collective excitations of a new pair of distinct classes of nonlinear mode structures in new parametric space. The first family indicates periodic electrostatic compressive eigenmodes in the form of soliton-chains. Likewise, the second one reveals gravitational rarefactive solitary patterns. Their microphysical multi-parametric dependencies of the eigen-patterns are illustratively analyzed and bolstered. The paper ends up with some promising implications and applications in the astro-cosmo-plasmic context of wave-induced accretive triggering processes responsible for gravitationally bounded (gravito-condensed) astro-structure formation, such as stellesimals, planetsimals, etc.

Oscillation Mode Variability in Evolved Compact Pulsators from Kepler Photometry. I. The Hot B Subdwarf Star KIC 3527751

NASA Astrophysics Data System (ADS)

Zong, Weikai; Charpinet, Stéphane; Fu, Jian-Ning; Vauclair, Gérard; Niu, Jia-Shu; Su, Jie

2018-02-01

We present the first results of an ensemble and systematic survey of oscillation mode variability in pulsating hot B subdwarf (sdB) and white dwarf stars observed with the original Kepler mission. The satellite provides uninterrupted high-quality photometric data with a time baseline that can reach up to 4 yr collected on pulsating stars. This is a unique opportunity to characterize long-term behaviors of oscillation modes. A mode modulation in amplitude and frequency can be independently inferred by its fine structure in the Fourier spectrum, from the sLSP, or with prewhitening methods applied to various parts of the light curve. We apply all these techniques to the sdB star KIC 3527751, a long-period-dominated hybrid pulsator. We find that all the detected modes with sufficiently large amplitudes to be thoroughly studied show amplitude and/or frequency variations. Components of three identified quintuplets around 92, 114, and 253 μHz show signatures that can be linked to nonlinear interactions according to the resonant mode coupling theory. This interpretation is further supported by the fact that many oscillation modes are found to have amplitudes and frequencies showing correlated or anticorrelated variations, a behavior that can be linked to the amplitude equation formalism, where nonlinear frequency corrections are determined by their amplitude variations. Our results suggest that oscillation modes varying with diverse patterns are a very common phenomenon in pulsating sdB stars. Close structures around main frequencies therefore need to be carefully interpreted in light of this finding to secure a robust identification of real eigenfrequencies, which is crucial for seismic modeling. The various modulation patterns uncovered should encourage further developments in the field of nonlinear stellar oscillation theory. It also raises a warning to any long-term project aiming at measuring the rate of period change of pulsations caused by stellar evolution, or at discovering stellar (planetary) companions around pulsating stars using timing methods, as both require very stable pulsation modes.

Evapotranspiration patterns in complex upland forests reveal contrasting topographic thresholds of non-linearity

NASA Astrophysics Data System (ADS)

Metzen, D.; Sheridan, G. J.; Benyon, R. G.; Bolstad, P. V.; Nyman, P.; Lane, P. N. J.

2017-12-01

Large areas of forest are often treated as being homogeneous just because they fall in a single climate category. However, we observe strong vegetation patterns in relation to topography in SE Australian forests and thus hypothesise that ET will vary spatially as well. Spatial heterogeneity evolves over different temporal scales in response to climatic forcing with increasing time lag from soil moisture (sub-yearly), to vegetation (10s -100s of years) to soil properties and topography (>100s of years). Most importantly, these processes and time scales are not independent, creating feedbacks that result in "co-evolved stable states" which yield the current spatial terrain, vegetation and ET patterns. We used up-scaled sap flux and understory ET measurements from water-balance plots, as well as LiDAR derived terrain and vegetation information, to infer links between spatio-temporal energy and water fluxes, topography and vegetation patterns at small catchment scale. Topography caused variations in aridity index between polar and equatorial-facing slopes (1.3 vs 1.8), which in turn manifested in significant differences in sapwood area index (6.9 vs 5.8), overstory LAI (3.0 vs 2.3), understory LAI (0.5 vs 0.4), sub-canopy radiation load (4.6 vs 6.8 MJ m-2 d-1), overstory transpiration (501 vs 347 mm a-1) and understory ET (79 vs 155 mm a-1). Large spatial variation in overstory transpiration (195 to 891 mm a-1) was observed over very short distances (100s m); a range representative of diverse forests such as arid open woodlands and wet mountain ash forests. Contrasting, non-linear overstory and understory ET patterns were unveiled between aspects, and topographic thresholds were lower for overstory than understory ET. While ET partitioning remained stable on polar-facing slopes regardless of slope position, overstory contribution gradually decreased with increasing slope inclination on equatorial aspects. Further, we show that ET patterns and controls underlie strong seasonality and overstory LAI explained 61% of variations in ET partitioning over the entire domain. Strong links between vegetation, topography and energy and water fluxes offer the potential to exploit terrain and vegetation patterns to infer spatio-temporal ET dynamics ultimately helping manage water resources in a changing climate.

Cross-entropy clustering framework for catchment classification

NASA Astrophysics Data System (ADS)

Tongal, Hakan; Sivakumar, Bellie

2017-09-01

There is an increasing interest in catchment classification and regionalization in hydrology, as they are useful for identification of appropriate model complexity and transfer of information from gauged catchments to ungauged ones, among others. This study introduces a nonlinear cross-entropy clustering (CEC) method for classification of catchments. The method specifically considers embedding dimension (m), sample entropy (SampEn), and coefficient of variation (CV) to represent dimensionality, complexity, and variability of the time series, respectively. The method is applied to daily streamflow time series from 217 gauging stations across Australia. The results suggest that a combination of linear and nonlinear parameters (i.e. m, SampEn, and CV), representing different aspects of the underlying dynamics of streamflows, could be useful for determining distinct patterns of flow generation mechanisms within a nonlinear clustering framework. For the 217 streamflow time series, nine hydrologically homogeneous clusters that have distinct patterns of flow regime characteristics and specific dominant hydrological attributes with different climatic features are obtained. Comparison of the results with those obtained using the widely employed k-means clustering method (which results in five clusters, with the loss of some information about the features of the clusters) suggests the superiority of the cross-entropy clustering method. The outcomes from this study provide a useful guideline for employing the nonlinear dynamic approaches based on hydrologic signatures and for gaining an improved understanding of streamflow variability at a large scale.

The impact of breathing on HRV measurements: implications for the longitudinal follow-up of athletes.

PubMed

Saboul, Damien; Pialoux, Vincent; Hautier, Christophe

2013-01-01

The purpose of the present work was to compare daily variations of heart rate variability (HRV) parameters between controlled breathing (CB) and spontaneous breathing (SB) sessions during a longitudinal follow-up of athletes. HRV measurements were performed daily on 10 healthy male runners for 21 consecutive days. The signals were recorded during two successive randomised 5-minutes sessions. One session was performed in CB and the other in SB. The results showed significant differences between the two respiration methods in the temporal, nonlinear and frequency domains. However, significant correlations were observed between CB and SB (higher than 0.70 for RMSSD and SD1), demonstrating that during a longitudinal follow-up, these markers provide the same HRV variations regardless of breathing pattern. By contrast, independent day-to-day variations were observed with HF and LF/HF frequency markers, indicating no significant relationship between SB and CB data over time. Therefore, we consider that SB and CB may be used for HRV longitudinal follow-ups only for temporal and nonlinear markers. Indeed, the same daily increases and decreases were observed whatever the breathing method employed. Conversely, frequency markers did not provide the same variations between SB and CB and we propose that these indicators are not reliable enough to be used for day-to-day HRV monitoring.

On the vortices for the nonlinear Schrödinger equation in higher dimensions.

PubMed

Feng, Wen; Stanislavova, Milena

2018-04-13

We consider the nonlinear Schrödinger equation in n space dimensions [Formula: see text]and study the existence and stability of standing wave solutions of the form [Formula: see text]and [Formula: see text]For n =2 k , ( r j , θ j ) are polar coordinates in [Formula: see text], j =1,2,…, k ; for n =2 k +1, ( r j , θ j ) are polar coordinates in [Formula: see text], ( r k , θ k , z ) are cylindrical coordinates in [Formula: see text], j =1,2,…, k -1. We show the existence of functions ϕ w , which are constructed variationally as minimizers of appropriate constrained functionals. These waves are shown to be spectrally stable (with respect to perturbations of the same type), if 1< p <1+4/ n This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'. © 2018 The Author(s).

All-Optical Switching and Unidirectional Plasmon Launching with Nonlinear Dielectric Nanoantennas

NASA Astrophysics Data System (ADS)

Krasnok, Alex; Li, Sergey; Lepeshov, Sergey; Savelev, Roman; Baranov, Denis G.; Alú, Andrea

2018-01-01

High-index dielectric nanoparticles have become a powerful platform for nonlinear nanophotonics due to special types of optical nonlinearity, e.g. caused by electron-hole plasma (EHP) photoexcitation. We propose a highly tunable dielectric nanoantenna consisting of a chain of silicon particles excited by a dipole emitter. The nanoantenna exhibits slow group-velocity guided modes, corresponding to the Van Hove singularity in an infinite structure, which enable a large Purcell factor up to several hundred and are very sensitive to the nanoparticle permittivity. This sensitivity enables the nanoantenna tuning via EHP excitation with an ultrafast laser pumping. Dramatic variations in the nanoantenna radiation patterns and Purcell factor caused by ultrafast laser pumping of several boundary nanoparticles with relatively low intensities of about 25 GW /cm2 are shown. Unidirectional surface-plasmon polaritons launching with EHP excitation in the nanoantenna on a Ag substrate is demonstrated.

Barotropic instability with divergence - Theory and applications to Venus

NASA Technical Reports Server (NTRS)

Dobrovolskis, Anthony R.; Diner, David J.

1990-01-01

IR images of Venus reveal a curious double-lobed hot spot in the polar region. Elson (1982) has suggested that this dipole represents a barotropic instability associated with a high-latitude jet. Unfortunately, the classical theory of barotropic instability cannot predict temperature variations. This paper generalizes the theory to include horizontal divergence, vertical motions, and temperature variations, and applies it to the stratosphere of Venus. The fastest-growing barotropic instability in the nominal model matches the observed dipole in period and horizontal temperature pattern. The accompanying wind variations are comparable to the speed of the mean jet, indicating strong nonlinear effects. It is concluded that the Venus dipole may represent the self-limited stage of a barotropic instability with divergence.

Plant functional trait diversity regulates the nonlinear response of productivity to regional climate change in Tibetan alpine grasslands.

PubMed

Wu, Jianshuang; Wurst, Susanne; Zhang, Xianzhou

2016-10-19

The biodiversity-productivity relationship is still under debate for alpine grasslands on the Tibetan Plateau. We know little about direct and indirect effects of biotic and abiotic drivers on this relationship, especially in regard to plant functional trait diversity. Here, we examine how aboveground net primary productivity (ANPP) and precipitation use efficiency (PUE) respond to climate, soil and community structure across alpine grasslands on the Northern Tibetan Plateau. We found that both ANPP and PUE showed nonlinear patterns along water availability and site altitude variation, which together accounted for 80.3% and 68.8% of variation in ANPP and PUE, respectively, by optimal generalized additive models. Functional trait divergence (FTD) and community weighted mean (CWM) of plant functional traits were as important as plant species diversity (PSD) for explaining the nonlinear productivity-climate relationship. These findings were confirmed by results from principal component analyses and structural equation models. We also found that FTD was negatively correlated with PSD across different alpine grasslands. Our results implicate: first, the combinatorial influences of temperature and precipitation gradients are important for predicting alpine grassland dynamics; second, the convergence and divergence of plant functional traits may have the potential to elucidate the effect of plant diversity on ecosystem functionality.

Plant functional trait diversity regulates the nonlinear response of productivity to regional climate change in Tibetan alpine grasslands

PubMed Central

Wu, Jianshuang; Wurst, Susanne; Zhang, Xianzhou

2016-01-01

The biodiversity-productivity relationship is still under debate for alpine grasslands on the Tibetan Plateau. We know little about direct and indirect effects of biotic and abiotic drivers on this relationship, especially in regard to plant functional trait diversity. Here, we examine how aboveground net primary productivity (ANPP) and precipitation use efficiency (PUE) respond to climate, soil and community structure across alpine grasslands on the Northern Tibetan Plateau. We found that both ANPP and PUE showed nonlinear patterns along water availability and site altitude variation, which together accounted for 80.3% and 68.8% of variation in ANPP and PUE, respectively, by optimal generalized additive models. Functional trait divergence (FTD) and community weighted mean (CWM) of plant functional traits were as important as plant species diversity (PSD) for explaining the nonlinear productivity-climate relationship. These findings were confirmed by results from principal component analyses and structural equation models. We also found that FTD was negatively correlated with PSD across different alpine grasslands. Our results implicate: first, the combinatorial influences of temperature and precipitation gradients are important for predicting alpine grassland dynamics; second, the convergence and divergence of plant functional traits may have the potential to elucidate the effect of plant diversity on ecosystem functionality. PMID:27759112

The application of neural network model to the simulation nitrous oxide emission in the hydro-fluctuation belt of Three Gorges Reservoir

NASA Astrophysics Data System (ADS)

Song, Lanlan

2017-04-01

Nitrous oxide is much more potent greenhouse gas than carbon dioxide. However, the estimation of N2O flux is usually clouded with uncertainty, mainly due to high spatial and temporal variations. This hampers the development of general mechanistic models for N2O emission as well, as most previously developed models were empirical or exhibited low predictability with numerous assumptions. In this study, we tested General Regression Neural Networks (GRNN) as an alternative to classic empirical models for simulating N2O emission in riparian zones of Reservoirs. GRNN and nonlinear regression (NLR) were applied to estimate the N2O flux of 1-year observations in riparian zones of Three Gorge Reservoir. NLR resulted in lower prediction power and higher residuals compared to GRNN. Although nonlinear regression model estimated similar average values of N2O, it could not capture the fluctuation patterns accurately. In contrast, GRNN model achieved a fairly high predictability, with an R2 of 0.59 for model validation, 0.77 for model calibration (training), and a low root mean square error (RMSE), indicating a high capacity to simulate the dynamics of N2O flux. According to a sensitivity analysis of the GRNN, nonlinear relationships between input variables and N2O flux were well explained. Our results suggest that the GRNN developed in this study has a greater performance in simulating variations in N2O flux than nonlinear regressions.

Photometric Characterization of the Dark Energy Camera

DOE PAGES

Bernstein, G. M.; Abbott, T. M. C.; Armstrong, R.; ...

2018-04-02

We characterize the variation in photometric response of the Dark Energy Camera (DECam) across its 520 Mpix science array during 4 years of operation. These variations are measured using high signal-to-noise aperture photometry of >10 7 stellar images in thousands of exposures of a few selected fields, with the telescope dithered to move the sources around the array. A calibration procedure based on these results brings the rms variation in aperture magnitudes of bright stars on cloudless nights down to 2–3 mmag, with <1 mmag of correlated photometric errors for stars separated by ≥20''. On cloudless nights, any departures ofmore » the exposure zeropoints from a secant airmass law exceeding 1 mmag are plausibly attributable to spatial/temporal variations in aperture corrections. These variations can be inferred and corrected by measuring the fraction of stellar light in an annulus between 6'' and 8'' diameter. Key elements of this calibration include: correction of amplifier nonlinearities; distinguishing pixel-area variations and stray light from quantum-efficiency variations in the flat fields; field-dependent color corrections; and the use of an aperture-correction proxy. The DECam response pattern across the 2° field drifts over months by up to ±9 mmag, in a nearly wavelength-independent low-order pattern. Here, we find no fundamental barriers to pushing global photometric calibrations toward mmag accuracy.« less

Astrometric Calibration and Performance of the Dark Energy Camera

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

Bernstein, G. M.; Armstrong, R.; Plazas, A. A.

2017-05-30

We characterize the variation in photometric response of the Dark Energy Camera (DECam) across its 520~Mpix science array during 4 years of operation. These variations are measured using high signal-to-noise aperture photometry ofmore » $>10^7$ stellar images in thousands of exposures of a few selected fields, with the telescope dithered to move the sources around the array. A calibration procedure based on these results brings the RMS variation in aperture magnitudes of bright stars on cloudless nights down to 2--3 mmag, with <1 mmag of correlated photometric errors for stars separated by $$\\ge20$$". On cloudless nights, any departures of the exposure zeropoints from a secant airmass law exceeding >1 mmag are plausibly attributable to spatial/temporal variations in aperture corrections. These variations can be inferred and corrected by measuring the fraction of stellar light in an annulus between 6" and 8" diameter. Key elements of this calibration include: correction of amplifier nonlinearities; distinguishing pixel-area variations and stray light from quantum-efficiency variations in the flat fields; field-dependent color corrections; and the use of an aperture-correction proxy. The DECam response pattern across the 2-degree field drifts over months by up to $$\\pm7$$ mmag, in a nearly-wavelength-independent low-order pattern. We find no fundamental barriers to pushing global photometric calibrations toward mmag accuracy.« less

Photometric Characterization of the Dark Energy Camera

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

Bernstein, G. M.; Abbott, T. M. C.; Armstrong, R.

We characterize the variation in photometric response of the Dark Energy Camera (DECam) across its 520 Mpix science array during 4 years of operation. These variations are measured using high signal-to-noise aperture photometry of >10 7 stellar images in thousands of exposures of a few selected fields, with the telescope dithered to move the sources around the array. A calibration procedure based on these results brings the rms variation in aperture magnitudes of bright stars on cloudless nights down to 2–3 mmag, with <1 mmag of correlated photometric errors for stars separated by ≥20''. On cloudless nights, any departures ofmore » the exposure zeropoints from a secant airmass law exceeding 1 mmag are plausibly attributable to spatial/temporal variations in aperture corrections. These variations can be inferred and corrected by measuring the fraction of stellar light in an annulus between 6'' and 8'' diameter. Key elements of this calibration include: correction of amplifier nonlinearities; distinguishing pixel-area variations and stray light from quantum-efficiency variations in the flat fields; field-dependent color corrections; and the use of an aperture-correction proxy. The DECam response pattern across the 2° field drifts over months by up to ±9 mmag, in a nearly wavelength-independent low-order pattern. Here, we find no fundamental barriers to pushing global photometric calibrations toward mmag accuracy.« less

Photometric Characterization of the Dark Energy Camera

NASA Astrophysics Data System (ADS)

Bernstein, G. M.; Abbott, T. M. C.; Armstrong, R.; Burke, D. L.; Diehl, H. T.; Gruendl, R. A.; Johnson, M. D.; Li, T. S.; Rykoff, E. S.; Walker, A. R.; Wester, W.; Yanny, B.

2018-05-01

We characterize the variation in photometric response of the Dark Energy Camera (DECam) across its 520 Mpix science array during 4 years of operation. These variations are measured using high signal-to-noise aperture photometry of >107 stellar images in thousands of exposures of a few selected fields, with the telescope dithered to move the sources around the array. A calibration procedure based on these results brings the rms variation in aperture magnitudes of bright stars on cloudless nights down to 2–3 mmag, with <1 mmag of correlated photometric errors for stars separated by ≥20″. On cloudless nights, any departures of the exposure zeropoints from a secant airmass law exceeding 1 mmag are plausibly attributable to spatial/temporal variations in aperture corrections. These variations can be inferred and corrected by measuring the fraction of stellar light in an annulus between 6″ and 8″ diameter. Key elements of this calibration include: correction of amplifier nonlinearities; distinguishing pixel-area variations and stray light from quantum-efficiency variations in the flat fields; field-dependent color corrections; and the use of an aperture-correction proxy. The DECam response pattern across the 2° field drifts over months by up to ±9 mmag, in a nearly wavelength-independent low-order pattern. We find no fundamental barriers to pushing global photometric calibrations toward mmag accuracy.

The Influence of Weather Variation, Urban Design and Built Environment on Objectively Measured Sedentary Behaviour in Children

PubMed Central

Katapally, Tarun Reddy; Rainham, Daniel; Muhajarine, Nazeem

2016-01-01

With emerging evidence indicating that independent of physical activity, sedentary behaviour (SB) can be detrimental to health, researchers are increasingly aiming to understand the influence of multiple contexts such as urban design and built environment on SB. However, weather variation, a factor that continuously interacts with all other environmental variables, has been consistently underexplored. This study investigated the influence of diverse environmental exposures (including weather variation, urban design and built environment) on SB in children. This cross-sectional observational study is part of an active living research initiative set in the Canadian prairie city of Saskatoon. Saskatoon's neighbourhoods were classified based on urban street design into grid-pattern, fractured grid-pattern and curvilinear types of neighbourhoods. Diverse environmental exposures were measured including, neighbourhood built environment, and neighbourhood and household socioeconomic environment. Actical accelerometers were deployed between April and June 2010 (spring-summer) to derive SB of 331 10–14 year old children in 25 one week cycles. Each cycle of accelerometry was conducted on a different cohort of children within the total sample. Accelerometer data were matched with localized weather patterns derived from Environment Canada weather data. Multilevel modeling using Hierarchical Linear and Non-linear Modeling software was conducted by factoring in weather variation to depict the influence of diverse environmental exposures on SB. Both weather variation and urban design played a significant role in SB. After factoring in weather variation, it was observed that children living in grid-pattern neighbourhoods closer to the city centre (with higher diversity of destinations) were less likely to be sedentary. This study demonstrates a methodology that could be replicated to integrate geography-specific weather patterns with existing cross-sectional accelerometry data to understand the influence of urban design and built environment on SB in children. PMID:29546188

Investigation about relationships between the symmetries of ferroelectric crystal Ca0.28Ba0.72Nb2O6 and second-harmonic patterns

NASA Astrophysics Data System (ADS)

Xu, Tianxiang; Yu, Haohai; Zhang, Huaijin; Wang, Jiyang

2015-08-01

The broadband quasi-phase matching (QPM) process in a uniaxial ferroelectric crystal Ca0.28Ba0.72Nb2O6 (CBN-28) was demonstrated with the second-harmonic wavelength range from 450 nm to 650 nm, and the relationship between the symmetries of CBN-28 and the second-harmonic patterns was experimentally and theoretically investigated based on the random anti-parallel domains in the crystal and QPM conditions. The dependences of frequency-doubled patterns on the wavelength and anisotropy of the nonlinear crystal were also studied, and the frequency-doubled photons were found to be trapped on circles. By analyzing the light-matter interacting Hamiltonians, the trapping force for second-harmonic photons was found to be centripetal and tunable by the fundamental lasers, and the variation tendencies of the rotational velocity of second-harmonic generation photons could also be predicated. The results indicate that the CBN-28 ferroelectric crystal is a promising nonlinear optical material for the generation of broadband frequency-doubled waves, and the analysis on centripetal force based on the interaction Hamiltonians may provide a novel recognition for the investigation of QPM process to be further studied.

Extracting Leading Nonlinear Modes of Changing Climate From Global SST Time Series

NASA Astrophysics Data System (ADS)

Mukhin, D.; Gavrilov, A.; Loskutov, E. M.; Feigin, A. M.; Kurths, J.

2017-12-01

Data-driven modeling of climate requires adequate principal variables extracted from observed high-dimensional data. For constructing such variables it is needed to find spatial-temporal patterns explaining a substantial part of the variability and comprising all dynamically related time series from the data. The difficulties of this task rise from the nonlinearity and non-stationarity of the climate dynamical system. The nonlinearity leads to insufficiency of linear methods of data decomposition for separating different processes entangled in the observed time series. On the other hand, various forcings, both anthropogenic and natural, make the dynamics non-stationary, and we should be able to describe the response of the system to such forcings in order to separate the modes explaining the internal variability. The method we present is aimed to overcome both these problems. The method is based on the Nonlinear Dynamical Mode (NDM) decomposition [1,2], but takes into account external forcing signals. An each mode depends on hidden, unknown a priori, time series which, together with external forcing time series, are mapped onto data space. Finding both the hidden signals and the mapping allows us to study the evolution of the modes' structure in changing external conditions and to compare the roles of the internal variability and forcing in the observed behavior. The method is used for extracting of the principal modes of SST variability on inter-annual and multidecadal time scales accounting the external forcings such as CO2, variations of the solar activity and volcanic activity. The structure of the revealed teleconnection patterns as well as their forecast under different CO2 emission scenarios are discussed.[1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016). Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101.

On the implications of the classical ergodic theorems: analysis of developmental processes has to focus on intra-individual variation.

PubMed

Molenaar, Peter C M

2008-01-01

It is argued that general mathematical-statistical theorems imply that standard statistical analysis techniques of inter-individual variation are invalid to investigate developmental processes. Developmental processes have to be analyzed at the level of individual subjects, using time series data characterizing the patterns of intra-individual variation. It is shown that standard statistical techniques based on the analysis of inter-individual variation appear to be insensitive to the presence of arbitrary large degrees of inter-individual heterogeneity in the population. An important class of nonlinear epigenetic models of neural growth is described which can explain the occurrence of such heterogeneity in brain structures and behavior. Links with models of developmental instability are discussed. A simulation study based on a chaotic growth model illustrates the invalidity of standard analysis of inter-individual variation, whereas time series analysis of intra-individual variation is able to recover the true state of affairs. (c) 2007 Wiley Periodicals, Inc.

A generalized reaction diffusion model for spatial structure formed by motile cells.

PubMed

Ochoa, F L

1984-01-01

A non-linear stability analysis using a multi-scale perturbation procedure is carried out on a model of a generalized reaction diffusion mechanism which involves only a single equation but which nevertheless exhibits bifurcation to non-uniform states. The patterns generated by this model by variation in a parameter related to the scalar dimensions of domain of definition, indicate its capacity to represent certain key morphogenetic features of multicellular systems formed by motile cells.

Nouvelles bornes et estimations pour les milieux poreux à matrice rigide parfaitement plastique

NASA Astrophysics Data System (ADS)

Bilger, Nicolas; Auslender, François; Bornert, Michel; Masson, Renaud

We derive new rigorous bounds and self-consistent estimates for the effective yield surface of porous media with a rigid perfectly plastic matrix and a microstructure similar to Hashin's composite spheres assemblage. These results arise from a homogenisation technique that combines a pattern-based modelling for linear composite materials and a variational formulation for nonlinear media. To cite this article: N. Bilger et al., C. R. Mecanique 330 (2002) 127-132.

Quantifying patterns of change in marine ecosystem response to multiple pressures.

PubMed

Large, Scott I; Fay, Gavin; Friedland, Kevin D; Link, Jason S

2015-01-01

The ability to understand and ultimately predict ecosystem response to multiple pressures is paramount to successfully implement ecosystem-based management. Thresholds shifts and nonlinear patterns in ecosystem responses can be used to determine reference points that identify levels of a pressure that may drastically alter ecosystem status, which can inform management action. However, quantifying ecosystem reference points has proven elusive due in large part to the multi-dimensional nature of both ecosystem pressures and ecosystem responses. We used ecological indicators, synthetic measures of ecosystem status and functioning, to enumerate important ecosystem attributes and to reduce the complexity of the Northeast Shelf Large Marine Ecosystem (NES LME). Random forests were used to quantify the importance of four environmental and four anthropogenic pressure variables to the value of ecological indicators, and to quantify shifts in aggregate ecological indicator response along pressure gradients. Anthropogenic pressure variables were critical defining features and were able to predict an average of 8-13% (up to 25-66% for individual ecological indicators) of the variation in ecological indicator values, whereas environmental pressures were able to predict an average of 1-5 % (up to 9-26% for individual ecological indicators) of ecological indicator variation. Each pressure variable predicted a different suite of ecological indicator's variation and the shapes of ecological indicator responses along pressure gradients were generally nonlinear. Threshold shifts in ecosystem response to exploitation, the most important pressure variable, occurred when commercial landings were 20 and 60% of total surveyed biomass. Although present, threshold shifts in ecosystem response to environmental pressures were much less important, which suggests that anthropogenic pressures have significantly altered the ecosystem structure and functioning of the NES LME. Gradient response curves provide ecologically informed transformations of pressure variables to explain patterns of ecosystem structure and functioning. By concurrently identifying thresholds for a suite of ecological indicator responses to multiple pressures, we demonstrate that ecosystem reference points can be evaluated and used to support ecosystem-based management.

Coordinated observations of PHEMU at radio wavelengths.

NASA Astrophysics Data System (ADS)

Pluchino, S.; Schillirò, F.; Salerno, E.; Pupillo, G.; Kraus, A.; Mack, K.-H.

We present preliminary results for our study of mutual phenomena of the Galilean satellites performed at radio wavelengths with the Medicina and Noto antennas of the Istituto di Radioastronomia \\textendash{} INAF, and with the Effelsberg 100-m radio telescope of the Max-Planck-Institute for Radioastronomy. Measurements of the radio flux density variation occurred during the mutual occultations of Io by Europa and Ganymede were carried out during the PHEMU09 campaign at K- and Q-band. Flux density variations observed for the first time at radio wavelengths are consistent with the typical optical patterns measured when partial occultations occurred. The flux density drops indicate a non-linear dependence with the percentage of overlapped area.

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.

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

NASA Astrophysics Data System (ADS)

Biria, Saeid; Morim, Derek R.; An Tsao, Fu; Saravanamuttu, Kalaichelvi; Hosein, Ian D.

2017-10-01

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

Translating natural genetic variation to gene expression in a computational model of the Drosophila gap gene regulatory network

PubMed Central

Kozlov, Konstantin N.; Kulakovskiy, Ivan V.; Zubair, Asif; Marjoram, Paul; Lawrie, David S.; Nuzhdin, Sergey V.; Samsonova, Maria G.

2017-01-01

Annotating the genotype-phenotype relationship, and developing a proper quantitative description of the relationship, requires understanding the impact of natural genomic variation on gene expression. We apply a sequence-level model of gap gene expression in the early development of Drosophila to analyze single nucleotide polymorphisms (SNPs) in a panel of natural sequenced D. melanogaster lines. Using a thermodynamic modeling framework, we provide both analytical and computational descriptions of how single-nucleotide variants affect gene expression. The analysis reveals that the sequence variants increase (decrease) gene expression if located within binding sites of repressors (activators). We show that the sign of SNP influence (activation or repression) may change in time and space and elucidate the origin of this change in specific examples. The thermodynamic modeling approach predicts non-local and non-linear effects arising from SNPs, and combinations of SNPs, in individual fly genotypes. Simulation of individual fly genotypes using our model reveals that this non-linearity reduces to almost additive inputs from multiple SNPs. Further, we see signatures of the action of purifying selection in the gap gene regulatory regions. To infer the specific targets of purifying selection, we analyze the patterns of polymorphism in the data at two phenotypic levels: the strengths of binding and expression. We find that combinations of SNPs show evidence of being under selective pressure, while individual SNPs do not. The model predicts that SNPs appear to accumulate in the genotypes of the natural population in a way biased towards small increases in activating action on the expression pattern. Taken together, these results provide a systems-level view of how genetic variation translates to the level of gene regulatory networks via combinatorial SNP effects. PMID:28898266

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

Numerical realization of the variational method for generating self-trapped beams

NASA Astrophysics Data System (ADS)

Duque, Erick I.; Lopez-Aguayo, Servando; Malomed, Boris A.

2018-03-01

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schr\\"odinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states and its bridge function study

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Bao, Lin; Tong, Binggang

2009-12-01

This paper is a research on the variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states by using theoretical analysis and numerical simulation methods. The newly developed near space hypersonic cruise vehicles have sharp noses and wingtips, which desires exact and relatively simple methods to estimate the stagnation point heat flux. With the decrease of the curvature radius of the leading edge, the flow becomes rarefied gradually, and viscous interaction effects and rarefied gas effects come forth successively, which results in that the classical Fay-Riddell equation under continuum hypothesis will become invalid and the variation of stagnation point heat flux is characterized by a new trend. The heat flux approaches the free molecular flow limit instead of an infinite value when the curvature radius of the leading edge tends to 0. The physical mechanism behind this phenomenon remains in need of theoretical study. Firstly, due to the fact that the whole flow regime can be described by Boltzmann equation, the continuum and rarefied flow are analyzed under a uniform framework. A relationship is established between the molecular collision insufficiency in rarefied flow and the failure of Fourier’s heat conduction law along with the increasing significance of the nonlinear heat flux. Then based on an inspiration drew from Burnett approximation, control factors are grasped and a specific heat flux expression containing the nonlinear term is designed in the stagnation region of hypersonic leading edge. Together with flow pattern analysis, the ratio of nonlinear to linear heat flux W r is theoretically obtained as a parameter which reflects the influence of nonlinear factors, i.e. a criterion to classify the hypersonic rarefied flows. Ultimately, based on the characteristic parameter W r , a bridge function with physical background is constructed, which predicts comparative reasonable results in coincidence well with DSMC and experimental data in the whole flow regime.

Second-order processing of four-stroke apparent motion.

PubMed

Mather, G; Murdoch, L

1999-05-01

In four-stroke apparent motion displays, pattern elements oscillate between two adjacent positions and synchronously reverse in contrast, but appear to move unidirectionally. For example, if rightward shifts preserve contrast but leftward shifts reverse contrast, consistent rightward motion is seen. In conventional first-order displays, elements reverse in luminance contrast (e.g. light elements become dark, and vice-versa). The resulting perception can be explained by responses in elementary motion detectors turned to spatio-temporal orientation. Second-order motion displays contain texture-defined elements, and there is some evidence that they excite second-order motion detectors that extract spatio-temporal orientation following the application of a non-linear 'texture-grabbing' transform by the visual system. We generated a variety of second-order four-stroke displays, containing texture-contrast reversals instead of luminance contrast reversals, and used their effectiveness as a diagnostic test for the presence of various forms of non-linear transform in the second-order motion system. Displays containing only forward or only reversed phi motion sequences were also tested. Displays defined by variation in luminance, contrast, orientation, and size were effective. Displays defined by variation in motion, dynamism, and stereo were partially or wholly ineffective. Results obtained with contrast-reversing and four-stroke displays indicate that only relatively simple non-linear transforms (involving spatial filtering and rectification) are available during second-order energy-based motion analysis.

Partitioning sources of variation in vertebrate species richness

USGS Publications Warehouse

Boone, R.B.; Krohn, W.B.

2000-01-01

Aim: To explore biogeographic patterns of terrestrial vertebrates in Maine, USA using techniques that would describe local and spatial correlations with the environment. Location: Maine, USA. Methods: We delineated the ranges within Maine (86,156 km2) of 275 species using literature and expert review. Ranges were combined into species richness maps, and compared to geomorphology, climate, and woody plant distributions. Methods were adapted that compared richness of all vertebrate classes to each environmental correlate, rather than assessing a single explanatory theory. We partitioned variation in species richness into components using tree and multiple linear regression. Methods were used that allowed for useful comparisons between tree and linear regression results. For both methods we partitioned variation into broad-scale (spatially autocorrelated) and fine-scale (spatially uncorrelated) explained and unexplained components. By partitioning variance, and using both tree and linear regression in analyses, we explored the degree of variation in species richness for each vertebrate group that Could be explained by the relative contribution of each environmental variable. Results: In tree regression, climate variation explained richness better (92% of mean deviance explained for all species) than woody plant variation (87%) and geomorphology (86%). Reptiles were highly correlated with environmental variation (93%), followed by mammals, amphibians, and birds (each with 84-82% deviance explained). In multiple linear regression, climate was most closely associated with total vertebrate richness (78%), followed by woody plants (67%) and geomorphology (56%). Again, reptiles were closely correlated with the environment (95%), followed by mammals (73%), amphibians (63%) and birds (57%). Main conclusions: Comparing variation explained using tree and multiple linear regression quantified the importance of nonlinear relationships and local interactions between species richness and environmental variation, identifying the importance of linear relationships between reptiles and the environment, and nonlinear relationships between birds and woody plants, for example. Conservation planners should capture climatic variation in broad-scale designs; temperatures may shift during climate change, but the underlying correlations between the environment and species richness will presumably remain.

Bursting as a source of non-linear determinism in the firing patterns of nigral dopamine neurons

PubMed Central

Jeong, Jaeseung; Shi, Wei-Xing; Hoffman, Ralph; Oh, Jihoon; Gore, John C.; Bunney, Benjamin S.; Peterson, Bradley S.

2012-01-01

Nigral dopamine (DA) neurons in vivo exhibit complex firing patterns consisting of tonic single-spikes and phasic bursts that encode information for certain types of reward-related learning and behavior. Non-linear dynamical analysis has previously demonstrated the presence of a non-linear deterministic structure in complex firing patterns of DA neurons, yet the origin of this non-linear determinism remains unknown. In this study, we hypothesized that bursting activity is the primary source of non-linear determinism in the firing patterns of DA neurons. To test this hypothesis, we investigated the dimension complexity of inter-spike interval data recorded in vivo from bursting and non-bursting DA neurons in the chloral hydrate-anesthetized rat substantia nigra. We found that bursting DA neurons exhibited non-linear determinism in their firing patterns, whereas non-bursting DA neurons showed truly stochastic firing patterns. Determinism was also detected in the isolated burst and inter-burst interval data extracted from firing patterns of bursting neurons. Moreover, less bursting DA neurons in halothane-anesthetized rats exhibited higher dimensional spiking dynamics than do more bursting DA neurons in chloral hydrate-anesthetized rats. These results strongly indicate that bursting activity is the main source of low-dimensional, non-linear determinism in the firing patterns of DA neurons. This finding furthermore suggests that bursts are the likely carriers of meaningful information in the firing activities of DA neurons. PMID:22831464

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

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.

A multivariate variational objective analysis-assimilation method. Part 2: Case study results with and without satellite data

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Kidder, Stanley Q.; Scott, Robert W.

1988-01-01

The variational multivariate assimilation method described in a companion paper by Achtemeier and Ochs is applied to conventional and conventional plus satellite data. Ground-based and space-based meteorological data are weighted according to the respective measurement errors and blended into a data set that is a solution of numerical forms of the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation for a dry atmosphere. The analyses serve first, to evaluate the accuracy of the model, and second to contrast the analyses with and without satellite data. Evaluation criteria measure the extent to which: (1) the assimilated fields satisfy the dynamical constraints, (2) the assimilated fields depart from the observations, and (3) the assimilated fields are judged to be realistic through pattern analysis. The last criterion requires that the signs, magnitudes, and patterns of the hypersensitive vertical velocity and local tendencies of the horizontal velocity components be physically consistent with respect to the larger scale weather systems.

Does Sex Trade with Violence among Genotypes in Drosophila melanogaster?

PubMed Central

Cabral, Larry G.; Foley, Brad R.; Nuzhdin, Sergey V.

2008-01-01

The evolutionary forces shaping the ability to win competitive interactions, such as aggressive encounters, are still poorly understood. Given a fitness advantage for competitive success, variance in aggressive and sexual display traits should be depleted, but a great deal of variation in these traits is consistently found. While life history tradeoffs have been commonly cited as a mechanism for the maintenance of variation, the variability of competing strategies of conspecifics may mean there is no single optimum strategy. We measured the genetically determined outcomes of aggressive interactions, and the resulting effects on mating success, in a panel of diverse inbred lines representing both natural variation and artificially selected genotypes. Males of one genotype which consistently lost territorial encounters with other genotypes were nonetheless successful against males that were artificially selected for supernormal aggression and dominated all other lines. Intransitive patterns of territorial success could maintain variation in aggressive strategies if there is a preference for territorial males. Territorial success was not always associated with male mating success however and females preferred ‘winners’ among some male genotypes, and ‘losers’ among other male genotypes. This suggests that studying behaviour from the perspective of population means may provide limited evolutionary and genetic insight. Overall patterns of competitive success among males and mating transactions between the sexes are consistent with mechanisms proposed for the maintenance of genetic variation due to nonlinear outcomes of competitive interactions. PMID:18414669

Does sex trade with violence among genotypes in Drosophila melanogaster?

PubMed

Cabral, Larry G; Foley, Brad R; Nuzhdin, Sergey V

2008-04-16

The evolutionary forces shaping the ability to win competitive interactions, such as aggressive encounters, are still poorly understood. Given a fitness advantage for competitive success, variance in aggressive and sexual display traits should be depleted, but a great deal of variation in these traits is consistently found. While life history tradeoffs have been commonly cited as a mechanism for the maintenance of variation, the variability of competing strategies of conspecifics may mean there is no single optimum strategy. We measured the genetically determined outcomes of aggressive interactions, and the resulting effects on mating success, in a panel of diverse inbred lines representing both natural variation and artificially selected genotypes. Males of one genotype which consistently lost territorial encounters with other genotypes were nonetheless successful against males that were artificially selected for supernormal aggression and dominated all other lines. Intransitive patterns of territorial success could maintain variation in aggressive strategies if there is a preference for territorial males. Territorial success was not always associated with male mating success however and females preferred 'winners' among some male genotypes, and 'losers' among other male genotypes. This suggests that studying behaviour from the perspective of population means may provide limited evolutionary and genetic insight. Overall patterns of competitive success among males and mating transactions between the sexes are consistent with mechanisms proposed for the maintenance of genetic variation due to nonlinear outcomes of competitive interactions.

Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system

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

Banerjee, Tanmoy, E-mail: tbanerjee@phys.buruniv.ac.in; Paul, Bishwajit; Sarkar, B. C.

2014-03-15

We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strengthmore » the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.« less

Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system.

PubMed

Banerjee, Tanmoy; Paul, Bishwajit; Sarkar, B C

2014-03-01

We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.

Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system

NASA Astrophysics Data System (ADS)

Banerjee, Tanmoy; Paul, Bishwajit; Sarkar, B. C.

2014-03-01

We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.

Investigation about relationships between the symmetries of ferroelectric crystal Ca{sub 0.28}Ba{sub 0.72}Nb{sub 2}O{sub 6} and second-harmonic patterns

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

Xu, Tianxiang; Yu, Haohai, E-mail: haohaiyu@sdu.edu.cn; Zhang, Huaijin, E-mail: huaijinzhang@sdu.edu.cn

2015-08-07

The broadband quasi-phase matching (QPM) process in a uniaxial ferroelectric crystal Ca{sub 0.28}Ba{sub 0.72}Nb{sub 2}O{sub 6} (CBN-28) was demonstrated with the second-harmonic wavelength range from 450 nm to 650 nm, and the relationship between the symmetries of CBN-28 and the second-harmonic patterns was experimentally and theoretically investigated based on the random anti-parallel domains in the crystal and QPM conditions. The dependences of frequency-doubled patterns on the wavelength and anisotropy of the nonlinear crystal were also studied, and the frequency-doubled photons were found to be trapped on circles. By analyzing the light-matter interacting Hamiltonians, the trapping force for second-harmonic photons was found tomore » be centripetal and tunable by the fundamental lasers, and the variation tendencies of the rotational velocity of second-harmonic generation photons could also be predicated. The results indicate that the CBN-28 ferroelectric crystal is a promising nonlinear optical material for the generation of broadband frequency-doubled waves, and the analysis on centripetal force based on the interaction Hamiltonians may provide a novel recognition for the investigation of QPM process to be further studied.« less

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

Variational algorithms for nonlinear smoothing applications

NASA Technical Reports Server (NTRS)

Bach, R. E., Jr.

1977-01-01

A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.

Probing Atomic Dynamics and Structures Using Optical Patterns

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie L.; Gauthier, Daniel J.

2015-05-01

Pattern formation is a widely studied phenomenon that can provide fundamental insights into nonlinear systems. Emergent patterns in cold atoms are of particular interest in condensed matter physics and quantum information science because one can relate optical patterns to spatial structures in the atoms. In our experimental system, we study multimode optical patterns generated from a sample of cold, thermal atoms. We observe this nonlinear optical phenomenon at record low input powers due to the highly nonlinear nature of the spatial bunching of atoms in an optical lattice. We present a detailed study of the dynamics of these bunched atoms during optical pattern formation. We show how small changes in the atomic density distribution affect the symmetry of the generated patterns as well as the nature of the nonlinearity that describes the light-atom interaction. We gratefully acknowledge the financial support of the National Science Foundation through Grant #PHY-1206040.

Bursting as a source of non-linear determinism in the firing patterns of nigral dopamine neurons.

PubMed

Jeong, Jaeseung; Shi, Wei-Xing; Hoffman, Ralph; Oh, Jihoon; Gore, John C; Bunney, Benjamin S; Peterson, Bradley S

2012-11-01

Nigral dopamine (DA) neurons in vivo exhibit complex firing patterns consisting of tonic single-spikes and phasic bursts that encode information for certain types of reward-related learning and behavior. Non-linear dynamical analysis has previously demonstrated the presence of a non-linear deterministic structure in complex firing patterns of DA neurons, yet the origin of this non-linear determinism remains unknown. In this study, we hypothesized that bursting activity is the primary source of non-linear determinism in the firing patterns of DA neurons. To test this hypothesis, we investigated the dimension complexity of inter-spike interval data recorded in vivo from bursting and non-bursting DA neurons in the chloral hydrate-anesthetized rat substantia nigra. We found that bursting DA neurons exhibited non-linear determinism in their firing patterns, whereas non-bursting DA neurons showed truly stochastic firing patterns. Determinism was also detected in the isolated burst and inter-burst interval data extracted from firing patterns of bursting neurons. Moreover, less bursting DA neurons in halothane-anesthetized rats exhibited higher dimensional spiking dynamics than do more bursting DA neurons in chloral hydrate-anesthetized rats. These results strongly indicate that bursting activity is the main source of low-dimensional, non-linear determinism in the firing patterns of DA neurons. This finding furthermore suggests that bursts are the likely carriers of meaningful information in the firing activities of DA neurons. © 2012 The Authors. European Journal of Neuroscience © 2012 Federation of European Neuroscience Societies and Blackwell Publishing Ltd.

A system of nonlinear set valued variational inclusions.

PubMed

Tang, Yong-Kun; Chang, Shih-Sen; Salahuddin, Salahuddin

2014-01-01

In this paper, we studied the existence theorems and techniques for finding the solutions of a system of nonlinear set valued variational inclusions in Hilbert spaces. To overcome the difficulties, due to the presence of a proper convex lower semicontinuous function ϕ and a mapping g which appeared in the considered problems, we have used the resolvent operator technique to suggest an iterative algorithm to compute approximate solutions of the system of nonlinear set valued variational inclusions. The convergence of the iterative sequences generated by algorithm is also proved. 49J40; 47H06.

Numerical realization of the variational method for generating self-trapped beams.

PubMed

Duque, Erick I; Lopez-Aguayo, Servando; Malomed, Boris A

2018-03-19

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational approximation in performing analytical Lagrangian integration and differentiation. Approximate soliton solutions of a generalized nonlinear Schrödinger equation are obtained, demonstrating robustness of the beams of various types (fundamental, vortices, multipoles, azimuthons) in the course of their propagation. The algorithm offers possibilities to produce more sophisticated soliton profiles in general nonlinear models.

Damage detection methodology under variable load conditions based on strain field pattern recognition using FBGs, nonlinear principal component analysis, and clustering techniques

NASA Astrophysics Data System (ADS)

Sierra-Pérez, Julián; Torres-Arredondo, M.-A.; Alvarez-Montoya, Joham

2018-01-01

Structural health monitoring consists of using sensors integrated within structures together with algorithms to perform load monitoring, damage detection, damage location, damage size and severity, and prognosis. One possibility is to use strain sensors to infer structural integrity by comparing patterns in the strain field between the pristine and damaged conditions. In previous works, the authors have demonstrated that it is possible to detect small defects based on strain field pattern recognition by using robust machine learning techniques. They have focused on methodologies based on principal component analysis (PCA) and on the development of several unfolding and standardization techniques, which allow dealing with multiple load conditions. However, before a real implementation of this approach in engineering structures, changes in the strain field due to conditions different from damage occurrence need to be isolated. Since load conditions may vary in most engineering structures and promote significant changes in the strain field, it is necessary to implement novel techniques for uncoupling such changes from those produced by damage occurrence. A damage detection methodology based on optimal baseline selection (OBS) by means of clustering techniques is presented. The methodology includes the use of hierarchical nonlinear PCA as a nonlinear modeling technique in conjunction with Q and nonlinear-T 2 damage indices. The methodology is experimentally validated using strain measurements obtained by 32 fiber Bragg grating sensors bonded to an aluminum beam under dynamic bending loads and simultaneously submitted to variations in its pitch angle. The results demonstrated the capability of the methodology for clustering data according to 13 different load conditions (pitch angles), performing the OBS and detecting six different damages induced in a cumulative way. The proposed methodology showed a true positive rate of 100% and a false positive rate of 1.28% for a 99% of confidence.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Impact of meteorological factors on the spatiotemporal patterns of dengue fever incidence.

PubMed

Chien, Lung-Chang; Yu, Hwa-Lung

2014-12-01

Dengue fever is one of the most widespread vector-borne diseases and has caused more than 50 million infections annually over the world. For the purposes of disease prevention and climate change health impact assessment, it is crucial to understand the weather-disease associations for dengue fever. This study investigated the nonlinear delayed impact of meteorological conditions on the spatiotemporal variations of dengue fever in southern Taiwan during 1998-2011. We present a novel integration of a distributed lag nonlinear model and Markov random fields to assess the nonlinear lagged effects of weather variables on temporal dynamics of dengue fever and to account for the geographical heterogeneity. This study identified the most significant meteorological measures to dengue fever variations, i.e., weekly minimum temperature, and the weekly maximum 24-hour rainfall, by obtaining the relative risk (RR) with respect to disease counts and a continuous 20-week lagged time. Results show that RR increased as minimum temperature increased, especially for the lagged period 5-18 weeks, and also suggest that the time to high disease risks can be decreased. Once the occurrence of maximum 24-hour rainfall is >50 mm, an associated increased RR lasted for up to 15 weeks. A temporary one-month decrease in the RR of dengue fever is noted following the extreme rain. In addition, the elevated incidence risk is identified in highly populated areas. Our results highlight the high nonlinearity of temporal lagged effects and magnitudes of temperature and rainfall on dengue fever epidemics. The results can be a practical reference for the early warning of dengue fever. Copyright © 2014 Elsevier Ltd. All rights reserved.

Nonlinear Pattern Selection in Bi-Modal Interfacial Instabilities

NASA Astrophysics Data System (ADS)

Picardo, Jason; Narayanan, Ranga

2016-11-01

We study the evolution of two interacting unstable interfaces, with the aim of understanding the role of non-linearity in pattern selection. Specifically, we consider two superposed thin films on a heated surface, that are susceptible to thermocapillary and Rayleigh-Taylor instabilities. Due to the presence of two unstable interfaces, the dispersion curve (linear growth rate plotted as a function of the perturbation wavelength) exhibits two peaks. If these peaks have equal heights, then the two corresponding disturbance patterns will grow with the same linear growth rate. Therefore, any selection between the two must occur via nonlinear effects. The two-interface problem under consideration provides a variety of such bi-modal situations, in which the role of nonlinearity in pattern selection is unveiled. We use a combination of long wave asymptotics, numerical simulations and amplitude expansions to understand the subtle nonlinear interactions between the two peak modes. Our results offer a counter-example to Rayleigh's principle of pattern formation, that the fastest growing linear mode will dominate the final pattern. Far from being governed by any such general dogma, the final selected pattern varies considerably from case to case. The authors acknowledge funding from NSF (0968313) and the Fulbright-Nehru fellowship.

Convenient total variation diminishing conditions for nonlinear difference schemes

NASA Technical Reports Server (NTRS)

Tadmor, Eitan

1986-01-01

Convenient conditions for nonlinear difference schemes to be total-variation diminishing (TVD) are reviewed. It is shown that such schemes share the TVD property, provided their numerical fluxes meet a certain positivity condition at extrema values but can be arbitrary otherwise. The conditions are invariant under different incremental representations of the nonlinear schemes, and thus provide a simplified generalization of the TVD conditions due to Harten and others.

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

NASA Astrophysics Data System (ADS)

Gholami, Raheb; Ansari, Reza

2018-02-01

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

Fully localized post-buckling states of cylindrical shells under axial compression

NASA Astrophysics Data System (ADS)

Kreilos, Tobias; Schneider, Tobias M.

2017-09-01

We compute nonlinear force equilibrium solutions for a clamped thin cylindrical shell under axial compression. The equilibrium solutions are dynamically unstable and located on the stability boundary of the unbuckled state. A fully localized single dimple deformation is identified as the edge state-the attractor for the dynamics restricted to the stability boundary. Under variation of the axial load, the single dimple undergoes homoclinic snaking in the azimuthal direction, creating states with multiple dimples arranged around the central circumference. Once the circumference is completely filled with a ring of dimples, snaking in the axial direction leads to further growth of the dimple pattern. These fully nonlinear solutions embedded in the stability boundary of the unbuckled state constitute critical shape deformations. The solutions may thus be a step towards explaining when the buckling and subsequent collapse of an axially loaded cylinder shell is triggered.

Using polynomials to simplify fixed pattern noise and photometric correction of logarithmic CMOS image sensors.

PubMed

Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan

2015-10-16

An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient.

The temporal patterns of disease severity and prevalence in schistosomiasis

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

Ciddio, Manuela; Gatto, Marino, E-mail: marino.gatto@polimi.it; Casagrandi, Renato, E-mail: renato.casagrandi@polimi.it

2015-03-15

Schistosomiasis is one of the most widespread public health problems in the world. In this work, we introduce an eco-epidemiological model for its transmission and dynamics with the purpose of explaining both intra- and inter-annual fluctuations of disease severity and prevalence. The model takes the form of a system of nonlinear differential equations that incorporate biological complexity associated with schistosome's life cycle, including a prepatent period in snails (i.e., the time between initial infection and onset of infectiousness). Nonlinear analysis is used to explore the parametric conditions that produce different temporal patterns (stationary, endemic, periodic, and chaotic). For the time-invariantmore » model, we identify a transcritical and a Hopf bifurcation in the space of the human and snail infection parameters. The first corresponds to the occurrence of an endemic equilibrium, while the latter marks the transition to interannual periodic oscillations. We then investigate a more realistic time-varying model in which fertility of the intermediate host population is assumed to seasonally vary. We show that seasonality can give rise to a cascade of period-doubling bifurcations leading to chaos for larger, though realistic, values of the amplitude of the seasonal variation of fertility.« less

The temporal patterns of disease severity and prevalence in schistosomiasis

NASA Astrophysics Data System (ADS)

Ciddio, Manuela; Mari, Lorenzo; Gatto, Marino; Rinaldo, Andrea; Casagrandi, Renato

2015-03-01

Schistosomiasis is one of the most widespread public health problems in the world. In this work, we introduce an eco-epidemiological model for its transmission and dynamics with the purpose of explaining both intra- and inter-annual fluctuations of disease severity and prevalence. The model takes the form of a system of nonlinear differential equations that incorporate biological complexity associated with schistosome's life cycle, including a prepatent period in snails (i.e., the time between initial infection and onset of infectiousness). Nonlinear analysis is used to explore the parametric conditions that produce different temporal patterns (stationary, endemic, periodic, and chaotic). For the time-invariant model, we identify a transcritical and a Hopf bifurcation in the space of the human and snail infection parameters. The first corresponds to the occurrence of an endemic equilibrium, while the latter marks the transition to interannual periodic oscillations. We then investigate a more realistic time-varying model in which fertility of the intermediate host population is assumed to seasonally vary. We show that seasonality can give rise to a cascade of period-doubling bifurcations leading to chaos for larger, though realistic, values of the amplitude of the seasonal variation of fertility.

Automated diagnosis of autism: in search of a mathematical marker.

PubMed

Bhat, Shreya; Acharya, U Rajendra; Adeli, Hojjat; Bairy, G Muralidhar; Adeli, Amir

2014-01-01

Autism is a type of neurodevelopmental disorder affecting the memory, behavior, emotion, learning ability, and communication of an individual. An early detection of the abnormality, due to irregular processing in the brain, can be achieved using electroencephalograms (EEG). The variations in the EEG signals cannot be deciphered by mere visual inspection. Computer-aided diagnostic tools can be used to recognize the subtle and invisible information present in the irregular EEG pattern and diagnose autism. This paper presents a state-of-the-art review of automated EEG-based diagnosis of autism. Various time domain, frequency domain, time-frequency domain, and nonlinear dynamics for the analysis of autistic EEG signals are described briefly. A focus of the review is the use of nonlinear dynamics and chaos theory to discover the mathematical biomarkers for the diagnosis of the autism analogous to biological markers. A combination of the time-frequency and nonlinear dynamic analysis is the most effective approach to characterize the nonstationary and chaotic physiological signals for the automated EEG-based diagnosis of autism spectrum disorder (ASD). The features extracted using these nonlinear methods can be used as mathematical markers to detect the early stage of autism and aid the clinicians in their diagnosis. This will expedite the administration of appropriate therapies to treat the disorder.

Pattern Driven Stress Localization

NASA Astrophysics Data System (ADS)

Croll, Andrew; Crosby, Alfred

2010-03-01

The self-assembly of patterns from isotropic initial states is a major driver of modern soft-matter research. This avenue of study is directed by the desire to understand the complex physics of the varied structures found in Nature, and by technological interest in functional materials that may be derived through biomimicry. In this work we show how a simple striped phase can respond with significant complexity to an appropriately chosen perturbation. In particular, we show how a buckled elastic plate transitions into a state of stress localization using a simple, self-assembled variation in surface topography. The collection of topographic boundaries act in concert to change the state from isotropic sinusoidal wrinkles, to sharp folds or creases separated by relatively flat regions. By varying the size of the imposed topographic pattern or the wavelength of the wrinkles, we construct a state diagram of the system. The localized state has implications for both biological systems, and for the control of non-linear pattern formation.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

Influence of electrode width of interdigital transducer on third-order nonlinearity of surface acoustic wave devices on 42°YX-LiTaO3 substrate

NASA Astrophysics Data System (ADS)

Nakagawa, Ryo; Hashimoto, Ken-ya

2018-07-01

In this paper, we discuss the influence of the electrode width of an interdigital transducer on the third-order nonlinearity of surface acoustic wave (SAW) devices. First, an estimation technique of third-order nonlinear signals based on the linear finite element method is proposed, and the variation of nonlinear signal level with electrode width is estimated. Then, several one-port SAW resonators with different electrode widths are fabricated, and measured nonlinear signal levels are compared with simulation. As predicted by the numerical simulation, nonlinear signal levels became large with electrode width. However, harmonics takes a minimum at a certain electrode width. This tendency disagrees with the simulation. The variation of nonlinear coefficients is evaluated by numerical fitting for the measured data using the nonlinear signal simulator proposed by the authors. As the result, it is concluded that the generation mechanism is not limited to the acoustic strain in electrodes.

Modeling Systematicity and Individuality in Nonlinear Second Language Development: The Case of English Grammatical Morphemes

ERIC Educational Resources Information Center

Murakami, Akira

2016-01-01

This article introduces two sophisticated statistical modeling techniques that allow researchers to analyze systematicity, individual variation, and nonlinearity in second language (L2) development. Generalized linear mixed-effects models can be used to quantify individual variation and examine systematic effects simultaneously, and generalized…

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Face-selective regions show invariance to linear, but not to non-linear, changes in facial images.

PubMed

Baseler, Heidi A; Young, Andrew W; Jenkins, Rob; Mike Burton, A; Andrews, Timothy J

2016-12-01

Familiar face recognition is remarkably invariant across huge image differences, yet little is understood concerning how image-invariant recognition is achieved. To investigate the neural correlates of invariance, we localized the core face-responsive regions and then compared the pattern of fMR-adaptation to different stimulus transformations in each region to behavioural data demonstrating the impact of the same transformations on familiar face recognition. In Experiment 1, we compared linear transformations of size and aspect ratio to a non-linear transformation affecting only part of the face. We found that adaptation to facial identity in face-selective regions showed invariance to linear changes, but there was no invariance to non-linear changes. In Experiment 2, we measured the sensitivity to non-linear changes that fell within the normal range of variation across face images. We found no adaptation to facial identity for any of the non-linear changes in the image, including to faces that varied in different levels of caricature. These results show a compelling difference in the sensitivity to linear compared to non-linear image changes in face-selective regions of the human brain that is only partially consistent with their effect on behavioural judgements of identity. We conclude that while regions such as the FFA may well be involved in the recognition of face identity, they are more likely to contribute to some form of normalisation that underpins subsequent recognition than to form the neural substrate of recognition per se. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stochastic nonlinear dynamics pattern formation and growth models

PubMed Central

Yaroslavsky, Leonid P

2007-01-01

Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing units. A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature. PMID:17908341

Homogenized description and retrieval method of nonlinear metasurfaces

NASA Astrophysics Data System (ADS)

Liu, Xiaojun; Larouche, Stéphane; Smith, David R.

2018-03-01

A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry and material composition, across the electromagnetic spectrum.

Using missing ordinal patterns to detect nonlinearity in time series data.

PubMed

Kulp, Christopher W; Zunino, Luciano; Osborne, Thomas; Zawadzki, Brianna

2017-08-01

The number of missing ordinal patterns (NMP) is the number of ordinal patterns that do not appear in a series after it has been symbolized using the Bandt and Pompe methodology. In this paper, the NMP is demonstrated as a test for nonlinearity using a surrogate framework in order to see if the NMP for a series is statistically different from the NMP of iterative amplitude adjusted Fourier transform (IAAFT) surrogates. It is found that the NMP works well as a test statistic for nonlinearity, even in the cases of very short time series. Both model and experimental time series are used to demonstrate the efficacy of the NMP as a test for nonlinearity.

Pattern Formations for Optical Switching Using Cold Atoms as a Nonlinear Medium

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie; Greenberg, Joel; Gauthier, Daniel

2011-05-01

The study of spatio-temporal pattern formation in nonlinear optical systems has both led to an increased understanding of nonlinear dynamics as well as given rise to sensitive new methods for all-optical switching. Whereas the majority of past experiments utilized warm atomic vapors as nonlinear media, we report the first observation of an optical instability leading to pattern formation in a cloud of cold Rubidium atoms. When we shine a pair of counterpropagating pump laser beams along the pencil-shaped cloud's long axis, new beams of light are generated along cones centered on the trap. This generated light produces petal-like patterns in the plane orthogonal to the pump beams that can be used for optical switching. We gratefully acknowledge the financial support of the NSF through Grant #PHY-0855399 and the DARPA Slow Light Program.

Nonlinear Field Equations and Solitons as Particles

NASA Astrophysics Data System (ADS)

Maccari, Attilio

2006-05-01

Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear field theories admit the existence of coherent solutions (dromions, solitons and so on). Moreover, one can construct lower dimensional chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution. We discuss in some detail a nonlinear Dirac field and a spontaneous symmetry breaking model that are reduced by means of the asymptotic perturbation method to a system of nonlinear evolution equations integrable via an appropriate change of variables. Their coherent, chaotic and fractal solutions are examined in some detail. Finally, we consider the possible identification of some types of coherent solutions with extended particles along the de Broglie-Bohm theory. However, the last findings suggest an inadequacy of the particle concept that appears only as a particular case of nonlinear field theories excitations.

Nonlinear channel equalization for QAM signal constellation using artificial neural networks.

PubMed

Patra, J C; Pal, R N; Baliarsingh, R; Panda, G

1999-01-01

Application of artificial neural networks (ANN's) to adaptive channel equalization in a digital communication system with 4-QAM signal constellation is reported in this paper. A novel computationally efficient single layer functional link ANN (FLANN) is proposed for this purpose. This network has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomials. Because of input pattern enhancement, the FLANN is capable of forming arbitrarily nonlinear decision boundaries and can perform complex pattern classification tasks. Considering channel equalization as a nonlinear classification problem, the FLANN has been utilized for nonlinear channel equalization. The performance of the FLANN is compared with two other ANN structures [a multilayer perceptron (MLP) and a polynomial perceptron network (PPN)] along with a conventional linear LMS-based equalizer for different linear and nonlinear channel models. The effect of eigenvalue ratio (EVR) of input correlation matrix on the equalizer performance has been studied. The comparison of computational complexity involved for the three ANN structures is also provided.

Understanding tree growth responses after partial cuttings: A new approach

PubMed Central

Rossi, Sergio; Lussier, Jean-Martin; Walsh, Denis; Morin, Hubert

2017-01-01

Forest ecosystem management heads towards the use of partial cuttings. However, the wide variation in growth response of residual trees remains unexplained, preventing a suitable prediction of forest productivity. The aim of the study was to assess individual growth and identify the driving factors involved in the responses of residual trees. Six study blocks in even-aged black spruce [Picea mariana (Mill.) B.S.P.] stands of the eastern Canadian boreal forest were submitted to experimental shelterwood and seed-tree treatments. Individual-tree models were applied to 1039 trees to analyze their patterns of radial growth during the 10 years after partial cutting by using the nonlinear Schnute function on tree-ring series. The trees exhibited different growth patterns. A sigmoid growth was detected in 32% of trees, mainly in control plots of older stands. Forty-seven percent of trees located in the interior of residual strips showed an S-shape, which was influenced by stand mortality, harvested intensity and dominant height. Individuals showing an exponential pattern produced the greatest radial growth after cutting and were edge trees of younger stands with higher dominant height. A steady growth decline was observed in 4% of trees, represented by the individuals suppressed and insensitive to the treatment. The analyses demonstrated that individual nonlinear models are able to assess the variability in growth within the stand and the factors involved in the occurrence of the different growth patterns, thus improving understanding of the tree responses to partial cutting. This new approach can sustain forest management strategies by defining the best conditions to optimize the growth yield of residual trees. PMID:28222200

Understanding tree growth responses after partial cuttings: A new approach.

PubMed

Montoro Girona, Miguel; Rossi, Sergio; Lussier, Jean-Martin; Walsh, Denis; Morin, Hubert

2017-01-01

Forest ecosystem management heads towards the use of partial cuttings. However, the wide variation in growth response of residual trees remains unexplained, preventing a suitable prediction of forest productivity. The aim of the study was to assess individual growth and identify the driving factors involved in the responses of residual trees. Six study blocks in even-aged black spruce [Picea mariana (Mill.) B.S.P.] stands of the eastern Canadian boreal forest were submitted to experimental shelterwood and seed-tree treatments. Individual-tree models were applied to 1039 trees to analyze their patterns of radial growth during the 10 years after partial cutting by using the nonlinear Schnute function on tree-ring series. The trees exhibited different growth patterns. A sigmoid growth was detected in 32% of trees, mainly in control plots of older stands. Forty-seven percent of trees located in the interior of residual strips showed an S-shape, which was influenced by stand mortality, harvested intensity and dominant height. Individuals showing an exponential pattern produced the greatest radial growth after cutting and were edge trees of younger stands with higher dominant height. A steady growth decline was observed in 4% of trees, represented by the individuals suppressed and insensitive to the treatment. The analyses demonstrated that individual nonlinear models are able to assess the variability in growth within the stand and the factors involved in the occurrence of the different growth patterns, thus improving understanding of the tree responses to partial cutting. This new approach can sustain forest management strategies by defining the best conditions to optimize the growth yield of residual trees.

Nonlinear gamma correction via normed bicoherence minimization in optical fringe projection metrology

NASA Astrophysics Data System (ADS)

Kamagara, Abel; Wang, Xiangzhao; Li, Sikun

2018-03-01

We propose a method to compensate for the projector intensity nonlinearity induced by gamma effect in three-dimensional (3-D) fringe projection metrology by extending high-order spectra analysis and bispectral norm minimization to digital sinusoidal fringe pattern analysis. The bispectrum estimate allows extraction of vital signal information features such as spectral component correlation relationships in fringe pattern images. Our approach exploits the fact that gamma introduces high-order harmonic correlations in the affected fringe pattern image. Estimation and compensation of projector nonlinearity is realized by detecting and minimizing the normed bispectral coherence of these correlations. The proposed technique does not require calibration information and technical knowledge or specification of fringe projection unit. This is promising for developing a modular and calibration-invariant model for intensity nonlinear gamma compensation in digital fringe pattern projection profilometry. Experimental and numerical simulation results demonstrate this method to be efficient and effective in improving the phase measuring accuracies with phase-shifting fringe pattern projection profilometry.

The nature of violence: a multilevel analysis of gun use and victim injury in violent interpersonal encounters.

PubMed

Burgason, Kyle A; Thomas, Shaun A; Berthelot, Emily R

2014-02-01

A large number of studies have examined predictors of crime quantities yet considerably less attention has been directed toward exploring patterns in the nature or quality of violence within and across communities. The current study adds to the literature on qualitative variations in violence by assessing the incident and contextual-level predictors of offender gun use and physical injuries sustained by victims of robbery and aggravated assault. Specifically, we examine incident-level data from the National Incident Based Reporting System in conjunction with contextual-level data on the cities in which the incidents occurred. We use hierarchical linear and nonlinear modeling techniques to explore variations in predictors of offender gun use and extent of victim injury. Supporting cultural effects explicated by Anderson, results reveal certain individual-level predictors are conditioned by community characteristics.

Dynamical Signatures of Living Systems

NASA Technical Reports Server (NTRS)

Zak, M.

1999-01-01

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

On a variational approach to some parameter estimation problems

NASA Technical Reports Server (NTRS)

Banks, H. T.

1985-01-01

Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

Flow patterns and transition characteristics for steam condensation in silicon microchannels

NASA Astrophysics Data System (ADS)

Ma, Xuehu; Fan, Xiaoguang; Lan, Zhong; Hao, Tingting

2011-07-01

This study investigated the two-phase flow patterns and transition characteristics for steam condensation in silicon microchannels with different cross-sectional geometries. Novel experimental techniques were developed to determine the local heat transfer rate and steam quality by testing the temperature profile of a copper cooler. Flow regime maps for different microchannels during condensation were established in terms of steam mass flux and steam quality. Meanwhile, the correlation for the flow pattern transition was obtained using different geometrical and dimensionless parameters for steam condensation in microchannels. To better understand the flow mechanisms in microchannels, the condensation flow patterns, such as annular flow, droplet flow, injection flow and intermittent flow, were captured and analyzed. The local heat transfer rate showed the nonlinear variations along the axial direction during condensation. The experimental results indicate that the flow patterns and transition characteristics strongly depend on the geometries of microchannels. With the increasing steam mass flux and steam quality, the annular/droplet flow expands and spans over a larger region in the microchannels; otherwise the intermittent flow occupies the microchannels. The dimensionless fitting data also reveal that the effect of surface tension and vapor inertia dominates gravity and viscous force at the specified flow pattern transitional position.

Stationary variational estimates for the effective response and field fluctuations in nonlinear composites

NASA Astrophysics Data System (ADS)

Ponte Castañeda, Pedro

2016-11-01

This paper presents a variational method for estimating the effective constitutive response of composite materials with nonlinear constitutive behavior. The method is based on a stationary variational principle for the macroscopic potential in terms of the corresponding potential of a linear comparison composite (LCC) whose properties are the trial fields in the variational principle. When used in combination with estimates for the LCC that are exact to second order in the heterogeneity contrast, the resulting estimates for the nonlinear composite are also guaranteed to be exact to second-order in the contrast. In addition, the new method allows full optimization with respect to the properties of the LCC, leading to estimates that are fully stationary and exhibit no duality gaps. As a result, the effective response and field statistics of the nonlinear composite can be estimated directly from the appropriately optimized linear comparison composite. By way of illustration, the method is applied to a porous, isotropic, power-law material, and the results are found to compare favorably with earlier bounds and estimates. However, the basic ideas of the method are expected to work for broad classes of composites materials, whose effective response can be given appropriate variational representations, including more general elasto-plastic and soft hyperelastic composites and polycrystals.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Nonlinear flap-lag axial equations of a rotating beam

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Kvaternik, R. G.

1977-01-01

It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.

Using Polynomials to Simplify Fixed Pattern Noise and Photometric Correction of Logarithmic CMOS Image Sensors

PubMed Central

Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan

2015-01-01

An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient. PMID:26501287

[Effect of climate change on the fisheries conununity pattern in the overwintering ground of open waters of northern East China Sea].

PubMed

Liu, Zun-lei; Yuan, Xing-wei; Yang, Lin-lin; Yan, Li-ping; Tian, Yong-jun; Chen, Jia-hua

2015-03-01

Data sets of 26 fisheries target species from the fishery-depen-dent and fishery-independent surveys in the overwintering ground of open waters of northern East China Sea (OW-NECS), combined sea surface temperature (SST), were used to examine the links between diversity index, pattern of common variability and climate changes based on the principal component analysis (PCA) and generalized additive model (GAM). The results showed that the shift from a cold regime to a warm regime was detected in SST during the 1970s-2011 with step changes around 1982/ 1983. SST increased during the cold regime and the warm regime before 1998 (warming trend period, 1972-1998), and decreased during the warm regime after 1998 (cooling trend period, 1999-2011). Shannon diversity index was largely dependent on the filefish, which contributed up to 50% of the total production as a single species, with low diversity in the waters of the OW-NECS, during the late 1980s and early 1990s. Excluding the filefish, the diversity index linearly increased and decreased during 1972-1998 and 1999-2011, respectively. The variation pattern generally corresponds with the trend in water temperature, strongly suggesting the effect of the SST on the diversity. The first two components (PC1 and PC2) of PCA for target species, which accounted for 32.43% of the total variance, showed evident decadal variation patterns with a step change during 1992-1999 and inter-annual variability with short-period fluctuation, respectively. It seems that PC1 was associated with large scale climatic change, while PC2 was related to inter-annual oceanographic variability such as ENSO events. Linear fitting results showed winEOF1 had significant effect on PC1, and GAM analysis for PC1 showed that winter EOF1 (winEOF1) and summer EOF2 (sumEOF2) can explain 88.9% of the total variance. Nonlinear effect was also found between PC2 and win EOF1, indicating that the fish community structure, which had predominantly decadal/inter-annual variation patterns, was influenced by inter-annual variations in oceanographic conditions.

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

PubMed

Ling, Liming; Zhao, Li-Chen; Yang, Zhan-Ying; Guo, Boling

2017-08-01

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation. Furthermore, our results show that N-component coupled nonlinear Schrödinger systems may possess N different fundamental rogue wave patterns at most. These results can be extended to evaluate the type and number of fundamental rogue wave structure in other coupled nonlinear systems.

Inherent smoothness of intensity patterns for intensity modulated radiation therapy generated by simultaneous projection algorithms

NASA Astrophysics Data System (ADS)

Xiao, Ying; Michalski, Darek; Censor, Yair; Galvin, James M.

2004-07-01

The efficient delivery of intensity modulated radiation therapy (IMRT) depends on finding optimized beam intensity patterns that produce dose distributions, which meet given constraints for the tumour as well as any critical organs to be spared. Many optimization algorithms that are used for beamlet-based inverse planning are susceptible to large variations of neighbouring intensities. Accurately delivering an intensity pattern with a large number of extrema can prove impossible given the mechanical limitations of standard multileaf collimator (MLC) delivery systems. In this study, we apply Cimmino's simultaneous projection algorithm to the beamlet-based inverse planning problem, modelled mathematically as a system of linear inequalities. We show that using this method allows us to arrive at a smoother intensity pattern. Including nonlinear terms in the simultaneous projection algorithm to deal with dose-volume histogram (DVH) constraints does not compromise this property from our experimental observation. The smoothness properties are compared with those from other optimization algorithms which include simulated annealing and the gradient descent method. The simultaneous property of these algorithms is ideally suited to parallel computing technologies.

A living mesoscopic cellular automaton made of skin scales.

PubMed

Manukyan, Liana; Montandon, Sophie A; Fofonjka, Anamarija; Smirnov, Stanislav; Milinkovitch, Michel C

2017-04-12

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction-diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction-diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

A living mesoscopic cellular automaton made of skin scales

NASA Astrophysics Data System (ADS)

Manukyan, Liana; Montandon, Sophie A.; Fofonjka, Anamarija; Smirnov, Stanislav; Milinkovitch, Michel C.

2017-04-01

In vertebrates, skin colour patterns emerge from nonlinear dynamical microscopic systems of cell interactions. Here we show that in ocellated lizards a quasi-hexagonal lattice of skin scales, rather than individual chromatophore cells, establishes a green and black labyrinthine pattern of skin colour. We analysed time series of lizard scale colour dynamics over four years of their development and demonstrate that this pattern is produced by a cellular automaton (a grid of elements whose states are iterated according to a set of rules based on the states of neighbouring elements) that dynamically computes the colour states of individual mesoscopic skin scales to produce the corresponding macroscopic colour pattern. Using numerical simulations and mathematical derivation, we identify how a discrete von Neumann cellular automaton emerges from a continuous Turing reaction-diffusion system. Skin thickness variation generated by three-dimensional morphogenesis of skin scales causes the underlying reaction-diffusion dynamics to separate into microscopic and mesoscopic spatial scales, the latter generating a cellular automaton. Our study indicates that cellular automata are not merely abstract computational systems, but can directly correspond to processes generated by biological evolution.

Stokes waves revisited: Exact solutions in the asymptotic limit

NASA Astrophysics Data System (ADS)

Davies, Megan; Chattopadhyay, Amit K.

2016-03-01

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic "secular variation" in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n -ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Soliton interactions and the formation of solitonic patterns

NASA Astrophysics Data System (ADS)

Sears, Suzanne M.

From the stripes of a zebra, to the spirals of cream in a hot cup of coffee, we are surrounded by patterns in the natural world. But why are there patterns? Why drives their formation? In this thesis we study some of the diverse ways patterns can arise due to the interactions between solitary waves in nonlinear systems, sometimes starting from nothing more than random noise. What follows is a set of three studies. In the first, we show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution of a single input soliton. In the second study, we investigate pattern formation initiated by modulation instability in nonlinear partially coherent wave fronts and show that anisotropic noise and/or anisotropic correlation statistics can lead to ordered patterns such as grids and stripes. For the final study, we demonstrate the spontaneous clustering of solitons in partially coherent wavefronts during the final stages of pattern formation initiated by modulation instability and noise. Experimental observations are in agreement with theoretical predictions and are confirmed using numerical simulations.

A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation.

PubMed

Rajeswaran, Jeevanantham; Blackstone, Eugene H

2017-02-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.

Nonlinear Filtering Effects of Reservoirs on Flood Frequency Curves at the Regional Scale: RESERVOIRS FILTER FLOOD FREQUENCY CURVES

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

Wang, Wei; Li, Hong-Yi; Leung, L. Ruby

Anthropogenic activities, e.g., reservoir operation, may alter the characteristics of Flood Frequency Curve (FFC) and challenge the basic assumption of stationarity used in flood frequency analysis. This paper presents a combined data-modeling analysis of the nonlinear filtering effects of reservoirs on the FFCs over the contiguous United States. A dimensionless Reservoir Impact Index (RII), defined as the total upstream reservoir storage capacity normalized by the annual streamflow volume, is used to quantify reservoir regulation effects. Analyses are performed for 388 river stations with an average record length of 50 years. The first two moments of the FFC, mean annual maximummore » flood (MAF) and coefficient of variations (CV), are calculated for the pre- and post-dam periods and compared to elucidate the reservoir regulation effects as a function of RII. It is found that MAF generally decreases with increasing RII but stabilizes when RII exceeds a threshold value, and CV increases with RII until a threshold value beyond which CV decreases with RII. The processes underlying the nonlinear threshold behavior of MAF and CV are investigated using three reservoir models with different levels of complexity. All models capture the non-linear relationships of MAF and CV with RII, suggesting that the basic flood control function of reservoirs is key to the non-linear relationships. The relative roles of reservoir storage capacity, operation objectives, available storage prior to a flood event, and reservoir inflow pattern are systematically investigated. Our findings may help improve flood-risk assessment and mitigation in regulated river systems at the regional scale.« less

Improved physiologically based pharmacokinetic model for oral exposures to chromium in mice, rats, and humans to address temporal variation and sensitive populations.

PubMed

Kirman, C R; Suh, M; Proctor, D M; Hays, S M

2017-06-15

A physiologically based pharmacokinetic (PBPK) model for hexavalent chromium [Cr(VI)] in mice, rats, and humans developed previously (Kirman et al., 2012, 2013), was updated to reflect an improved understanding of the toxicokinetics of the gastrointestinal tract following oral exposures. Improvements were made to: (1) the reduction model, which describes the pH-dependent reduction of Cr(VI) to Cr(III) in the gastrointestinal tract under both fasted and fed states; (2) drinking water pattern simulations, to better describe dosimetry in rodents under the conditions of the NTP cancer bioassay; and (3) parameterize the model to characterize potentially sensitive human populations. Important species differences, sources of non-linear toxicokinetics, and human variation are identified and discussed within the context of human health risk assessment. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

Interface Technology for Geometrically Nonlinear Analysis of Multiple Connected Subdomains

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

1997-01-01

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

Use of forecasting signatures to help distinguish periodicity, randomness, and chaos in ripples and other spatial patterns

USGS Publications Warehouse

Rubin, D.M.

1992-01-01

Forecasting of one-dimensional time series previously has been used to help distinguish periodicity, chaos, and noise. This paper presents two-dimensional generalizations for making such distinctions for spatial patterns. The techniques are evaluated using synthetic spatial patterns and then are applied to a natural example: ripples formed in sand by blowing wind. Tests with the synthetic patterns demonstrate that the forecasting techniques can be applied to two-dimensional spatial patterns, with the same utility and limitations as when applied to one-dimensional time series. One limitation is that some combinations of periodicity and randomness exhibit forecasting signatures that mimic those of chaos. For example, sine waves distorted with correlated phase noise have forecasting errors that increase with forecasting distance, errors that, are minimized using nonlinear models at moderate embedding dimensions, and forecasting properties that differ significantly between the original and surrogates. Ripples formed in sand by flowing air or water typically vary in geometry from one to another, even when formed in a flow that is uniform on a large scale; each ripple modifies the local flow or sand-transport field, thereby influencing the geometry of the next ripple downcurrent. Spatial forecasting was used to evaluate the hypothesis that such a deterministic process - rather than randomness or quasiperiodicity - is responsible for the variation between successive ripples. This hypothesis is supported by a forecasting error that increases with forecasting distance, a greater accuracy of nonlinear relative to linear models, and significant differences between forecasts made with the original ripples and those made with surrogate patterns. Forecasting signatures cannot be used to distinguish ripple geometry from sine waves with correlated phase noise, but this kind of structure can be ruled out by two geometric properties of the ripples: Successive ripples are highly correlated in wavelength, and ripple crests display dislocations such as branchings and mergers. ?? 1992 American Institute of Physics.

Nonlinear compensation techniques for magnetic suspension systems. Ph.D. Thesis - MIT

NASA Technical Reports Server (NTRS)

Trumper, David L.

1991-01-01

In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation.

Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application.

PubMed

Sakai, Kenshi; Upadhyaya, Shrinivasa K; Andrade-Sanchez, Pedro; Sviridova, Nina V

2017-03-01

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Neural net diagnostics for VLSI test

NASA Technical Reports Server (NTRS)

Lin, T.; Tseng, H.; Wu, A.; Dogan, N.; Meador, J.

1990-01-01

This paper discusses the application of neural network pattern analysis algorithms to the IC fault diagnosis problem. A fault diagnostic is a decision rule combining what is known about an ideal circuit test response with information about how it is distorted by fabrication variations and measurement noise. The rule is used to detect fault existence in fabricated circuits using real test equipment. Traditional statistical techniques may be used to achieve this goal, but they can employ unrealistic a priori assumptions about measurement data. Our approach to this problem employs an adaptive pattern analysis technique based on feedforward neural networks. During training, a feedforward network automatically captures unknown sample distributions. This is important because distributions arising from the nonlinear effects of process variation can be more complex than is typically assumed. A feedforward network is also able to extract measurement features which contribute significantly to making a correct decision. Traditional feature extraction techniques employ matrix manipulations which can be particularly costly for large measurement vectors. In this paper we discuss a software system which we are developing that uses this approach. We also provide a simple example illustrating the use of the technique for fault detection in an operational amplifier.

Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

PubMed Central

Zeng, Caibin; Yang, Qigui; Cao, Junfei

2014-01-01

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dB H(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

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

PubMed

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

2013-12-01

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

Nonlinear ring resonator: spatial pattern generation

NASA Astrophysics Data System (ADS)

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

2000-03-01

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

Variability in winter climate and winter extremes reduces population growth of an alpine butterfly.

PubMed

Roland, Jens; Matter, Stephen F

2013-01-01

We examined the long-term, 15-year pattern of population change in a network of 21 Rocky Mountain populations of Parnassius smintheus butterflies in response to climatic variation. We found that winter values of the broadscale climate variable, the Pacific Decadal Oscillation (PDO) index, were a strong predictor of annual population growth, much more so than were endogenous biotic factors related to population density. The relationship between PDO and population growth was nonlinear. Populations declined in years with extreme winter PDO values, when there were either extremely warm or extremely cold sea surface temperatures in the eastern Pacific relative to that in the western Pacific. Results suggest that more variable winters, and more frequent extremely cold or warm winters, will result in more frequent decline of these populations, a pattern exacerbated by the trend for increasingly variable winters seen over the past century.

Robustness of magnetic and electric domains against charge carrier doping in multiferroic hexagonal ErMnO 3

DOE PAGES

Hassanpour, E.; Wegmayr, V.; Schaab, J.; ...

2016-04-12

We investigate the effect of chemical doping on the electric and magnetic domain pattern in multiferroic hexagonal ErMnO 3 . Hole- and electron doping are achieved through the growth of Er 1-x Ca x MnO 3 and Er 1-x Zr x MnO 3 single crystals, which allows for a controlled introduction of divalent and tetravalent ions, respectively. Using conductance measurements, piezoresponse force microscopy and nonlinear optics we study doping-related variations in the electronic transport and image the corrsponding ferroelectric and antiferromagnetic domains. We find that moderate doping levels allow for adjusting the electronic conduction properties of ErMnO 3 without destroyingmore » its characteristic domain patterns. Our findings demonstrate the feasibility of chemical doping for nonperturbative property-engineering of intrinsic domain states in this important class of multiferroics.« less

Case Studies of Water Vapor and Surface Liquid Water from AVIRIS Data Measured Over Denver, CO and Death Valley, CA

NASA Technical Reports Server (NTRS)

Gao, B.-C.; Kierein-Young, K. S.; Goetz, A. F. H.; Westwater, E. R.; Stankov, B. B.; Birkenheuer, D.

1991-01-01

High spatial resolution column atmospheric water vapor amounts and equivalent liquid water thicknesses of surface targets are retrieved from spectral data collected by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The retrievals are made using a nonlinear least squares curve fitting technique. Two case studies from AVIRIS data acquired over Denver-Platteville area, Colorado and over Death Valley, California are presented. The column water vapor values derived from AVIRIS data over the Denver-Platteville area are compared with those obtained from radiosondes, ground level upward-looking microwave radiometers, and geostationary satellite measurements. The column water vapor image shows spatial variation patterns related to the passage of a weather front system. The column water vapor amounts derived from AVIRIS data over Death Valley decrease with increasing surface elevation. The derived liquid water image clearly shows surface drainage patterns.

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…

A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation

PubMed Central

Rajeswaran, Jeevanantham; Blackstone, Eugene H.

2014-01-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830

Nonlinear dynamics of cortical responses to color in the human cVEP.

PubMed

Nunez, Valerie; Shapley, Robert M; Gordon, James

2017-09-01

The main finding of this paper is that the human visual cortex responds in a very nonlinear manner to the color contrast of pure color patterns. We examined human cortical responses to color checkerboard patterns at many color contrasts, measuring the chromatic visual evoked potential (cVEP) with a dense electrode array. Cortical topography of the cVEPs showed that they were localized near the posterior electrode at position Oz, indicating that the primary cortex (V1) was the major source of responses. The choice of fine spatial patterns as stimuli caused the cVEP response to be driven by double-opponent neurons in V1. The cVEP waveform revealed nonlinear color signal processing in the V1 cortex. The cVEP time-to-peak decreased and the waveform's shape was markedly narrower with increasing cone contrast. Comparison of the linear dynamics of retinal and lateral geniculate nucleus responses with the nonlinear dynamics of the cortical cVEP indicated that the nonlinear dynamics originated in the V1 cortex. The nature of the nonlinearity is a kind of automatic gain control that adjusts cortical dynamics to be faster when color contrast is greater.

Complexity, self-organisation and variation in behaviour in meandering rivers

NASA Astrophysics Data System (ADS)

Hooke, J. M.

2007-11-01

River meanders are natural features on the surface of Earth that present some degree of regularity of form. They range from being highly dynamic to being stable under present conditions. Conventional theory is that meanders develop to an equilibrium form which is related to discharge and sediment load. Other research has demonstrated that many highly active meanders exhibit a continuous evolution over time and a non-linearity in rate of development. Ideas of autogenesis and of self-organised criticality as being an explanation of some meander changes have been proposed. In this paper data from rivers around the world are examined for further evidence of autogenic, self-organised or non-linear behaviour through analysis of change in sinuosity over time for reaches and change in individual bend form, particularly bend curvature and bend elongation. Some examples do exhibit trends of increasing sinuosity over time and a few show limits from which large decreases occur. Several case studies show non-linearity of behaviour and increasing complexity of form. Other case studies, however, do not exhibit such trends. Phase space plots are used to help uncover emergent behaviour but show a variety of patterns. The example of a reach in which multiple cut-offs occurred is analysed for mechanisms of self-organisation of the planform and in the pool-riffle pattern. Riffles are more closely spaced and also more transient in the more rapidly changing and higher sinuosity parts of the channel. Hypothetical trajectories of different meander behaviour, including for bedrock meanders, are plotted but the challenge remains to uncover the conditions for occurrence and for divergence of tendencies to stability and instability. Identification of attractors and phase space of behaviour of different meandering systems offer the potential for application to sustainable channel management.

Complex systems and the technology of variability analysis

PubMed Central

Seely, Andrew JE; Macklem, Peter T

2004-01-01

Characteristic patterns of variation over time, namely rhythms, represent a defining feature of complex systems, one that is synonymous with life. Despite the intrinsic dynamic, interdependent and nonlinear relationships of their parts, complex biological systems exhibit robust systemic stability. Applied to critical care, it is the systemic properties of the host response to a physiological insult that manifest as health or illness and determine outcome in our patients. Variability analysis provides a novel technology with which to evaluate the overall properties of a complex system. This review highlights the means by which we scientifically measure variation, including analyses of overall variation (time domain analysis, frequency distribution, spectral power), frequency contribution (spectral analysis), scale invariant (fractal) behaviour (detrended fluctuation and power law analysis) and regularity (approximate and multiscale entropy). Each technique is presented with a definition, interpretation, clinical application, advantages, limitations and summary of its calculation. The ubiquitous association between altered variability and illness is highlighted, followed by an analysis of how variability analysis may significantly improve prognostication of severity of illness and guide therapeutic intervention in critically ill patients. PMID:15566580

Subalpine tree growth, climate, and increasing CO sub 2 : An assessment of recent growth trends. [Pinus balfouriana; P. murrayana; Juniperus occidentalis

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

Graumlich, L.J.

1991-02-01

Five tree-ring series from foxtail pine (Pinus balfouriana), lodgepole pine (P. murrayana), and western juniper (Juniperus occidentalis) collected in the Sierra Nevada, California, were analyzed to determine if the temporal and spatial patterns of recent growth were consistent with the hypothesized CO{sub 2}-induced growth enhancement. Specifically, the author addresses the following questions: (1) can growth trends be explained solely in terms of climatic variation; (2) are recent growth trends unusual with respect to long-term growth records While the results offer no support for the hypothesized CO{sub 2} fertilization effect, they do provide insights into the response of subalpine conifers tomore » climatic variation. Response surfaces demonstrate that precipitation during previous winter and temperature during the current summer interact in controlling growth and that the response can be nonlinear. Although maximum growth rates occur under conditions of high winter precipitation and warm summers for all three species, substantial species-to-species variation occurs in the response to these two variables.« less

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

NASA Technical Reports Server (NTRS)

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

2009-01-01

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

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

PubMed

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

2014-04-01

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

Analysis of nonlinear axial vibration of single-walled carbon nanotubes using Homotopy perturbation method

NASA Astrophysics Data System (ADS)

Fatahi-Vajari, A.; Azimzadeh, Z.

2018-05-01

This paper investigates the nonlinear axial vibration of single-walled carbon nanotubes (SWCNTs) based on Homotopy perturbation method (HPM). A second order partial differential equation that governs the nonlinear axial vibration for such nanotubes is derived using doublet mechanics (DM) theory. To obtain the nonlinear natural frequency in axial vibration mode, this nonlinear equation is solved using HPM. The influences of some commonly used boundary conditions, amplitude of vibration, changes in vibration modes and variations of the nanotubes geometrical parameters on the nonlinear axial vibration characteristics of SWCNTs are discussed. It was shown that unlike the linear one, the nonlinear natural frequency is dependent to maximum vibration amplitude. Increasing the maximum vibration amplitude decreases the natural frequency of vibration compared to the predictions of the linear models. However, with increase in tube length, the effect of the amplitude on the natural frequency decreases. It was also shown that the amount and variation of nonlinear natural frequency is more apparent in higher mode vibration and two clamped boundary conditions. To show the accuracy and capability of this method, the results obtained herein were compared with the fourth order Runge-Kuta numerical results and good agreement was observed. It is notable that the results generated herein are new and can be served as a benchmark for future works.

Nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

Chen, L; Wang, Q; Shen, M; Zhao, H; Lin, Y-Y; Jeng, C-C; Lee, R-K; Krolikowski, W

2013-01-01

We investigate properties of dark solitons under competing nonlocal cubic-local quintic nonlinearities. Analytical results, based on a variational approach and confirmed by direct numerical simulations, reveal the existence of a unique dark soliton solutions with their width being independent of the degree of nonlocality, due to the competing cubic-quintic nonlinearities.

Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

NASA Astrophysics Data System (ADS)

Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.

2018-03-01

We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p  >  0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.

Deep Independence Network Analysis of Structural Brain Imaging: Application to Schizophrenia

PubMed Central

Castro, Eduardo; Hjelm, R. Devon; Plis, Sergey M.; Dinh, Laurent; Turner, Jessica A.; Calhoun, Vince D.

2016-01-01

Linear independent component analysis (ICA) is a standard signal processing technique that has been extensively used on neuroimaging data to detect brain networks with coherent brain activity (functional MRI) or covarying structural patterns (structural MRI). However, its formulation assumes that the measured brain signals are generated by a linear mixture of the underlying brain networks and this assumption limits its ability to detect the inherent nonlinear nature of brain interactions. In this paper, we introduce nonlinear independent component estimation (NICE) to structural MRI data to detect abnormal patterns of gray matter concentration in schizophrenia patients. For this biomedical application, we further addressed the issue of model regularization of nonlinear ICA by performing dimensionality reduction prior to NICE, together with an appropriate control of the complexity of the model and the usage of a proper approximation of the probability distribution functions of the estimated components. We show that our results are consistent with previous findings in the literature, but we also demonstrate that the incorporation of nonlinear associations in the data enables the detection of spatial patterns that are not identified by linear ICA. Specifically, we show networks including basal ganglia, cerebellum and thalamus that show significant differences in patients versus controls, some of which show distinct nonlinear patterns. PMID:26891483

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

USGS Publications Warehouse

Mehl, S.

2006-01-01

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

NASA Astrophysics Data System (ADS)

Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

2018-04-01

The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

Interactions across spatial scales among forest dieback, fire, and erosion in northern New Mexico landscapes

USGS Publications Warehouse

Allen, Craig D.

2007-01-01

Ecosystem patterns and disturbance processes at one spatial scale often interact with processes at another scale, and the result of such cross-scale interactions can be nonlinear dynamics with thresholds. Examples of cross-scale pattern-process relationships and interactions among forest dieback, fire, and erosion are illustrated from northern New Mexico (USA) landscapes, where long-term studies have recently documented all of these disturbance processes. For example, environmental stress, operating on individual trees, can cause tree death that is amplified by insect mortality agents to propagate to patch and then landscape or even regional-scale forest dieback. Severe drought and unusual warmth in the southwestern USA since the late 1990s apparently exceeded species-specific physiological thresholds for multiple tree species, resulting in substantial vegetation mortality across millions of hectares of woodlands and forests in recent years. Predictions of forest dieback across spatial scales are constrained by uncertainties associated with: limited knowledge of species-specific physiological thresholds; individual and site-specific variation in these mortality thresholds; and positive feedback loops between rapidly-responding insect herbivore populations and their stressed plant hosts, sometimes resulting in nonlinear “pest” outbreak dynamics. Fire behavior also exhibits nonlinearities across spatial scales, illustrated by changes in historic fire regimes where patch-scale grazing disturbance led to regional-scale collapse of surface fire activity and subsequent recent increases in the scale of extreme fire events in New Mexico. Vegetation dieback interacts with fire activity by modifying fuel amounts and configurations at multiple spatial scales. Runoff and erosion processes are also subject to scale-dependent threshold behaviors, exemplified by ecohydrological work in semiarid New Mexico watersheds showing how declines in ground surface cover lead to non-linear increases in bare patch connectivity and thereby accelerated runoff and erosion at hillslope and watershed scales. Vegetation dieback, grazing, and fire can change land surface properties and cross-scale hydrologic connectivities, directly altering ecohydrological patterns of runoff and erosion. The interactions among disturbance processes across spatial scales can be key drivers in ecosystem dynamics, as illustrated by these studies of recent landscape changes in northern New Mexico. To better anticipate and mitigate accelerating human impacts to the planetary ecosystem at all spatial scales, improvements are needed in our conceptual and quantitative understanding of cross-scale interactions among disturbance processes.

Development of a computational model on the neural activity patterns of a visual working memory in a hierarchical feedforward Network

NASA Astrophysics Data System (ADS)

An, Soyoung; Choi, Woochul; Paik, Se-Bum

2015-11-01

Understanding the mechanism of information processing in the human brain remains a unique challenge because the nonlinear interactions between the neurons in the network are extremely complex and because controlling every relevant parameter during an experiment is difficult. Therefore, a simulation using simplified computational models may be an effective approach. In the present study, we developed a general model of neural networks that can simulate nonlinear activity patterns in the hierarchical structure of a neural network system. To test our model, we first examined whether our simulation could match the previously-observed nonlinear features of neural activity patterns. Next, we performed a psychophysics experiment for a simple visual working memory task to evaluate whether the model could predict the performance of human subjects. Our studies show that the model is capable of reproducing the relationship between memory load and performance and may contribute, in part, to our understanding of how the structure of neural circuits can determine the nonlinear neural activity patterns in the human brain.

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

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

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less

Climate-mediated spatiotemporal variability in the terrestrial productivity across Europe

NASA Astrophysics Data System (ADS)

Wu, X.; Mahecha, M. D.; Reichstein, M.; Ciais, P.; Wattenbach, M.; Babst, F.; Frank, D.; Zang, C.

2013-11-01

Quantifying the interannual variability (IAV) of the terrestrial productivity and its sensitivity to climate is crucial for improving carbon budget predictions. However, the influence of climate and other mechanisms underlying the spatiotemporal patterns of IAV of productivity are not well understood. In this study we investigated the spatiotemporal patterns of IAV of historical observations of crop yields, tree ring width, remote sensing retrievals of FAPAR and NDVI, and other variables relevant to the terrestrial productivity in Europe in tandem with a set of climate variables. Our results reveal distinct spatial patterns in the IAV of most variables linked to terrestrial productivity. In particular, we find higher IAV in water-limited regions of Europe (Mediterranean and temperate continental Europe) compared to other regions. Our results further indicate that variations in the water balance during active growing season exert a more pronounced and direct effect than variations of temperature on explaining the spatial patterns in IAV of productivity related variables in temperate Europe. We also observe a~temporally increasing trend in the IAV of terrestrial productivity and an increasing sensitivity of productivity to water availability in dry regions of Europe, which is likely attributable to the recently increased IAV of water availability in these regions. These findings suggest nonlinear responses of carbon fluxes to climate variability in Europe and that the IAV of terrestrial productivity has become more sensitive and more vulnerable to changes in water availability in the dry regions in Europe. The changing climate sensitivity of terrestrial productivity accompanied by the changing IAV of climate could impact carbon stocks and the net carbon balance of European ecosystems.

A stochastic-geometric model of soil variation in Pleistocene patterned ground

NASA Astrophysics Data System (ADS)

Lark, Murray; Meerschman, Eef; Van Meirvenne, Marc

2013-04-01

In this paper we examine the spatial variability of soil in parent material with complex spatial structure which arises from complex non-linear geomorphic processes. We show that this variability can be better-modelled by a stochastic-geometric model than by a standard Gaussian random field. The benefits of the new model are seen in the reproduction of features of the target variable which influence processes like water movement and pollutant dispersal. Complex non-linear processes in the soil give rise to properties with non-Gaussian distributions. Even under a transformation to approximate marginal normality, such variables may have a more complex spatial structure than the Gaussian random field model of geostatistics can accommodate. In particular the extent to which extreme values of the variable are connected in spatially coherent regions may be misrepresented. As a result, for example, geostatistical simulation generally fails to reproduce the pathways for preferential flow in an environment where coarse infill of former fluvial channels or coarse alluvium of braided streams creates pathways for rapid movement of water. Multiple point geostatistics has been developed to deal with this problem. Multiple point methods proceed by sampling from a set of training images which can be assumed to reproduce the non-Gaussian behaviour of the target variable. The challenge is to identify appropriate sources of such images. In this paper we consider a mode of soil variation in which the soil varies continuously, exhibiting short-range lateral trends induced by local effects of the factors of soil formation which vary across the region of interest in an unpredictable way. The trends in soil variation are therefore only apparent locally, and the soil variation at regional scale appears random. We propose a stochastic-geometric model for this mode of soil variation called the Continuous Local Trend (CLT) model. We consider a case study of soil formed in relict patterned ground with pronounced lateral textural variations arising from the presence of infilled ice-wedges of Pleistocene origin. We show how knowledge of the pedogenetic processes in this environment, along with some simple descriptive statistics, can be used to select and fit a CLT model for the apparent electrical conductivity (ECa) of the soil. We use the model to simulate realizations of the CLT process, and compare these with realizations of a fitted Gaussian random field. We show how statistics that summarize the spatial coherence of regions with small values of ECa, which are expected to have coarse texture and so larger saturated hydraulic conductivity, are better reproduced by the CLT model than by the Gaussian random field. This suggests that the CLT model could be used to generate an unlimited supply of training images to allow multiple point geostatistical simulation or prediction of this or similar variables.

Investigation of a Nonlinear Control System

NASA Technical Reports Server (NTRS)

Flugge-Lotz, I; Taylor, C F; Lindberg, H E

1958-01-01

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Self-modulational formation of pulsar microstructures

NASA Technical Reports Server (NTRS)

Kennel, C. F.; Chian, A. C.-L.

1987-01-01

A nonlinear plasma theory for self modulation of pulsar radio pulses is discussed. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron positron plasma. The nonlinearities arising from wave intensity induced particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary waveforms may account for the formation of pulsar microstructures.

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.

Interfacial patterns in magnetorheological fluids: Azimuthal field-induced structures.

PubMed

Dias, Eduardo O; Lira, Sérgio A; Miranda, José A

2015-08-01

Despite their practical and academic relevance, studies of interfacial pattern formation in confined magnetorheological (MR) fluids have been largely overlooked in the literature. In this work, we present a contribution to this soft matter research topic and investigate the emergence of interfacial instabilities when an inviscid, initially circular bubble of a Newtonian fluid is surrounded by a MR fluid in a Hele-Shaw cell apparatus. An externally applied, in-plane azimuthal magnetic field produced by a current-carrying wire induces interfacial disturbances at the two-fluid interface, and pattern-forming structures arise. Linear stability analysis, weakly nonlinear theory, and a vortex sheet approach are used to access early linear and intermediate nonlinear time regimes, as well as to determine stationary interfacial shapes at fully nonlinear stages.

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

NASA Astrophysics Data System (ADS)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

Thermodiffusion as a means to manipulate liquid film dynamics on chemically patterned surfaces

PubMed Central

Kalpathy, Sreeram K.; Shreyes, Amrita Ravi

2017-01-01

The model problem examined here is the stability of a thin liquid film consisting of two miscible components, resting on a chemically patterned solid substrate and heated from below. In addition to surface tension gradients, the temperature variations also induce gradients in the concentration of the film by virtue of thermodiffusion/Soret effects. We study the stability and dewetting behaviour due to the coupled interplay between thermal gradients, Soret effects, long-range van der Waals forces, and wettability gradient-driven flows. Linear stability analysis is first employed to predict growth rates and the critical Marangoni number for chemically homogeneous surfaces. Then, nonlinear simulations are performed to unravel the interfacial dynamics and possible locations of the film rupture on chemically patterned substrates. Results suggest that appropriate tuning of the Soret parameter and its direction, in conjunction with either heating or cooling, can help manipulate the location and time scales of the film rupture. The Soret effect can either potentially aid or oppose film instability depending on whether the thermal and solutal contributions to flow are cooperative or opposed to each other. PMID:28595391

Factoring in weather variation to capture the influence of urban design and built environment on globally recommended levels of moderate to vigorous physical activity in children

PubMed Central

Katapally, Tarun Reddy; Muhajarine, Nazeem

2015-01-01

Objectives In curbing physical inactivity, as behavioural interventions directed at individuals have not produced a population-level change, an ecological perspective called active living research has gained prominence. However, active living research consistently underexplores the role played by a perennial phenomenon encompassing all other environmental exposures—variation in weather. After factoring in weather variation, this study investigated the influence of diverse environmental exposures (including urban design and built environment) on the accumulation of globally recommended moderate to vigorous physical activity levels (MVPA) in children. Design This cross-sectional observational study is part of an active living initiative set in the Canadian prairie city of Saskatoon. As part of this study, Saskatoon's neighbourhoods were classified based on urban street design into grid-pattern, fractured grid-pattern and curvilinear types of neighbourhoods. Moreover, diverse environmental exposures were measured including, neighbourhood built environment, and neighbourhood and household socioeconomic environment. Actical accelerometers were deployed between April and June 2010 (spring-summer) to derive MVPA of 331 10–14-year-old children in 25 1-week cycles. Each cycle of accelerometry was conducted on a different cohort of children within the total sample and matched with weather data obtained from Environment Canada. Multilevel modelling using Hierarchical Linear and Non-linear Modelling software was conducted by factoring in weather variation to depict the influence of diverse environmental exposures on the accumulation of recommended MVPA. Results Urban design, including diversity of destinations within neighbourhoods played a significant role in the accumulation of MVPA. After factoring in weather variation, it was observed that children living in neighbourhoods closer to the city centre (with higher diversity of destinations) were more likely to accumulate recommended MVPA. Conclusions The findings indicate that after factoring in weather variation, certain types of urban design are more likely to be associated with MVPA accumulation. PMID:26621516

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

Single-shot measurement of nonlinear absorption and nonlinear refraction.

PubMed

Jayabalan, J; Singh, Asha; Oak, Shrikant M

2006-06-01

A single-shot method for measurement of nonlinear optical absorption and refraction is described and analyzed. A spatial intensity variation of an elliptical Gaussian beam in conjugation with an array detector is the key element of this method. The advantages of this single-shot technique were demonstrated by measuring the two-photon absorption and free-carrier absorption in GaAs as well as the nonlinear refractive index of CS2 using a modified optical Kerr setup.

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

PubMed

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

2018-03-01

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

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

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

Measuring nonlinear signal combination using EEG.

PubMed

Cunningham, Darren G M; Baker, Daniel H; Peirce, Jonathan W

2017-05-01

Relatively little is known about the processes, both linear and nonlinear, by which signals are combined beyond V1. By presenting two stimulus components simultaneously, flickering at different temporal frequencies (frequency tagging) while measuring steady-state visual evoked potentials, we can assess responses to the individual components, including direct measurements of suppression on each other, and various nonlinear responses to their combination found at intermodulation frequencies. The result is a rather rich dataset of frequencies at which responses can be found. We presented pairs of sinusoidal gratings at different temporal frequencies, forming plaid patterns that were "coherent" (looking like a checkerboard) and "noncoherent" (looking like a pair of transparently overlaid gratings), and found clear intermodulation responses to compound stimuli, indicating nonlinear summation. This might have been attributed to cross-orientation suppression except that the pattern of intermodulation responses differed for coherent and noncoherent patterns, whereas the effects of suppression (measured at the component frequencies) did not. A two-stage model of nonlinear summation involving conjunction detection with a logical AND gate described the data well, capturing the difference between coherent and noncoherent plaids over a wide array of possible response frequencies. Multistimulus frequency-tagged EEG in combination with computational modeling may be a very valuable tool in studying the conjunction of these signals. In the current study the results suggest a second-order mechanism responding selectively to coherent plaid patterns.

EMG patterns during assisted walking in the exoskeleton

PubMed Central

Sylos-Labini, Francesca; La Scaleia, Valentina; d'Avella, Andrea; Pisotta, Iolanda; Tamburella, Federica; Scivoletto, Giorgio; Molinari, Marco; Wang, Shiqian; Wang, Letian; van Asseldonk, Edwin; van der Kooij, Herman; Hoellinger, Thomas; Cheron, Guy; Thorsteinsson, Freygardur; Ilzkovitz, Michel; Gancet, Jeremi; Hauffe, Ralf; Zanov, Frank; Lacquaniti, Francesco; Ivanenko, Yuri P.

2014-01-01

Neuroprosthetic technology and robotic exoskeletons are being developed to facilitate stepping, reduce muscle efforts, and promote motor recovery. Nevertheless, the guidance forces of an exoskeleton may influence the sensory inputs, sensorimotor interactions and resulting muscle activity patterns during stepping. The aim of this study was to report the muscle activation patterns in a sample of intact and injured subjects while walking with a robotic exoskeleton and, in particular, to quantify the level of muscle activity during assisted gait. We recorded electromyographic (EMG) activity of different leg and arm muscles during overground walking in an exoskeleton in six healthy individuals and four spinal cord injury (SCI) participants. In SCI patients, EMG activity of the upper limb muscles was augmented while activation of leg muscles was typically small. Contrary to our expectations, however, in neurologically intact subjects, EMG activity of leg muscles was similar or even larger during exoskeleton-assisted walking compared to normal overground walking. In addition, significant variations in the EMG waveforms were found across different walking conditions. The most variable pattern was observed in the hamstring muscles. Overall, the results are consistent with a non-linear reorganization of the locomotor output when using the robotic stepping devices. The findings may contribute to our understanding of human-machine interactions and adaptation of locomotor activity patterns. PMID:24982628

EMG patterns during assisted walking in the exoskeleton.

PubMed

Sylos-Labini, Francesca; La Scaleia, Valentina; d'Avella, Andrea; Pisotta, Iolanda; Tamburella, Federica; Scivoletto, Giorgio; Molinari, Marco; Wang, Shiqian; Wang, Letian; van Asseldonk, Edwin; van der Kooij, Herman; Hoellinger, Thomas; Cheron, Guy; Thorsteinsson, Freygardur; Ilzkovitz, Michel; Gancet, Jeremi; Hauffe, Ralf; Zanov, Frank; Lacquaniti, Francesco; Ivanenko, Yuri P

2014-01-01

Neuroprosthetic technology and robotic exoskeletons are being developed to facilitate stepping, reduce muscle efforts, and promote motor recovery. Nevertheless, the guidance forces of an exoskeleton may influence the sensory inputs, sensorimotor interactions and resulting muscle activity patterns during stepping. The aim of this study was to report the muscle activation patterns in a sample of intact and injured subjects while walking with a robotic exoskeleton and, in particular, to quantify the level of muscle activity during assisted gait. We recorded electromyographic (EMG) activity of different leg and arm muscles during overground walking in an exoskeleton in six healthy individuals and four spinal cord injury (SCI) participants. In SCI patients, EMG activity of the upper limb muscles was augmented while activation of leg muscles was typically small. Contrary to our expectations, however, in neurologically intact subjects, EMG activity of leg muscles was similar or even larger during exoskeleton-assisted walking compared to normal overground walking. In addition, significant variations in the EMG waveforms were found across different walking conditions. The most variable pattern was observed in the hamstring muscles. Overall, the results are consistent with a non-linear reorganization of the locomotor output when using the robotic stepping devices. The findings may contribute to our understanding of human-machine interactions and adaptation of locomotor activity patterns.

Experimental investigation of acoustic streaming in a cylindrical wave guide up to high streaming Reynolds numbers.

PubMed

Reyt, Ida; Bailliet, Hélène; Valière, Jean-Christophe

2014-01-01

Measurements of streaming velocity are performed by means of Laser Doppler Velocimetry and Particle Image Velociimetry in an experimental apparatus consisting of a cylindrical waveguide having one loudspeaker at each end for high intensity sound levels. The case of high nonlinear Reynolds number ReNL is particularly investigated. The variation of axial streaming velocity with respect to the axial and to the transverse coordinates are compared to available Rayleigh streaming theory. As expected, the measured streaming velocity agrees well with the Rayleigh streaming theory for small ReNL but deviates significantly from such predictions for high ReNL. When the nonlinear Reynolds number is increased, the outer centerline axial streaming velocity gets distorted towards the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes. This kind of behavior is followed by outer streaming cells only and measurements in the near wall region show that inner streaming vortices are less affected by this substantial evolution of fast streaming pattern. Measurements of the transient evolution of streaming velocity provide an additional insight into the evolution of fast streaming.

Some optical properties of KTP, LiIO3, and LiNbO3

NASA Technical Reports Server (NTRS)

Gettemy, Donald J.; Harker, William C.; Lindholm, Glenn; Barnes, Norman P.

1988-01-01

Measurements of the absorption coefficient for KTP, LiIO3, and LiNbO3 are discussed. The variation of the refractive index with temperature has been measured for KTP and LiIO3. It is necessary to know both the absorption coefficient beta and the variation in the indexes of refraction with temperature change dn/dT to determine the average power limit of a nonlinear interaction. With the dn/dT information, it is also possible to estimate the temperature half width of any nonlinear interaction by calculating the variation of the phase-matching condition with temperature.

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity, solutions of the PDE converge strongly to weak solutions of the inviscid Burgers equation. We provide numerical evidence that this limit satisfies an entropy inequality for the inviscid Burgers equation. We demonstrate a Hamiltonian structure for the PDE.

Nonlinear electron transport mobility in asymmetric wide quantum well structure

NASA Astrophysics Data System (ADS)

Nayak, Rasmita K.; Das, Sudhakar; Panda, Ajit K.; Sahu, Trinath

2018-05-01

The nonlinearity of multisubband electron mobility µ in a GaAs/AlxGa1-xAs wide quantum well structure is studied by varying the well width w and doping concentration Nd b (Nd t ) lying in the bottom (top) barrier. The electrons diffuse into the well and accumulate near the interfaces forming two sheets of coupled two dimensional electron gases equivalent to a double quantum well structure. We show that interchange of doping concentrations N db and N dt lead to the enhancement of µ as a function of w as long as N dt > N db , even though the surface electron density remains unaltered. Further, keeping Nd b unchanged, variation of Nd t leads to nonlinearity in µ near the resonance of subband states at Nd t = Nd b at which the subband energy levels exhibit anticrossing. The variation of µ becomes prominent by increasing the well width and resonant doping concentration. The nonlinearity in µ is mostly because of the change in the interface roughness scattering potential through intersubband effects due to the substantial changes in the distributions of the subband wave functions around resonance. Our results of nonmonotonic variation of µ can be utilized for low temperature coupled quantum well devices.

Annual ecosystem respiration variability of alpine peatland on the eastern Qinghai-Tibet Plateau and its controlling factors.

PubMed

Peng, Haijun; Hong, Bing; Hong, Yetang; Zhu, Yongxuan; Cai, Chen; Yuan, Lingui; Wang, Yu

2015-09-01

Peatlands are widely developed in the eastern Qinghai-Tibet Plateau, but little is known about carbon budgets for these alpine peatland ecosystems. In this study, we used an automatic chamber system to measure ecosystem respiration in the Hongyuan peatland, which is located in the eastern Qinghai-Tibet Plateau. Annual ecosystem respiration measurements showed a typical seasonal pattern, with the peak appearing in June. The highest respiration was 10.43 μmol CO2/m(2)/s, and the lowest was 0.20 μmol CO2/m(2)/s. The annual average ecosystem respiration was 2.06 μmol CO2/m(2)/s. The total annual respiration was 599.98 g C/m(2), and respiration during the growing season (from May to September) accounted for 78 % of the annual sum. Nonlinear regression revealed that ecosystem respiration has a significant exponential correlation with soil temperature at 10-cm depth (R (2) = 0.98). The Q 10 value was 3.90, which is far higher than the average Q 10 value of terrestrial ecosystems. Ecosystem respiration had an apparent diurnal variation pattern in growing season, with peaks and valleys appearing at approximately 14:00 and 10:00, respectively, which could be explained by soil temperature and soil water content variation at 10-cm depth.

Landscape genomics of Sphaeralcea ambigua in the Mojave Desert: a multivariate, spatially-explicit approach to guide ecological restoration

USGS Publications Warehouse

Shryock, Daniel F.; Havrilla, Caroline A.; DeFalco, Lesley; Esque, Todd C.; Custer, Nathan; Wood, Troy E.

2015-01-01

Local adaptation influences plant species’ responses to climate change and their performance in ecological restoration. Fine-scale physiological or phenological adaptations that direct demographic processes may drive intraspecific variability when baseline environmental conditions change. Landscape genomics characterize adaptive differentiation by identifying environmental drivers of adaptive genetic variability and mapping the associated landscape patterns. We applied such an approach to Sphaeralcea ambigua, an important restoration plant in the arid southwestern United States, by analyzing variation at 153 amplified fragment length polymorphism loci in the context of environmental gradients separating 47 Mojave Desert populations. We identified 37 potentially adaptive loci through a combination of genome scan approaches. We then used a generalized dissimilarity model (GDM) to relate variability in potentially adaptive loci with spatial gradients in temperature, precipitation, and topography. We identified non-linear thresholds in loci frequencies driven by summer maximum temperature and water stress, along with continuous variation corresponding to temperature seasonality. Two GDM-based approaches for mapping predicted patterns of local adaptation are compared. Additionally, we assess uncertainty in spatial interpolations through a novel spatial bootstrapping approach. Our study presents robust, accessible methods for deriving spatially-explicit models of adaptive genetic variability in non-model species that will inform climate change modelling and ecological restoration.

Simulations of temporal patterns of oral airflow in men and women using a two-mass model of the vocal folds under dynamic control

NASA Astrophysics Data System (ADS)

Lucero, Jorge C.; Koenig, Laura L.

2005-03-01

In this study we use a low-dimensional laryngeal model to reproduce temporal variations in oral airflow produced by speakers in the vicinity of an abduction gesture. It attempts to characterize these temporal patterns in terms of biomechanical parameters such as glottal area, vocal fold stiffness, subglottal pressure, and gender differences in laryngeal dimensions. A two-mass model of the vocal folds coupled to a two-tube approximation of the vocal tract is fitted to oral airflow records measured in men and women during the production of /aha/ utterances, using the subglottal pressure, glottal width, and Q factor as control parameters. The results show that the model is capable of reproducing the airflow records with good approximation. A nonlinear damping characteristics is needed, to reproduce the flow variation at glottal abduction. Devoicing is achieved by the combined action of vocal fold abduction, the decrease of subglottal pressure, and the increase of vocal fold tension. In general, the female larynx has a more restricted region of vocal fold oscillation than the male one. This would explain the more frequent devoicing in glottal abduction-adduction gestures for /h/ in running speech by women, compared to men. .

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

The effect of excitation intensity variation and silver nanoparticle codoping on nonlinear optical properties of mixed tellurite and zinc oxide glass doped with Nd2O3 studied through ultrafast z-scan spectroscopy

NASA Astrophysics Data System (ADS)

Moreira, L.; Falci, R. F.; Darabian, H.; Anjos, V.; Bell, M. J. V.; Kassab, L. R. P.; Bordon, C. D. S.; Doualan, J. L.; Camy, P.; Moncorgé, R.

2018-05-01

The research on Nd3+ doped new solid-state laser hosts with specific thermo-mechanical and optical properties is very active. Nd3+ doped tellurite glasses are suitable for these applications. They have high linear and nonlinear refraction index, wide transmittance range. The TeO2-ZnO (TZO) glass considered in the present work combines all those features and the nonlinear optical properties can be used for the development of Kerr-lens mode-locked sub picosecond lasers. Recently the laser performance of Nd3+ doped TZO glass and was reported and laser slope efficiency of 21% was observed. We investigate how the intensity variation and the silver nanoparticles codoping affects the nonlinear optical properties of Nd3+ doped TZO glasses. Intensity dependent nonlinear refraction indices coefficients at 750, 800 and 850 nm were observed. The nonlinear optical features were obtained through ultrafast single beam z-scan technique with excitations at 750, 800 and 850 nm and are up to two orders of magnitude higher than those reported in the literature.

Functional Nonlinear Mixed Effects Models For Longitudinal Image Data

PubMed Central

Luo, Xinchao; Zhu, Lixing; Kong, Linglong; Zhu, Hongtu

2015-01-01

Motivated by studying large-scale longitudinal image data, we propose a novel functional nonlinear mixed effects modeling (FN-MEM) framework to model the nonlinear spatial-temporal growth patterns of brain structure and function and their association with covariates of interest (e.g., time or diagnostic status). Our FNMEM explicitly quantifies a random nonlinear association map of individual trajectories. We develop an efficient estimation method to estimate the nonlinear growth function and the covariance operator of the spatial-temporal process. We propose a global test and a simultaneous confidence band for some specific growth patterns. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply FNMEM to investigate the spatial-temporal dynamics of white-matter fiber skeletons in a national database for autism research. Our FNMEM may provide a valuable tool for charting the developmental trajectories of various neuropsychiatric and neurodegenerative disorders. PMID:26213453

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

PubMed

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

2017-12-19

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

Experimentally observed evolution between dynamic patterns and intrinsic localized modes in a driven nonlinear electrical cyclic lattice

NASA Astrophysics Data System (ADS)

Shige, S.; Miyasaka, K.; Shi, W.; Soga, Y.; Sato, M.; Sievers, A. J.

2018-02-01

Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial modes (LSMs) have been experimentally measured for a driven 1-D nonlinear cyclic electric transmission line, where the nonlinear element is a saturable capacitor. Depending on the number of cells and electrical lattice damping an LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by tuning the driver frequency away from this spectrum the LSM can be continuously converted into ILMs and vice versa. The differences in pattern formation between simulations and experimental findings are due to a low concentration of impurities. Through this novel nonlinear excitation and switching channel in cyclic lattices either energy balanced or unbalanced LSMs and ILMs may occur. Because of the general nature of these dynamical results for nonintegrable lattices applications are to be expected. The ultimate stability of driven aero machinery containing nonlinear periodic structures may be one example.

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits.

PubMed

Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté

2015-12-24

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits.

Spatiotemporal polarization modulation microscopy with a microretarder array

NASA Astrophysics Data System (ADS)

Ding, Changqin; Ulcickas, James R. W.; Simpson, Garth J.

2018-02-01

A patterned microretarder array positioned in the rear conjugate plane of a microscope enables rapid polarizationdependent nonlinear optical microscopy. The pattern introduced to the array results in periodic modulation of the polarization-state of the incident light as a function of position within the field of view with no moving parts or active control. Introduction of a single stationary optical element and a fixed polarizer into the beam of a nonlinear optical microscope enabled nonlinear optical tensor recovery, which informs on local structure and orientation. Excellent agreement was observed between the measured and predicted second harmonic generation (SHG) of z-cut quartz, selected as a test system with well-established nonlinear optical properties. Subsequent studies of spatially varying samples further support the general applicability of this relatively simple strategy for detailed polarization analysis in both conventional and nonlinear optical imaging of structurally diverse samples.

Optical Pattern Formation in Spatially Bunched Atoms: A Self-Consistent Model and Experiment

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie L.; Gauthier, Daniel J.

2014-05-01

The nonlinear optics and optomechanical physics communities use different theoretical models to describe how optical fields interact with a sample of atoms. There does not yet exist a model that is valid for finite atomic temperatures but that also produces the zero temperature results that are generally assumed in optomechanical systems. We present a self-consistent model that is valid for all atomic temperatures and accounts for the back-action of the atoms on the optical fields. Our model provides new insights into the competing effects of the bunching-induced nonlinearity and the saturable nonlinearity. We show that it is crucial to keep the fifth and seventh-order nonlinearities that arise when there exists atomic bunching, even at very low optical field intensities. We go on to apply this model to the results of our experimental system where we observe spontaneous, multimode, transverse optical pattern formation at ultra-low light levels. We show that our model accurately predicts our experimentally observed threshold for optical pattern formation, which is the lowest threshold ever reported for pattern formation. We gratefully acknowledge the financial support of the NSF through Grant #PHY-1206040.

Annual Review of Research Under the Joint Service Electronics Program.

DTIC Science & Technology

1979-10-01

Contents: Quadratic Optimization Problems; Nonlinear Control; Nonlinear Fault Analysis; Qualitative Analysis of Large Scale Systems; Multidimensional System Theory ; Optical Noise; and Pattern Recognition.

Inhibition of viscous fluid fingering: A variational scheme for optimal flow rates

NASA Astrophysics Data System (ADS)

Miranda, Jose; Dias, Eduardo; Alvarez-Lacalle, Enrique; Carvalho, Marcio

2012-11-01

Conventional viscous fingering flow in radial Hele-Shaw cells employs a constant injection rate, resulting in the emergence of branched interfacial shapes. The search for mechanisms to prevent the development of these bifurcated morphologies is relevant to a number of areas in science and technology. A challenging problem is how best to choose the pumping rate in order to restrain growth of interfacial amplitudes. We use an analytical variational scheme to look for the precise functional form of such an optimal flow rate. We find it increases linearly with time in a specific manner so that interface disturbances are minimized. Experiments and nonlinear numerical simulations support the effectiveness of this particularly simple, but not at all obvious, pattern controlling process. J.A.M., E.O.D. and M.S.C. thank CNPq/Brazil for financial support. E.A.L. acknowledges support from Secretaria de Estado de IDI Spain under project FIS2011-28820-C02-01.

High-order rogue waves in vector nonlinear Schrödinger equations.

PubMed

Ling, Liming; Guo, Boling; Zhao, Li-Chen

2014-04-01

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

Investigation on Nonlinear-Optical Properties of Palm Oil/Silver Nanoparticles

NASA Astrophysics Data System (ADS)

Zamiri, R.; Parvizi, R.; Zakaria, A.; Sadrolhosseini, A. R.; Zamiri, G.; Darroudi, M.; Husin, M. S.

2012-06-01

We have investigated the spatial self phase modulation of palm oil containing silver nanoparticles (palm oil/Ag-NPs). The study carried out using continuous wave diode pumped solid state laser with wavelength of 405 nm and power of 50 mW. The strong spatial self phase modulation patterns were observed that suggest the palm oil/Ag-NPs have a relatively large nonlinear refractive index. The obtained values of nonlinear refractive index were increased with the increment in the volume fractions. The observed experimental patterns were also theoretically modeled which are in good agreement with experimental results.

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.

Nonlinear Growth Models in M"plus" and SAS

ERIC Educational Resources Information Center

Grimm, Kevin J.; Ram, Nilam

2009-01-01

Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the M"plus" structural modeling program and the nonlinear…

Firn thickness variations across the Northeast Greenland Ice Stream margins indicating nonlinear densification rates

NASA Astrophysics Data System (ADS)

Riverman, K. L.; Anandakrishnan, S.; Alley, R. B.; Peters, L. E.; Christianson, K. A.; Muto, A.

2013-12-01

Northeast Greenland Ice Stream (NEGIS) is the largest ice stream in Greenland, draining approximately 8.4% of the ice sheet's area. The flow pattern and stability mechanism of this ice stream are unique to others in Greenland and Antarctica, and merit further study to ascertain the sensitivity of this ice stream to future climate change. Geophysical methods are valuable tools for this application, but their results are sensitive to the structure of the firn and any spatial variations in firn properties across a given study region. Here we present firn data from a 40-km-long seismic profile across the upper reaches of NEGIS, collected in the summer of 2012 as part of an integrated ground-based geophysical survey. We find considerable variations in firn thickness that are coincident with the ice stream shear margins, where a thinner firn layer is present within the margins, and a thicker, more uniform firn layer is present elsewhere in our study region. Higher accumulation rates in the marginal surface troughs due to drift-snow trapping can account for some of this increased densification; however, our seismic results also highlight enhanced anisotropy within the firn and upper ice column that is confined to narrow bands within the shear margins. We thus interpret these large firn thickness variations and abrupt changes in anisotropy as indicators of firn densification dependent on the effective stress state as well as the overburden pressure, suggesting that the strain rate increases nonlinearly with stress across the shear margins. A GPS strain grid maintained for three weeks across both margins observed strong side shearing, with rapid stretching and then compression along particle paths, indicating large deviatoric stresses in the margins. This work demonstrates the importance of developing a high-resolution firn densification model when conducting geophysical field work in regions possessing a complex ice flow history; it also motivates the need for a more detailed firn densification study along NEGIS to better understand the evolution of these abrupt structural variations within the firn.

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

NASA Astrophysics Data System (ADS)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Ochs, Harry T., III

1988-01-01

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

Time series analyses of breathing patterns of lung cancer patients using nonlinear dynamical system theory.

PubMed

Tewatia, D K; Tolakanahalli, R P; Paliwal, B R; Tomé, W A

2011-04-07

The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.

Nonlinear dynamics of a pulse-coupled neural oscillator model of orientation tuning in the visual cortex

NASA Astrophysics Data System (ADS)

Bressloff, P. C.; Bressloff, N. W.

2000-02-01

Orientation tuning in a ring of pulse-coupled integrate-and-fire (IF) neurons is analyzed in terms of spontaneous pattern formation. It is shown how the ring bifurcates from a synchronous state to a non-phase-locked state whose spike trains are characterized by quasiperiodic variations of the inter-spike intervals (ISIs) on closed invariant circles. The separation of these invariant circles in phase space results in a localized peak of activity as measured by the time-averaged firing rate of the neurons. This generates a sharp orientation tuning curve that can lock to a slowly rotating, weakly tuned external stimulus. For fast synapses, breakup of the quasiperiodic orbits occurs leading to high spike time variability suggestive of chaos.

Diffraction-limited real-time terahertz imaging by optical frequency up-conversion in a DAST crystal.

PubMed

Fan, Shuzhen; Qi, Feng; Notake, Takashi; Nawata, Kouji; Takida, Yuma; Matsukawa, Takeshi; Minamide, Hiroaki

2015-03-23

Real-time terahertz (THz) wave imaging has wide applications in areas such as security, industry, biology, medicine, pharmacy, and the arts. This report describes real-time room-temperature THz imaging by nonlinear optical frequency up-conversion in an organic 4-dimethylamino-N'-methyl-4'-stilbazolium tosylate (DAST) crystal, with high resolution reaching the diffraction limit. THz-wave images were converted to the near infrared region and then captured using an InGaAs camera in a tandem imaging system. The resolution of the imaging system was analyzed. Diffraction and interference of THz wave were observed in the experiments. Videos are supplied to show the interference pattern variation that occurs with sample moving and tilting.

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

NASA Astrophysics Data System (ADS)

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

2005-04-01

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

Landscape prediction and mapping of game fish biomass, an ecosystem service of Michigan rivers

USGS Publications Warehouse

Esselman, Peter C.; Stevenson, R Jan; Lupi, Frank; Riseng, Catherine M.; Wiley, Michael J.

2015-01-01

The increased integration of ecosystem service concepts into natural resource management places renewed emphasis on prediction and mapping of fish biomass as a major provisioning service of rivers. The goals of this study were to predict and map patterns of fish biomass as a proxy for the availability of catchable fish for anglers in rivers and to identify the strongest landscape constraints on fish productivity. We examined hypotheses about fish responses to total phosphorus (TP), as TP is a growth-limiting nutrient known to cause increases (subsidy response) and/or decreases (stress response) in fish biomass depending on its concentration and the species being considered. Boosted regression trees were used to define nonlinear functions that predicted the standing crops of Brook Trout Salvelinus fontinalis, Brown Trout Salmo trutta, Smallmouth Bass Micropterus dolomieu, panfishes (seven centrarchid species), and Walleye Sander vitreus by using landscape and modeled local-scale predictors. Fitted models were highly significant and explained 22–56% of the variation in validation data sets. Nonlinear and threshold responses were apparent for numerous predictors, including TP concentration, which had significant effects on all except the Walleye fishery. Brook Trout and Smallmouth Bass exhibited both subsidy and stress responses, panfish biomass exhibited a subsidy response only, and Brown Trout exhibited a stress response. Maps of reach-specific standing crop predictions showed patterns of predicted fish biomass that corresponded to spatial patterns in catchment area, water temperature, land cover, and nutrient availability. Maps illustrated predictions of higher trout biomass in coldwater streams draining glacial till in northern Michigan, higher Smallmouth Bass and panfish biomasses in warmwater systems of southern Michigan, and high Walleye biomass in large main-stem rivers throughout the state. Our results allow fisheries managers to examine the biomass potential of streams, describe geographic patterns of fisheries, explore possible nutrient management targets, and identify habitats that are candidates for species management.

Analysis of factors affecting the accuracy, reproducibility, and interpretation of microbial community carbon source utilization patterns

USGS Publications Warehouse

Haack, S.K.; Garchow, H.; Klug, M.J.; Forney, L.J.

1995-01-01

We determined factors that affect responses of bacterial isolates and model bacterial communities to the 95 carbon substrates in Biolog microliter plates. For isolates and communities of three to six bacterial strains, substrate oxidation rates were typically nonlinear and were delayed by dilution of the inoculum. When inoculum density was controlled, patterns of positive and negative responses exhibited by microbial communities to each of the carbon sources were reproducible. Rates and extents of substrate oxidation by the communities were also reproducible but were not simply the sum of those exhibited by community members when tested separately. Replicates of the same model community clustered when analyzed by principal- components analysis (PCA), and model communities with different compositions were clearly separated un the first PCA axis, which accounted for >60% of the dataset variation. PCA discrimination among different model communities depended on the extent to which specific substrates were oxidized. However, the substrates interpreted by PCA to be most significant in distinguishing the communities changed with reading time, reflecting the nonlinearity of substrate oxidation rates. Although whole-community substrate utilization profiles were reproducible signatures for a given community, the extent of oxidation of specific substrates and the numbers or activities of microorganisms using those substrates in a given community were not correlated. Replicate soil samples varied significantly in the rate and extent of oxidation of seven tested substrates, suggesting microscale heterogeneity in composition of the soil microbial community.

Stability of nonlinear waves and patterns and related topics

NASA Astrophysics Data System (ADS)

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-01

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Theoretical Studies of Alfven Waves and Energetic Particle Physics in Fusion Plasmas

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

Chen, Liu

This report summarizes major theoretical findings in the linear as well as nonlinear physics of Alfvén waves and energetic particles in magnetically confined fusion plasmas. On the linear physics, a variational formulation, based on the separation of singular and regular spatial scales, for drift-Alfvén instabilities excited by energetic particles is established. This variational formulation is then applied to derive the general fishbone-like dispersion relations corresponding to the various Alfvén eigenmodes and energetic-particle modes. It is further employed to explore in depth the low-frequency Alfvén eigenmodes and demonstrate the non-perturbative nature of the energetic particles. On the nonlinear physics, new novelmore » findings are obtained on both the nonlinear wave-wave interactions and nonlinear wave-energetic particle interactions. It is demonstrated that both the energetic particles and the fine radial mode structures could qualitatively affect the nonlinear evolution of Alfvén eigenmodes. Meanwhile, a theoretical approach based on the Dyson equation is developed to treat self-consistently the nonlinear interactions between Alfvén waves and energetic particles, and is then applied to explain simulation results of energetic-particle modes. Relevant list of journal publications on the above findings is also included.« less

Spatial eigenmodes and synchronous oscillation: co-incidence detection in simulated cerebral cortex.

PubMed

Chapman, Clare L; Wright, James J; Bourke, Paul D

2002-07-01

Zero-lag synchronisation arises between points on the cerebral cortex receiving concurrent independent inputs; an observation generally ascribed to nonlinear mechanisms. Using simulations of cerebral cortex and Principal Component Analysis (PCA) we show patterns of zero-lag synchronisation (associated with empirically realistic spectral content) can arise from both linear and nonlinear mechanisms. For low levels of activation, we show the synchronous field is described by the eigenmodes of the resultant damped wave activity. The first and second spatial eigenmodes (which capture most of the signal variance) arise from the even and odd components of the independent input signals. The pattern of zero-lag synchronisation can be accounted for by the relative dominance of the first mode over the second, in the near-field of the inputs. The simulated cortical surface can act as a few millisecond response coincidence detector for concurrent, but uncorrelated, inputs. As cortical activation levels are increased, local damped oscillations in the gamma band undergo a transition to highly nonlinear undamped activity with 40 Hz dominant frequency. This is associated with "locking" between active sites and spatially segregated phase patterns. The damped wave synchronisation and the locked nonlinear oscillations may combine to permit fast representation of multiple patterns of activity within the same field of neurons.

Characterising infant inter-breath interval patterns during active and quiet sleep using recurrence plot analysis.

PubMed

Terrill, Philip I; Wilson, Stephen J; Suresh, Sadasivam; Cooper, David M

2009-01-01

Breathing patterns are characteristically different between active and quiet sleep states in infants. It has been previously identified that breathing dynamics are governed by a non-linear controller which implies the need for a nonlinear analytical tool. Further, it has been shown that quantified nonlinear variables are different between adult sleep states. This study aims to determine whether a nonlinear analytical tool known as recurrence plot analysis can characterize breath intervals of active and quiet sleep states in infants. Overnight polysomnograms were obtained from 32 healthy infants. The 6 longest periods each of active and quiet sleep were identified and a software routine extracted inter-breath interval data for recurrence plot analysis. Determinism (DET), laminarity (LAM) and radius (RAD) values were calculated for an embedding dimension of 4, 6, 8 and 16, and fixed recurrence of 0.5, 1, 2, 3.5 and 5%. Recurrence plots exhibited characteristically different patterns for active and quiet sleep. Active sleep periods typically had higher values of RAD, DET and LAM than for quiet sleep, and this trend was invariant to a specific choice of embedding dimension or fixed recurrence. These differences may provide a basis for automated sleep state classification, and the quantitative investigation of pathological breathing patterns.

Sensitivity analysis for parametric generalized implicit quasi-variational-like inclusions involving P-[eta]-accretive mappings

NASA Astrophysics Data System (ADS)

Kazmi, K. R.; Khan, F. A.

2008-01-01

In this paper, using proximal-point mapping technique of P-[eta]-accretive mapping and the property of the fixed-point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of a parametric generalized implicit quasi-variational-like inclusion involving P-[eta]-accretive mapping in real uniformly smooth Banach space. Further, under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to the parameter. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [R.P. Agarwal, Y.-J. Cho, N.-J. Huang, Sensitivity analysis for strongly nonlinear quasi-variational inclusions, Appl. MathE Lett. 13 (2002) 19-24; S. Dafermos, Sensitivity analysis in variational inequalities, Math. Oper. Res. 13 (1988) 421-434; X.-P. Ding, Sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions, Appl. Math. Lett. 17 (2) (2004) 225-235; X.-P. Ding, Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings, J. Comput. Appl. Math. 182 (2) (2005) 252-269; X.-P. Ding, C.L. Luo, On parametric generalized quasi-variational inequalities, J. Optim. Theory Appl. 100 (1999) 195-205; Z. Liu, L. Debnath, S.M. Kang, J.S. Ume, Sensitivity analysis for parametric completely generalized nonlinear implicit quasi-variational inclusions, J. Math. Anal. Appl. 277 (1) (2003) 142-154; R.N. Mukherjee, H.L. Verma, Sensitivity analysis of generalized variational inequalities, J. Math. Anal. Appl. 167 (1992) 299-304; M.A. Noor, Sensitivity analysis framework for general quasi-variational inclusions, Comput. Math. Appl. 44 (2002) 1175-1181; M.A. Noor, Sensitivity analysis for quasivariational inclusions, J. Math. Anal. Appl. 236 (1999) 290-299; J.Y. Park, J.U. Jeong, Parametric generalized mixed variational inequalities, Appl. Math. Lett. 17 (2004) 43-48].

Differences between direct current and alternating current capacitance nonlinearities in high-k dielectrics and their relation to hopping conduction

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

Khaldi, O.; Kassmi, M.; El Manar University, LMOP, 2092 Tunis

2014-08-28

Capacitance nonlinearities were studied in atomic layer deposited HfO{sub 2} films using two types of signals: a pure ac voltage of large magnitude (ac nonlinearities) and a small ac voltage superimposed to a large dc voltage (dc nonlinearities). In theory, ac and dc nonlinearities should be of the same order of magnitude. However, in practice, ac nonlinearities are found to be an order of magnitude higher than dc nonlinearities. Besides capacitance nonlinearities, hopping conduction is studied using low-frequency impedance measurements and is discussed through the correlated barrier hopping model. The link between hopping and nonlinearity is established. The ac nonlinearitiesmore » are ascribed to the polarization of isolated defect pairs, while dc nonlinearities are attributed to electrode polarization which originates from defect percolation paths. Both the ac and dc capacitance nonlinearities display an exponential variation with voltage, which results from field-induced lowering of the hopping barrier energy.« less

Physical mechanisms of solar activity effects in the middle atmosphere

NASA Technical Reports Server (NTRS)

Ebel, A.

1989-01-01

A great variety of physical mechanisms of possibly solar induced variations in the middle atmosphere has been discussed in the literature during the last decades. The views which have been put forward are often controversial in their physical consequences. The reason may be the complexity and non-linearity of the atmospheric response to comparatively weak forcing resulting from solar activity. Therefore this review focuses on aspects which seem to indicate nonlinear processes in the development of solar induced variations. Results from observations and numerical simulations are discussed.

Systems for controlling the intensity variations in a laser beam and for frequency conversion thereof

DOEpatents

Skupsky, S.; Craxton, R.S.; Soures, J.

1990-10-02

In order to control the intensity of a laser beam so that its intensity varies uniformly and provides uniform illumination of a target, such as a laser fusion target, a broad bandwidth laser pulse is spectrally dispersed spatially so that the frequency components thereof are spread apart. A disperser (grating) provides an output beam which varies spatially in wavelength in at least one direction transverse to the direction of propagation of the beam. Temporal spread (time delay) across the beam is corrected by using a phase delay device (a time delay compensation echelon). The dispersed beam may be amplified with laser amplifiers and frequency converted (doubled, tripled or quadrupled in frequency) with nonlinear optical elements (birefringent crystals). The spectral variation across the beam is compensated by varying the angle of incidence on one of the crystals with respect to the crystal optical axis utilizing a lens which diverges the beam. Another lens after the frequency converter may be used to recollimate the beam. The frequency converted beam is recombined so that portions of different frequency interfere and, unlike interference between waves of the same wavelength, there results an intensity pattern with rapid temporal oscillations which average out rapidly in time thereby producing uniform illumination on target. A distributed phase plate (also known as a random phase mask), through which the spectrally dispersed beam is passed and then focused on a target, is used to provide the interference pattern which becomes nearly modulation free and uniform in intensity in the direction of the spectral variation. 16 figs.

Systems for controlling the intensity variations in a laser beam and for frequency conversion thereof

DOEpatents

Skupsky, Stanley; Craxton, R. Stephen; Soures, John

1990-01-01

In order to control the intensity of a laser beam so that its intensity varies uniformly and provides uniform illumination of a target, such as a laser fusion target, a broad bandwidth laser pulse is spectrally dispersed spatially so that the frequency components thereof are spread apart. A disperser (grating) provides an output beam which varies spatially in wavelength in at least one direction transverse to the direction of propagation of the beam. Temporal spread (time delay) across the beam is corrected by using a phase delay device (a time delay compensation echelon). The dispersed beam may be amplified with laser amplifiers and frequency converted (doubled, tripled or quadrupled in frequency) with nonlinear optical elements (birefringent crystals). The spectral variation across the beam is compensated by varying the angle of incidence on one of the crystals with respect to the crystal optical axis utilizing a lens which diverges the beam. Another lens after the frequency converter may be used to recollimate the beam. The frequency converted beam is recombined so that portions of different frequency interfere and, unlike interference between waves of the same wavelength, there results an intensity pattern with rapid temoral oscillations which average out rapidly in time thereby producing uniform illumination on target. A distributed phase plate (also known as a random phase mask), through which the spectrally dispersed beam is passed and then focused on a target, is used to provide the interference pattern which becomes nearly modulation free and uniform in intensity in the direction of the spectral variation.

Improving the quantification of contrast enhanced ultrasound using a Bayesian approach

NASA Astrophysics Data System (ADS)

Rizzo, Gaia; Tonietto, Matteo; Castellaro, Marco; Raffeiner, Bernd; Coran, Alessandro; Fiocco, Ugo; Stramare, Roberto; Grisan, Enrico

2017-03-01

Contrast Enhanced Ultrasound (CEUS) is a sensitive imaging technique to assess tissue vascularity, that can be useful in the quantification of different perfusion patterns. This can be particularly important in the early detection and staging of arthritis. In a recent study we have shown that a Gamma-variate can accurately quantify synovial perfusion and it is flexible enough to describe many heterogeneous patterns. Moreover, we have shown that through a pixel-by-pixel analysis the quantitative information gathered characterizes more effectively the perfusion. However, the SNR ratio of the data and the nonlinearity of the model makes the parameter estimation difficult. Using classical non-linear-leastsquares (NLLS) approach the number of unreliable estimates (those with an asymptotic coefficient of variation greater than a user-defined threshold) is significant, thus affecting the overall description of the perfusion kinetics and of its heterogeneity. In this work we propose to solve the parameter estimation at the pixel level within a Bayesian framework using Variational Bayes (VB), and an automatic and data-driven prior initialization. When evaluating the pixels for which both VB and NLLS provided reliable estimates, we demonstrated that the parameter values provided by the two methods are well correlated (Pearson's correlation between 0.85 and 0.99). Moreover, the mean number of unreliable pixels drastically reduces from 54% (NLLS) to 26% (VB), without increasing the computational time (0.05 s/pixel for NLLS and 0.07 s/pixel for VB). When considering the efficiency of the algorithms as computational time per reliable estimate, VB outperforms NLLS (0.11 versus 0.25 seconds per reliable estimate respectively).

Superregular breathers, characteristics of nonlinear stage of modulation instability induced by higher-order effects

PubMed Central

Zhang, Jian-Hui; Liu, Chong

2017-01-01

We study the higher-order generalized nonlinear Schrödinger (NLS) equation describing the propagation of ultrashort optical pulse in optical fibres. By using Darboux transformation, we derive the superregular breather solution that develops from a small localized perturbation. This type of solution can be used to characterize the nonlinear stage of the modulation instability (MI) of the condensate. In particular, we show some novel characteristics of the nonlinear stage of MI arising from higher-order effects: (i) coexistence of a quasi-Akhmediev breather and a multipeak soliton; (ii) two multipeak solitons propagation in opposite directions; (iii) a beating pattern followed by two multipeak solitons in the same direction. It is found that these patterns generated from a small localized perturbation do not have the analogues in the standard NLS equation. Our results enrich Zakharov’s theory of superregular breathers and could provide helpful insight on the nonlinear stage of MI in presence of the higher-order effects. PMID:28413335

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits

PubMed Central

Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté

2015-01-01

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits. DOI: http://dx.doi.org/10.7554/eLife.10056.001 PMID:26705334

Cellular automata and integrodifferential equation models for cell renewal in mosaic tissues

PubMed Central

Bloomfield, J. M.; Sherratt, J. A.; Painter, K. J.; Landini, G.

2010-01-01

Mosaic tissues are composed of two or more genetically distinct cell types. They occur naturally, and are also a useful experimental method for exploring tissue growth and maintenance. By marking the different cell types, one can study the patterns formed by proliferation, renewal and migration. Here, we present mathematical modelling suggesting that small changes in the type of interaction that cells have with their local cellular environment can lead to very different outcomes for the composition of mosaics. In cell renewal, proliferation of each cell type may depend linearly or nonlinearly on the local proportion of cells of that type, and these two possibilities produce very different patterns. We study two variations of a cellular automaton model based on simple rules for renewal. We then propose an integrodifferential equation model, and again consider two different forms of cellular interaction. The results of the continuous and cellular automata models are qualitatively the same, and we observe that changes in local environment interaction affect the dynamics for both. Furthermore, we demonstrate that the models reproduce some of the patterns seen in actual mosaic tissues. In particular, our results suggest that the differing patterns seen in organ parenchymas may be driven purely by the process of cell replacement under different interaction scenarios. PMID:20375040

On Non-Linear Sensitivity of Marine Biological Models to Parameter Variations

DTIC Science & Technology

2007-01-01

M.B., 2002. Understanding uncertain enviromental systems. In: Grasman, J., van Straten, G. (Eds.), Predictability and Nonlinear Modelling in Natural...model evaluations to compute sensitivity indices. Comput. Phys. Commun. 145, 280–297. Saltelli, A., Andres, T.H., Homma, T., 1993. Some new techniques

A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

NASA Astrophysics Data System (ADS)

Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.

2017-09-01

Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.

Estimation of wing nonlinear aerodynamic characteristics at supersonic speeds

NASA Technical Reports Server (NTRS)

Carlson, H. W.; Mack, R. J.

1980-01-01

A computational system for estimation of nonlinear aerodynamic characteristics of wings at supersonic speeds was developed and was incorporated in a computer program. This corrected linearized theory method accounts for nonlinearities in the variation of basic pressure loadings with local surface slopes, predicts the degree of attainment of theoretical leading edge thrust, and provides an estimate of detached leading edge vortex loadings that result when the theoretical thrust forces are not fully realized.

Investigation into image quality difference between total variation and nonlinear sparsifying transform based compressed sensing

NASA Astrophysics Data System (ADS)

Dong, Jian; Kudo, Hiroyuki

2017-03-01

Compressed sensing (CS) is attracting growing concerns in sparse-view computed tomography (CT) image reconstruction. The most standard approach of CS is total variation (TV) minimization. However, images reconstructed by TV usually suffer from distortions, especially in reconstruction of practical CT images, in forms of patchy artifacts, improper serrate edges and loss of image textures. Most existing CS approaches including TV achieve image quality improvement by applying linear transforms to object image, but linear transforms usually fail to take discontinuities into account, such as edges and image textures, which is considered to be the key reason for image distortions. Actually, discussions on nonlinear filter based image processing has a long history, leading us to clarify that the nonlinear filters yield better results compared to linear filters in image processing task such as denoising. Median root prior was first utilized by Alenius as nonlinear transform in CT image reconstruction, with significant gains obtained. Subsequently, Zhang developed the application of nonlocal means-based CS. A fact is gradually becoming clear that the nonlinear transform based CS has superiority in improving image quality compared with the linear transform based CS. However, it has not been clearly concluded in any previous paper within the scope of our knowledge. In this work, we investigated the image quality differences between the conventional TV minimization and nonlinear sparsifying transform based CS, as well as image quality differences among different nonlinear sparisying transform based CSs in sparse-view CT image reconstruction. Additionally, we accelerated the implementation of nonlinear sparsifying transform based CS algorithm.

Hybrid associative memory using an incoherent correlation system

NASA Astrophysics Data System (ADS)

Taniguchi, Masaki; Ichioka, Yoshiki; Matsuoka, Katsunori

1990-10-01

A hybrid heteroassociative memory is presented that uses an incoherent system in which two correlators and a nonlinear element form a nonlinear feedback system. This system can recall any pattern from an input pattern without cross-talk or ghosts by properly designing a pair of filters installed in the correlators. Experiments on a simple hybrid system were performed to ensure the operation of the system and to demonstrate the usefulness of this proposed system.

Nonlinear Structured Growth Mixture Models in Mplus and OpenMx

PubMed Central

Grimm, Kevin J.; Ram, Nilam; Estabrook, Ryne

2014-01-01

Growth mixture models (GMMs; Muthén & Muthén, 2000; Muthén & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models because of their common use, flexibility in modeling many types of change patterns, the availability of statistical programs to fit such models, and the ease of programming. In this paper, we present additional ways of modeling nonlinear change patterns with GMMs. Specifically, we show how LCMs that follow specific nonlinear functions can be extended to examine the presence of multiple latent classes using the Mplus and OpenMx computer programs. These models are fit to longitudinal reading data from the Early Childhood Longitudinal Study-Kindergarten Cohort to illustrate their use. PMID:25419006

Stability of nonlinear waves and patterns and related topics.

PubMed

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-13

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'. © 2018 The Author(s).

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1993-01-01

A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.

Polarization-induced interference within electromagnetically induced transparency for atoms of double-V linkage

NASA Astrophysics Data System (ADS)

Sun, Yuan; Liu, Chang; Chen, Ping-Xing; Liu, Liang

2018-02-01

People have been paying attention to the role of atoms' complex internal level structures in the research of electromagnetically induced transparency (EIT) for a long time, where the various degenerate Zeeman levels usually generate complex linkage patterns for the atomic transitions. It turns out, with special choices of the atomic states and the atomic transitions' linkage structure, clear signatures of quantum interference induced by the probe and coupling light's polarizations can emerge from a typical EIT phenomena. We propose to study a four-state system with double-V linkage pattern for the transitions and analyze the polarization-induced interference under the EIT condition. We show that such interference arises naturally under mild conditions on the optical field and atom manipulation techniques. Moreover, we construct a variation form of double-M linkage pattern where the polarization-induced interference enables polarization-dependent cross modulation between incident weak lights that can be effective even at the few-photon level. The theme is to gain more insight into the essential question: how can we build a nontrivial optical medium where incident lights experience polarization-dependent nonlinear optical interactions, valid for a wide range of incidence intensities down to the few-photon level?

Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother

NASA Astrophysics Data System (ADS)

Fillion, Anthony; Bocquet, Marc; Gratton, Serge

2018-04-01

The analysis in nonlinear variational data assimilation is the solution of a non-quadratic minimization. Thus, the analysis efficiency relies on its ability to locate a global minimum of the cost function. If this minimization uses a Gauss-Newton (GN) method, it is critical for the starting point to be in the attraction basin of a global minimum. Otherwise the method may converge to a local extremum, which degrades the analysis. With chaotic models, the number of local extrema often increases with the temporal extent of the data assimilation window, making the former condition harder to satisfy. This is unfortunate because the assimilation performance also increases with this temporal extent. However, a quasi-static (QS) minimization may overcome these local extrema. It accomplishes this by gradually injecting the observations in the cost function. This method was introduced by Pires et al. (1996) in a 4D-Var context. We generalize this approach to four-dimensional strong-constraint nonlinear ensemble variational (EnVar) methods, which are based on both a nonlinear variational analysis and the propagation of dynamical error statistics via an ensemble. This forces one to consider the cost function minimizations in the broader context of cycled data assimilation algorithms. We adapt this QS approach to the iterative ensemble Kalman smoother (IEnKS), an exemplar of nonlinear deterministic four-dimensional EnVar methods. Using low-order models, we quantify the positive impact of the QS approach on the IEnKS, especially for long data assimilation windows. We also examine the computational cost of QS implementations and suggest cheaper algorithms.

A spatiotemporal dengue fever early warning model accounting for nonlinear associations with meteorological factors: a Bayesian maximum entropy approach

NASA Astrophysics Data System (ADS)

Lee, Chieh-Han; Yu, Hwa-Lung; Chien, Lung-Chang

2014-05-01

Dengue fever has been identified as one of the most widespread vector-borne diseases in tropical and sub-tropical. In the last decade, dengue is an emerging infectious disease epidemic in Taiwan especially in the southern area where have annually high incidences. For the purpose of disease prevention and control, an early warning system is urgently needed. Previous studies have showed significant relationships between climate variables, in particular, rainfall and temperature, and the temporal epidemic patterns of dengue cases. However, the transmission of the dengue fever is a complex interactive process that mostly understated the composite space-time effects of dengue fever. This study proposes developing a one-week ahead warning system of dengue fever epidemics in the southern Taiwan that considered nonlinear associations between weekly dengue cases and meteorological factors across space and time. The early warning system based on an integration of distributed lag nonlinear model (DLNM) and stochastic Bayesian Maximum Entropy (BME) analysis. The study identified the most significant meteorological measures including weekly minimum temperature and maximum 24-hour rainfall with continuous 15-week lagged time to dengue cases variation under condition of uncertainty. Subsequently, the combination of nonlinear lagged effects of climate variables and space-time dependence function is implemented via a Bayesian framework to predict dengue fever occurrences in the southern Taiwan during 2012. The result shows the early warning system is useful for providing potential outbreak spatio-temporal prediction of dengue fever distribution. In conclusion, the proposed approach can provide a practical disease control tool for environmental regulators seeking more effective strategies for dengue fever prevention.

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

PubMed

Kumar, Dinesh; Kumar, P; Rai, K N

2017-11-01

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

On the nonlinear variation of dc conductivity with dielectric relaxation time

NASA Astrophysics Data System (ADS)

Johari, G. P.; Andersson, Ove

2006-09-01

The long-known observations that dc conductivity σdc of an ultraviscous liquid varies nonlinearly with the dielectric relaxation time τ, and the slope of the logσdc against logτ plot deviates from -1 are currently seen as two of the violations of the Debye-Stokes-Einstein equation. Here we provide a formalism using a zeroth order Bjerrum description for ion association to show that in addition to its variation with temperature T and pressure P, impurity ion population varies with a liquid's equilibrium dielectric permittivity. Inclusion of this electrostatic effect modifies the Debye-Stokes-Einstein equation to log(σdcτ )=constant+logα, where α is the T and P-dependent degree of ionic dissociation of an electrolytic impurity. Variation of a liquid's shear modulus with T and P would add to the nonlinearity of σdc-τ relation, as would a nonequivalence of the shear and dielectric relaxation times, proton transfer along the hydrogen bonds, or occurrence of another chemical process. This is illustrated by using the data for ultraviscous acetaminophen-aspirin liquid.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Structural characterization and observation of variable range hopping conduction mechanism at high temperature in CdSe quantum dot solids

NASA Astrophysics Data System (ADS)

Sinha, Subhojyoti; Kumar Chatterjee, Sanat; Ghosh, Jiten; Kumar Meikap, Ajit

2013-03-01

We have used Rietveld refinement technique to extract the microstructural parameters of thioglycolic acid capped CdSe quantum dots. The quantum dot formation and its efficient capping are further confirmed by HR-TEM, UV-visible and FT-IR spectroscopy. Comparative study of the variation of dc conductivity with temperature (298 K ≤ T ≤ 460 K) is given considering Arrhenius formalism, small polaron hopping and Schnakenberg model. We observe that only Schnakenberg model provides good fit to the non-linear region of the variation of dc conductivity with temperature. Experimental variation of ac conductivity and dielectric parameters with temperature (298 K ≤ T ≤ 460 K) and frequency (80 Hz ≤ f ≤ 2 MHz) are discussed in the light of hopping theory and quantum confinement effect. We have elucidated the observed non-linearity in the I-V curves (measured within ±50 V), at dark and at ambient light, in view of tunneling mechanism. Tunnel exponents and non-linearity weight factors have also been evaluated in this regard.

A reexamination of age-related variation in body weight and morphometry of Maryland nutria

USGS Publications Warehouse

Sherfy, M.H.; Mollett, T.A.; McGowan, K.R.; Daugherty, S.L.

2006-01-01

Age-related variation in morphometry has been documented for many species. Knowledge of growth patterns can be useful for modeling energetics, detecting physiological influences on populations, and predicting age. These benefits have shown value in understanding population dynamics of invasive species, particularly in developing efficient control and eradication programs. However, development and evaluation of descriptive and predictive models is a critical initial step in this process. Accordingly, we used data from necropsies of 1,544 nutria (Myocastor coypus) collected in Maryland, USA, to evaluate the accuracy of previously published models for prediction of nutria age from body weight. Published models underestimated body weights of our animals, especially for ages <3. We used cross-validation procedures to develop and evaluate models for describing nutria growth patterns and for predicting nutria age. We derived models from a randomly selected model-building data set (n = 192-193 M, 217-222 F) and evaluated them with the remaining animals (n = 487-488 M, 642-647 F). We used nonlinear regression to develop Gompertz growth-curve models relating morphometric variables to age. Predicted values of morphometric variables fell within the 95% confidence limits of their true values for most age classes. We also developed predictive models for estimating nutria age from morphometry, using linear regression of log-transformed age on morphometric variables. The evaluation data set corresponded with 95% prediction intervals from the new models. Predictive models for body weight and length provided greater accuracy and less bias than models for foot length and axillary girth. Our growth models accurately described age-related variation in nutria morphometry, and our predictive models provided accurate estimates of ages from morphometry that will be useful for live-captured individuals. Our models offer better accuracy and precision than previously published models, providing a capacity for modeling energetics and growth patterns of Maryland nutria as well as an empirical basis for determining population age structure from live-captured animals.

Intensity Biased PSP Measurement

NASA Technical Reports Server (NTRS)

Subramanian, Chelakara S.; Amer, Tahani R.; Oglesby, Donald M.; Burkett, Cecil G., Jr.

2000-01-01

The current pressure sensitive paint (PSP) technique assumes a linear relationship (Stern-Volmer Equation) between intensity ratio (I(sub 0)/I) and pressure ratio (P/P(sub 0)) over a wide range of pressures (vacuum to ambient or higher). Although this may be valid for some PSPs, in most PSPs the relationship is nonlinear, particularly at low pressures (less than 0.2 psia when the oxygen level is low). This non-linearity can be attributed to variations in the oxygen quenching (de-activation) rates (which otherwise is assumed constant) at these pressures. Other studies suggest that some paints also have non-linear calibrations at high pressures; because of heterogeneous (non-uniform) oxygen diffusion and c quenching. Moreover, pressure sensitive paints require correction for the output intensity due to light intensity variation, paint coating variation, model dynamics, wind-off reference pressure variation, and temperature sensitivity. Therefore to minimize the measurement uncertainties due to these causes, an in- situ intensity correction method was developed. A non-oxygen quenched paint (which provides a constant intensity at all pressures, called non-pressure sensitive paint, NPSP) was used for the reference intensity (I(sub NPSP)) with respect to which all the PSP intensities (I) were measured. The results of this study show that in order to fully reap the benefits of this technique, a totally oxygen impermeable NPSP must be available.

Intensity Biased PSP Measurement

NASA Technical Reports Server (NTRS)

Subramanian, Chelakara S.; Amer, Tahani R.; Oglesby, Donald M.; Burkett, Cecil G., Jr.

2000-01-01

The current pressure sensitive paint (PSP) technique assumes a linear relationship (Stern-Volmer Equation) between intensity ratio (I(sub o)/I) and pressure ratio (P/P(sub o)) over a wide range of pressures (vacuum to ambient or higher). Although this may be valid for some PSPs, in most PSPs the relationship is nonlinear, particularly at low pressures (less than 0.2 psia when the oxygen level is low). This non-linearity can be attributed to variations in the oxygen quenching (de-activation) rates (which otherwise is assumed constant) at these pressures. Other studies suggest that some paints also have non-linear calibrations at high pressures; because of heterogeneous (non-uniform) oxygen diffusion and quenching. Moreover, pressure sensitive paints require correction for the output intensity due to light intensity variation, paint coating variation, model dynamics, wind-off reference pressure variation, and temperature sensitivity. Therefore to minimize the measurement uncertainties due to these causes, an insitu intensity correction method was developed. A non-oxygen quenched paint (which provides a constant intensity at all pressures, called non-pressure sensitive paint, NPSP) was used for the reference intensity (I(sub NPSP) with respect to which all the PSP intensities (I) were measured. The results of this study show that in order to fully reap the benefits of this technique, a totally oxygen impermeable NPSP must be available.

Multi-objective control of nonlinear boiler-turbine dynamics with actuator magnitude and rate constraints.

PubMed

Chen, Pang-Chia

2013-01-01

This paper investigates multi-objective controller design approaches for nonlinear boiler-turbine dynamics subject to actuator magnitude and rate constraints. System nonlinearity is handled by a suitable linear parameter varying system representation with drum pressure as the system varying parameter. Variation of the drum pressure is represented by suitable norm-bounded uncertainty and affine dependence on system matrices. Based on linear matrix inequality algorithms, the magnitude and rate constraints on the actuator and the deviations of fluid density and water level are formulated while the tracking abilities on the drum pressure and power output are optimized. Variation ranges of drum pressure and magnitude tracking commands are used as controller design parameters, determined according to the boiler-turbine's operation range. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

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

PubMed

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

2006-01-01

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

Nonlinear Real-Time Optical Signal Processing

DTIC Science & Technology

1990-09-01

pattern recognition. Additional work concerns the relationship of parallel computation paradigms to optical computing and halftone screen techniques...paradigms to optical computing and halftone screen techniques for implementing general nonlinear functions. 3\\ 2 Research Progress This section...Vol. 23, No. 8, pp. 34-57, 1986. 2.4 Nonlinear Optical Processing with Halftones : Degradation and Compen- sation Models This paper is concerned with

A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2012-01-01

A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.

A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2011-01-01

A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.

A new similarity index for nonlinear signal analysis based on local extrema patterns

NASA Astrophysics Data System (ADS)

Niknazar, Hamid; Motie Nasrabadi, Ali; Shamsollahi, Mohammad Bagher

2018-02-01

Common similarity measures of time domain signals such as cross-correlation and Symbolic Aggregate approximation (SAX) are not appropriate for nonlinear signal analysis. This is because of the high sensitivity of nonlinear systems to initial points. Therefore, a similarity measure for nonlinear signal analysis must be invariant to initial points and quantify the similarity by considering the main dynamics of signals. The statistical behavior of local extrema (SBLE) method was previously proposed to address this problem. The SBLE similarity index uses quantized amplitudes of local extrema to quantify the dynamical similarity of signals by considering patterns of sequential local extrema. By adding time information of local extrema as well as fuzzifying quantized values, this work proposes a new similarity index for nonlinear and long-term signal analysis, which extends the SBLE method. These new features provide more information about signals and reduce noise sensitivity by fuzzifying them. A number of practical tests were performed to demonstrate the ability of the method in nonlinear signal clustering and classification on synthetic data. In addition, epileptic seizure detection based on electroencephalography (EEG) signal processing was done by the proposed similarity to feature the potentials of the method as a real-world application tool.

COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

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

Sun, Y.; Borland, Michael

Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.

The Trail Less Traveled: Individual Decision-Making and Its Effect on Group Behavior

PubMed Central

Lanan, Michele C.; Dornhaus, Anna; Jones, Emily I.; Waser, Andrew; Bronstein, Judith L.

2012-01-01

Social insect colonies are complex systems in which the interactions of many individuals lead to colony-level collective behaviors such as foraging. However, the emergent properties of collective behaviors may not necessarily be adaptive. Here, we examine symmetry breaking, an emergent pattern exhibited by some social insects that can lead colonies to focus their foraging effort on only one of several available food patches. Symmetry breaking has been reported to occur in several ant species. However, it is not clear whether it arises as an unavoidable epiphenomenon of pheromone recruitment, or whether it is an adaptive behavior that can be controlled through modification of the individual behavior of workers. In this paper, we used a simulation model to test how symmetry breaking is affected by the degree of non-linearity of recruitment, the specific mechanism used by individuals to choose between patches, patch size, and forager number. The model shows that foraging intensity on different trails becomes increasingly asymmetric as the recruitment response of individuals varies from linear to highly non-linear, supporting the predictions of previous work. Surprisingly, we also found that the direction of the relationship between forager number (i.e., colony size) and asymmetry varied depending on the specific details of the decision rule used by individuals. Limiting the size of the resource produced a damping effect on asymmetry, but only at high forager numbers. Variation in the rule used by individual ants to choose trails is a likely mechanism that could cause variation among the foraging behaviors of species, and is a behavior upon which selection could act. PMID:23112880

Specificities of Acoustic Streaming in Cylindrical Cavity with Increasing Nonlinearity of the Process

NASA Astrophysics Data System (ADS)

Gubaidullin, A. A.; Pyatkova, A. V.

2018-01-01

This paper presents a numerical study of a gas acoustic streaming in a cylindrical cavity under a vibratory action. The walls of the cavity are considered impermeable and maintained at a constant temperature. The test gas is air. Variations in acoustic streaming and period-average temperature of the gas in the cavity with increasing nonlinearity of the process are shown. The increase in the nonlinearity is caused by an increase in the vibration amplitude.

Nonlinear dynamics in cardiac conduction

NASA Technical Reports Server (NTRS)

Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.

1988-01-01

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

Factoring in weather variation to capture the influence of urban design and built environment on globally recommended levels of moderate to vigorous physical activity in children.

PubMed

Katapally, Tarun Reddy; Rainham, Daniel; Muhajarine, Nazeem

2015-11-30

In curbing physical inactivity, as behavioural interventions directed at individuals have not produced a population-level change, an ecological perspective called active living research has gained prominence. However, active living research consistently underexplores the role played by a perennial phenomenon encompassing all other environmental exposures-variation in weather. After factoring in weather variation, this study investigated the influence of diverse environmental exposures (including urban design and built environment) on the accumulation of globally recommended moderate to vigorous physical activity levels (MVPA) in children. This cross-sectional observational study is part of an active living initiative set in the Canadian prairie city of Saskatoon. As part of this study, Saskatoon's neighbourhoods were classified based on urban street design into grid-pattern, fractured grid-pattern and curvilinear types of neighbourhoods. Moreover, diverse environmental exposures were measured including, neighbourhood built environment, and neighbourhood and household socioeconomic environment. Actical accelerometers were deployed between April and June 2010 (spring-summer) to derive MVPA of 331 10-14-year-old children in 25 1-week cycles. Each cycle of accelerometry was conducted on a different cohort of children within the total sample and matched with weather data obtained from Environment Canada. Multilevel modelling using Hierarchical Linear and Non-linear Modelling software was conducted by factoring in weather variation to depict the influence of diverse environmental exposures on the accumulation of recommended MVPA. Urban design, including diversity of destinations within neighbourhoods played a significant role in the accumulation of MVPA. After factoring in weather variation, it was observed that children living in neighbourhoods closer to the city centre (with higher diversity of destinations) were more likely to accumulate recommended MVPA. The findings indicate that after factoring in weather variation, certain types of urban design are more likely to be associated with MVPA accumulation. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Nonlocal nonlinear refraction in Hibiscus sabdariffa with large phase shifts.

PubMed

Ramírez-Martínez, D; Alvarado-Méndez, E; Trejo-Durán, M; Vázquez-Guevara, M A

2014-10-20

In this work we present a study of nonlinear optical properties in organic materials (hibiscus sabdariffa). Our results demonstrate that the medium exhibits a highly nonlocal nonlinear response. We show preliminary numerical results of the transmittance as nonlocal response by considering, simultaneously, the nonlinear absorption and refraction in media. Numerical results are accord to measurement obtained by Z- scan technique where we observe large phase shifts. We also analyze the far field diffraction ring patterns of the sample.

Variational methods in supersymmetric lattice field theory: The vacuum sector

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

Duncan, A.; Meyer-Ortmanns, H.; Roskies, R.

1987-12-15

The application of variational methods to the computation of the spectrum in supersymmetric lattice theories is considered, with special attention to O(N) supersymmetric sigma models. Substantial cancellations are found between bosonic and fermionic contributions even in approximate Ansa$uml: tze for the vacuum wave function. The nonlinear limit of the linear sigma model is studied in detail, and it is shown how to construct an appropriate non-Gaussian vacuum wave function for the nonlinear model. The vacuum energy is shown to be of order unity in lattice units in the latter case, after infinite cancellations.

The structural studies of vanadium substituted lithium-bismuth-boro-tellurite glass

NASA Astrophysics Data System (ADS)

Madhu, A.; Eraiah, B.

2018-05-01

The structural studies of vanadium substituted lithium-bismuth-boro-tellurite glass is successfully prepared and certain analysis like XRD,FTIR,DTA/TGA with density, molar volume are done. The amorphous phase has been identified based on X-ray diffraction analysis. The vanadium oxide plays the role as a glass-modifier and influences on BO3 ↔ BO4 conversion. The observed nonlinear variation in Tg with vanadium oxide increase, it reflects structural changes. The nonlinear variation of density and molar volume can be attributed to vanadium oxide incorporation have increased the number of Non-bridging oxygen (NBO'S).

Experimental quantification of nonlinear time scales in inertial wave rotating turbulence

NASA Astrophysics Data System (ADS)

Yarom, Ehud; Salhov, Alon; Sharon, Eran

2017-12-01

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

Employment, Production and Consumption model: Patterns of phase transitions

NASA Astrophysics Data System (ADS)

Lavička, H.; Lin, L.; Novotný, J.

2010-04-01

We have simulated the model of Employment, Production and Consumption (EPC) using Monte Carlo. The EPC model is an agent based model that mimics very basic rules of industrial economy. From the perspective of physics, the nature of the interactions in the EPC model represents multi-agent interactions where the relations among agents follow the key laws for circulation of capital and money. Monte Carlo simulations of the stochastic model reveal phase transition in the model economy. The two phases are the phase with full unemployment and the phase with nearly full employment. The economy switches between these two states suddenly as a reaction to a slight variation in the exogenous parameter, thus the system exhibits strong non-linear behavior as a response to the change of the exogenous parameters.

Double-wavelet approach to study frequency and amplitude modulation in renal autoregulation

NASA Astrophysics Data System (ADS)

Sosnovtseva, O. V.; Pavlov, A. N.; Mosekilde, E.; Holstein-Rathlou, N.-H.; Marsh, D. J.

2004-09-01

Biological time series often display complex oscillations with several interacting rhythmic components. Renal autoregulation, for instance, involves at least two separate mechanisms both of which can produce oscillatory variations in the pressures and flows of the individual nephrons. Using double-wavelet analysis we propose a method to examine how the instantaneous frequency and amplitude of a fast mode is modulated by the presence of a slower mode. Our method is applied both to experimental data from normotensive and hypertensive rats showing different oscillatory patterns and to simulation results obtained from a physiologically based model of the nephron pressure and flow control. We reveal a nonlinear interaction between the two mechanisms that regulate the renal blood flow in the form of frequency and amplitude modulation of the myogenic oscillations.

Design and Performance Investigation for the Optical Combinational Networks at High Data Rate

NASA Astrophysics Data System (ADS)

Tripathi, Devendra Kr.

2017-05-01

This article explores performance study for optical combinational designs based on nonlinear characteristics with semiconductor optical amplifier (SOA). Two configurations for optical half-adder with non-return-to-zero modulation pattern altogether with Mach-Zehnder modulator, interferometer at 50-Gbps data rate have been successfully realized. Accordingly, SUM and CARRY outputs have been concurrently executed and verified for their output waveforms. Numerical simulations for variation of data rate and key design parameters have been effectively executed outcome with optimum performance. Investigations depict overall good performance of the design in terms of the extinction factor. It also inferred that all-optical realization based on SOA is competent scheme, as it circumvents costly optoelectronic translation. This could be well supportive to erect larger complex optical combinational circuits.

Pattern formation based on complex coupling mechanism in dielectric barrier discharge

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

Liu, Weibo; College of Aeronautical Engineering, Binzhou University, Binzhou 256603; Dong, Lifang, E-mail: donglfhbu@163.com, E-mail: pyy1616@163.com

2016-08-15

The pattern formation of cinque-dice square superlattice pattern (CDSSP) is investigated based on the complex coupling mechanism in a dielectric barrier discharge (DBD) system. The spatio-temporal structure of CDSSP obtained by using an intensified-charge coupled device indicates that CDSSP is an interleaving of two kinds of subpatterns (mixture of rectangle and square, and dot-line square) which discharge twice in one half voltage, respectively. Selected by the complex coupling of two subpatterns, the CDSSP can be formed and shows good stability. This investigation based on gas discharge theory together with nonlinear theory may provide a deeper understanding for the nonlinear characteristicsmore » and even the formation mechanism of patterns in DBD.« less

A network model of successive partitioning-limited solute diffusion through the stratum corneum.

PubMed

Schumm, Phillip; Scoglio, Caterina M; van der Merwe, Deon

2010-02-07

As the most exposed point of contact with the external environment, the skin is an important barrier to many chemical exposures, including medications, potentially toxic chemicals and cosmetics. Traditional dermal absorption models treat the stratum corneum lipids as a homogenous medium through which solutes diffuse according to Fick's first law of diffusion. This approach does not explain non-linear absorption and irregular distribution patterns within the stratum corneum lipids as observed in experimental data. A network model, based on successive partitioning-limited solute diffusion through the stratum corneum, where the lipid structure is represented by a large, sparse, and regular network where nodes have variable characteristics, offers an alternative, efficient, and flexible approach to dermal absorption modeling that simulates non-linear absorption data patterns. Four model versions are presented: two linear models, which have unlimited node capacities, and two non-linear models, which have limited node capacities. The non-linear model outputs produce absorption to dose relationships that can be best characterized quantitatively by using power equations, similar to the equations used to describe non-linear experimental data.

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

NASA Astrophysics Data System (ADS)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

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

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

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

2010-07-15

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

On the Effect of Variability on Fermi, Pasta and Ulam Matrices

NASA Astrophysics Data System (ADS)

Nelson, Heather; Choubey, Bhaskar

The first numerical experiment by Fermi, Pasta, Ulam and Tsingou in 1955 observed recurrence in an array of non-linear systems. This has led to a large number of nonlinear numerical experiments with various new results from a chain of ideal oscillators. FPUT arrays consists of linear oscillators connected nonlinearly which leads to recurrence of energy mode with time. However, if such a system were to be physically constructed, inherent process variations would introduce a manufacturing tolerance into the parameters of the system. This abstract reports investigation into the effects of these tolerances on the FPU matrices. It has been observed that tolerance in the oscillators can degrade the observance of recurrence and with a chain of even 64 oscillators, recurrence cannot be observed with tolerances more than 10%. It has also been observed that linear oscillators tolerances have more effects on recurrence than those of the nonlinear coupling. Even with very small tolerances of +/- 1% on the linear components, one start to observe variations in the quality and magnitude of the recurrence and at +/- 5%, recurrence is starting to break down.

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

NASA Technical Reports Server (NTRS)

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

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

PubMed Central

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

2016-01-01

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

Improved physiologically based pharmacokinetic model for oral exposures to chromium in mice, rats, and humans to address temporal variation and sensitive populations

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

Kirman, C.R., E-mail: ckirman@summittoxicology.com

A physiologically based pharmacokinetic (PBPK) model for hexavalent chromium [Cr(VI)] in mice, rats, and humans developed previously (Kirman et al., 2012, 2013), was updated to reflect an improved understanding of the toxicokinetics of the gastrointestinal tract following oral exposures. Improvements were made to: (1) the reduction model, which describes the pH-dependent reduction of Cr(VI) to Cr(III) in the gastrointestinal tract under both fasted and fed states; (2) drinking water pattern simulations, to better describe dosimetry in rodents under the conditions of the NTP cancer bioassay; and (3) parameterize the model to characterize potentially sensitive human populations. Important species differences, sourcesmore » of non-linear toxicokinetics, and human variation are identified and discussed within the context of human health risk assessment. - Highlights: • An improved version of the PBPK model for Cr(VI) toxicokinetics was developed. • The model incorporates data collected to fill important data gaps. • Model predictions for specific age groups and sensitive subpopulations are provided. • Implications to human health risk assessment are discussed.« less

Rogue-wave pattern transition induced by relative frequency.

PubMed

Zhao, Li-Chen; Xin, Guo-Guo; Yang, Zhan-Ying

2014-08-01

We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution. Furthermore, spectrum analysis is performed on these different type rogue waves, and the spectrum relations between them are discussed. We demonstrate qualitatively that different modulation instability gain distribution can induce different rogue wave excitation patterns. These results would deepen our understanding of rogue wave dynamics in complex systems.

New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations

NASA Astrophysics Data System (ADS)

Yan, Zhenya; Bluman, George

2002-11-01

The special exact solutions of nonlinearly dispersive Boussinesq equations (called B( m, n) equations), utt- uxx- a( un) xx+ b( um) xxxx=0, is investigated by using four direct ansatze. As a result, abundant new compactons: solitons with the absence of infinite wings, solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions of these two equations are obtained. The variant is extended to include linear dispersion to support compactons and solitary patterns in the linearly dispersive Boussinesq equations with m=1. Moreover, another new compacton solution of the special case, B(2,2) equation, is also found.

Nonlinear instability of half-solitons on star graphs

NASA Astrophysics Data System (ADS)

Kairzhan, Adilbek; Pelinovsky, Dmitry E.

2018-06-01

We consider a half-soliton stationary state of the nonlinear Schrödinger equation with the power nonlinearity on a star graph consisting of N edges and a single vertex. For the subcritical power nonlinearity, the half-soliton state is a degenerate critical point of the action functional under the mass constraint such that the second variation is nonnegative. By using normal forms, we prove that the degenerate critical point is a saddle point, for which the small perturbations to the half-soliton state grow slowly in time resulting in the nonlinear instability of the half-soliton state. The result holds for any N ≥ 3 and arbitrary subcritical power nonlinearity. It gives a precise dynamical characterization of the previous result of Adami et al. (2012) [2], where the half-soliton state was shown to be a saddle point of the action functional under the mass constraint for N = 3 and for cubic nonlinearity.

Optical Pattern Recognition

NASA Astrophysics Data System (ADS)

Yu, Francis T. S.; Jutamulia, Suganda

2008-10-01

Contributors; Preface; 1. Pattern recognition with optics Francis T. S. Yu and Don A. Gregory; 2. Hybrid neural networks for nonlinear pattern recognition Taiwei Lu; 3. Wavelets, optics, and pattern recognition Yao Li and Yunglong Sheng; 4. Applications of the fractional Fourier transform to optical pattern recognition David Mendlovic, Zeev Zalesky and Haldum M. Oxaktas; 5. Optical implementation of mathematical morphology Tien-Hsin Chao; 6. Nonlinear optical correlators with improved discrimination capability for object location and recognition Leonid P. Yaroslavsky; 7. Distortion-invariant quadratic filters Gregory Gheen; 8. Composite filter synthesis as applied to pattern recognition Shizhou Yin and Guowen Lu; 9. Iterative procedures in electro-optical pattern recognition Joseph Shamir; 10. Optoelectronic hybrid system for three-dimensional object pattern recognition Guoguang Mu, Mingzhe Lu and Ying Sun; 11. Applications of photrefractive devices in optical pattern recognition Ziangyang Yang; 12. Optical pattern recognition with microlasers Eung-Gi Paek; 13. Optical properties and applications of bacteriorhodopsin Q. Wang Song and Yu-He Zhang; 14. Liquid-crystal spatial light modulators Aris Tanone and Suganda Jutamulia; 15. Representations of fully complex functions on real-time spatial light modulators Robert W. Cohn and Laurence G. Hassbrook; Index.

Study of large nonlinear change phase in Hibiscus Sabdariffa

NASA Astrophysics Data System (ADS)

Trejo-Durán, M.; Alvarado-Méndez, E.; Andrade-Lucio, J. A.; Rojas-Laguna, R.; Vázquez-Guevara, M. A.

2015-09-01

High intensities electromagnetic energy interacting with organic media gives rise to nonlinear optical effects. Hibiscus Sabdariffa is a flower whose concentrated solution presents interesting nonlinear optical properties. This organic material shows an important self-phase modulation with changes bigger than 2π. We present a diffraction ring patterns study of the Hibiscus Sabdariffa solution. Numerical results of transmittance, with refraction and simultaneous absorption, are shown.

The local, remote, and global consequences of climate feedbacks

NASA Astrophysics Data System (ADS)

Feldl, Nicole

Climate feedbacks offer a powerful framework for revealing the energetic pathways by which the system adjusts to an imposed forcing, such as an increase in atmospheric CO2. We investigate how local atmospheric feedbacks, such as those associated with Arctic sea ice and the Walker circulation, affect both global climate sensitivity and spatial patterns of warming. Emphasis is placed on a general circulation model with idealized boundary conditions, for the clarity it provides. For this aquaplanet simulation, we account for rapid tropospheric adjustments to CO2 and explicitly diagnose feedbacks (using radiative kernels) and forcing for this precise model set-up. In particular, a detailed closure of the energy budget within a clean experimental set-up allows us to consider nonlinear interactions between feedbacks. The inclusion of a tropical Walker circulation is found to prime the Hadley Circulation for a larger deceleration under CO2 doubling, by altering subtropical stratus decks and the meridional feedback gradient. We perform targeted experiments to isolate the atmospheric processes responsible for the variability in climate sensitivity, with implications for high-sensitivity paleoclimates. The local climate response is characterized in terms of the meridional structure of feedbacks, atmospheric heat transport, nonlinearities, and forcing. Our results display a combination of positive subtropical feedbacks and polar amplified warming. These two factors imply a critical role for transport and nonlinear effects, with the latter acting to substantially reduce global climate sensitivity. At the hemispheric scale, a rich picture emerges: anomalous divergence of heat flux away from positive feedbacks in the subtropics; clear-sky nonlinearities that reinforce the pattern of tropical cooling and high-latitude warming tendencies; and strong ice-line feedbacks that drive further amplification of polar warming. These results have implications for regional climate predictability, by providing an indication of how spatial patterns in feedbacks combine to affect both the local and nonlocal climate response, and how constraining uncertainty in those feedbacks may constrain the climate response. We also consider how competing definitions of feedbacks influence interpretation of climate sensitivity. While climate feedbacks represent a convenient breakdown of the energy balance, their widespread appeal has led to a profusion of definitions, and to variations upon the traditional decomposition. We demonstrate that a locally defined feedback framework does provide several advantages from the perspective of regional climate predictability. Namely, it enables a partial temperature change analysis which quantifies contributions to spatial patterns of warming; it also ensures feedbacks are not biased at high latitudes due to polar amplification. Alternative approaches to characterizing feedbacks can also isolate and illuminate different atmospheric processes. In particular, comparison of two versions of the water vapor feedback, one focused on specific humidity and the other on relative humidity, allows for an elegant dissection of the relative importance of thermodynamical and dynamical changes in a warmer world.

Strongly nonlinear parabolic variational inequalities.

PubMed

Browder, F E; Brézis, H

1980-02-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form partial differentialu/ partial differentialt + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications.

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

NASA Astrophysics Data System (ADS)

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

2008-04-01

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

Automatic Assessment and Reduction of Noise using Edge Pattern Analysis in Non-Linear Image Enhancement

NASA Technical Reports Server (NTRS)

Jobson, Daniel J.; Rahman, Zia-Ur; Woodell, Glenn A.; Hines, Glenn D.

2004-01-01

Noise is the primary visibility limit in the process of non-linear image enhancement, and is no longer a statistically stable additive noise in the post-enhancement image. Therefore novel approaches are needed to both assess and reduce spatially variable noise at this stage in overall image processing. Here we will examine the use of edge pattern analysis both for automatic assessment of spatially variable noise and as a foundation for new noise reduction methods.

Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Assessing non-linear variation of temperature and precipitation for different growth periods of maize and their impacts on phenology in the Midwest of Jilin Province, China

NASA Astrophysics Data System (ADS)

Guo, Enliang; Zhang, Jiquan; Wang, Yongfang; Alu, Si; Wang, Rui; Li, Danjun; Ha, Si

2018-05-01

In the past two decades, the regional climate in China has undergone significant change, resulting in crop yield reduction and complete failure. The goal of this study is to detect the variation of temperature and precipitation for different growth periods of maize and assess their impact on phenology. The daily meteorological data in the Midwest of Jilin Province during 1960-2014 were used in the study. The ensemble empirical mode decomposition method was adopted to analyze the non-linear trend and fluctuation in temperature and precipitation, and the sensitivity of the length of the maize growth period to temperature and precipitation was analyzed by the wavelet cross-transformation method. The results show that the trends of temperature and precipitation change are non-linear for different growth periods of maize, and the average temperature in the sowing-jointing stage was different from that in the other growth stages, showing a slight decrease trend, while the variation amplitude of maximum temperature is smaller than that of the minimum temperature. This indicates that the temperature difference between day and night shows a gradually decreasing trend. Precipitation in the growth period also showed a decreasing non-linear trend, while the inter-annual variability with period of quasi-3-year and quasi-6-year dominated the variation of temperature and precipitation. The whole growth period was shortened by 10.7 days, and the sowing date was advanced by approximately 11 days. We also found that there was a significant resonance period among temperature, precipitation, and phenology. Overall, a negative correlation between phenology and temperature is evident, while a positive correlation with precipitation is exhibited. The results illustrate that the climate suitability for maize has reduced over the past decades.

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.

Spectral characterization of a supercontinuum source based on nonlinear broadening in an aqueous K_2ZnCl_4 salt solution

DOE PAGES

Robinson, Timothy S.; Patankar, Siddharth; Floyd, Emma; ...

2017-01-01

We report on investigations concerning the shot-to-shot spectral stability properties of a supercontinuum source based on nonlinear processes such as self-phase modulation and optical wave-breaking in a highly concentrated K 2ZnCl 4 double salt solution. The use of a liquid medium offers both damage resistance and high third-order optical nonlinearity. Approximately 40 μJ pulses spanning a spectral range between 390 and 960 nm were produced with 3.8% RMS energy stability, using infrared input pulses of 500±50 fs FWHM durations and 2.42±0.04 mJ energies with an RMS stability of 2%. The spectral stability was quantified via acquiring single-shot spectra and studyingmore » shot-to-shot variation across a spectral range of 200–1100 nm, as well as by considering spectral correlations. The regional spectral correlation variations were indicative of nonlinear processes leading to sideband generation. Spectral stability and efficiency of energy transfer into the supercontinuum were found to weakly improve with increasing driver pulse energy, suggesting that the nonlinear broadening processes are more stable when driven more strongly, or that self-guiding effects in a filament help to stabilize the supercontinuum generation.« less

Spectral characterization of a supercontinuum source based on nonlinear broadening in an aqueous K_2ZnCl_4 salt solution

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

Robinson, Timothy S.; Patankar, Siddharth; Floyd, Emma

We report on investigations concerning the shot-to-shot spectral stability properties of a supercontinuum source based on nonlinear processes such as self-phase modulation and optical wave-breaking in a highly concentrated K 2ZnCl 4 double salt solution. The use of a liquid medium offers both damage resistance and high third-order optical nonlinearity. Approximately 40 μJ pulses spanning a spectral range between 390 and 960 nm were produced with 3.8% RMS energy stability, using infrared input pulses of 500±50 fs FWHM durations and 2.42±0.04 mJ energies with an RMS stability of 2%. The spectral stability was quantified via acquiring single-shot spectra and studyingmore » shot-to-shot variation across a spectral range of 200–1100 nm, as well as by considering spectral correlations. The regional spectral correlation variations were indicative of nonlinear processes leading to sideband generation. Spectral stability and efficiency of energy transfer into the supercontinuum were found to weakly improve with increasing driver pulse energy, suggesting that the nonlinear broadening processes are more stable when driven more strongly, or that self-guiding effects in a filament help to stabilize the supercontinuum generation.« less

Nonlinear Dynamics and Bifurcation Analysis of a Boost Converter for Battery Charging in Photovoltaic Applications

NASA Astrophysics Data System (ADS)

Al-Hindawi, Mohammed M.; Abusorrah, Abdullah; Al-Turki, Yusuf; Giaouris, Damian; Mandal, Kuntal; Banerjee, Soumitro

Photovoltaic (PV) systems with a battery back-up form an integral part of distributed generation systems and therefore have recently attracted a lot of interest. In this paper, we consider a system of charging a battery from a PV panel through a current mode controlled boost dc-dc converter. We analyze its complete nonlinear/nonsmooth dynamics, using a piecewise model of the converter and realistic nonlinear v-i characteristics of the PV panel. Through this study, it is revealed that system design without taking into account the nonsmooth dynamics of the converter combined with the nonlinear v-i characteristics of the PV panel can lead to unpredictable responses of the overall system with high current ripple and other undesirable phenomena. This analysis can lead to better designed converters that can operate under a wide variation of the solar irradiation and the battery's state of charge. We show that the v-i characteristics of the PV panel combined with the battery's output voltage variation can increase or decrease the converter's robustness, both under peak current mode control and average current mode control. We justify the observation in terms of the change in the discrete-time map caused by the nonlinear v-i characteristics of the PV panel. The theoretical results are validated experimentally.

Model reduction and frequency residuals for a robust estimation of nonlinearities in subspace identification

NASA Astrophysics Data System (ADS)

De Filippis, G.; Noël, J. P.; Kerschen, G.; Soria, L.; Stephan, C.

2017-09-01

The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 constitutes one in a series of recent attempts toward developing a realistic, first-generation framework applicable to complex structures. If this method showed promising capabilities when applied to academic structures, it is still confronted with a number of limitations which needs to be addressed. In particular, the removal of nonphysical poles in the identified nonlinear models is a distinct challenge. In the present paper, it is proposed as a first contribution to operate directly on the identified state-space matrices to carry out spurious pole removal. A modal-space decomposition of the state and output matrices is examined to discriminate genuine from numerical poles, prior to estimating the extended input and feedthrough matrices. The final state-space model thus contains physical information only and naturally leads to nonlinear coefficients free of spurious variations. Besides spurious variations due to nonphysical poles, vibration modes lying outside the frequency band of interest may also produce drifts of the nonlinear coefficients. The second contribution of the paper is to include residual terms, accounting for the existence of these modes. The proposed improved FNSI methodology is validated numerically and experimentally using a full-scale structure, the Morane-Saulnier Paris aircraft.

Numerical assessment of factors affecting nonlinear internal waves in the South China Sea

NASA Astrophysics Data System (ADS)

Li, Qiang

2014-02-01

Nonlinear internal waves in the South China Sea exhibit diverse characteristics, which are associated with the complex conditions in Luzon Strait, such as the double ridge topography, the Earth’s rotation, variations in stratification and the background current induced by the Kuroshio. These effects are individually assessed using the MITgcm. The performance of the model is first validated through comparison with field observations. Because of in-phased ray interaction, the western ridge in Luzon Strait intensifies the semidiurnal internal tides generated from the eastern ridge, thus reinforcing the formation of nonlinear internal waves. However, the ray interaction for K1 forcing becomes anti-phased so that the K1 internal tide generation is reduced by the western ridge. Not only does the rotational dispersion suppress internal tide generation, it also inhibits nonlinear steepening and consequent internal solitary wave formation. As a joint effect, the double ridges and the rotational dispersion result in a paradoxical phenomenon: diurnal barotropic tidal forcing is dominant in Luzon Strait, but semidiurnal internal tides prevail in the deep basin of the South China Sea. The seasonal variation of the Kuroshio is consistent with the seasonal appearance of nonlinear internal waves in the South China Sea. The model results show that the westward inflow due to the Kuroshio intrusion reduces the amplitude of internal tides in the South China Sea, causing the weakening or absence of internal solitary waves. Winter stratification cannot account for the significant reduction of nonlinear internal waves, because the amplitude growth of internal tides due to increased thermocline tilting counteracts the reduced nonlinearity caused by thermocline deepening.

Variational symmetries, conserved quantities and identities for several equations of mathematical physics

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

Donchev, Veliko, E-mail: velikod@ie.bas.bg

2014-03-15

We find variational symmetries, conserved quantities and identities for several equations: envelope equation, Böcher equation, the propagation of sound waves with losses, flow of a gas with losses, and the nonlinear Schrödinger equation with losses or gains, and an electro-magnetic interaction. Most of these equations do not have a variational description with the classical variational principle and we find such a description with the generalized variational principle of Herglotz.

Semiquantitative color profiling of soils over a land degradation gradient in Sakaerat, Thailand.

PubMed

Doi, Ryoichi; Wachrinrat, Chongrak; Teejuntuk, Sakhan; Sakurai, Katsutoshi; Sahunalu, Pongsak

2010-11-01

In this study, we attempted multivariate color profiling of soils over a land degradation gradient represented by dry evergreen forest (original vegetation), dry deciduous forest (moderately disturbed by fire), and bare ground (severely degraded) in Sakaerat, Thailand. The soils were sampled in a dry-to-wet seasonal transition. Values of the red-green-blue (RGB), cyan-magenta-yellow-key black (CMYK), L*a*b*, and hue-intensity-saturation (HIS) color models were determined using the digital software Adobe Photoshop. Land degradation produced significant variations (p<0.05) in R, C, Y, L*, a*, b*, S, and I values (p<0.05). The seasonal transition produced significant variations (p<0.05) in R, G, B, C, M, K, L*, b*, and I values. In discriminating the soils, the color models did not differ in discriminatory power, while discriminatory power was affected by seasonal changes. Most color variation patterns had nonlinear relationships with the intensity of the land degradation gradient, due to effects of fire that darkened the deciduous forest soil, masking the nature of the soil as the intermediate between the evergreen forest and the bare ground soils. Taking these findings into account, the utilization of color profiling of soils in land conservation and rehabilitation is discussed.

Nonlinear Dynamics, Noise and Cooperative Behavior in Affective Disorders

NASA Astrophysics Data System (ADS)

Huber, Martin

2001-03-01

Mood disorders tend to be recurrent and progressive and illness patterns typically evolve from isolated episodes at the beginning to more rapid, rhythmic and finally irregular "chaotic" mood patterns. This chararacteristic timecourse prompted the consideration of nonlinear dynamics as a way to describe and analyze course and disease states of mood disorders. Indeed, some evidences now exist indicating that low-dimensional dynamics underly the illness progression. To gain an understanding of prinicple mechanisms that might underly the course and disease patterns of mood disorders, we developed a phenomenological mathematical model for the disease course. In doing so, we made use of a neuronal analogy that exists between disease patterns and neuronal spike patterns and which is commonly referred to as the kindling model of mood disorders (Post, Am J of Psychiatry 1992,149:999-1010; Huber, Braun, Krieg, Biol Psychiatry 1999,46:256-262; Huber, Braun, Krieg, Biol Psychiatry 2000,47:634-642). Using a computational implementation of this approach we investigated the possible relevance of nonlinear dynamics for the disease course, the role of cooperative interactions between nonlinear and noisy dynamics as well as the effect of sensitization mechanisms between disease episodes and disease system. Our simulations show that a low-dimensional model can phenomenologically map the timecourse of mood disorders. From a functional perspective, the model indicates an important role for stochastic fluctuations which can amplify subthreshold states into disease states and can induce transitions to irregular rapidly changing disease patterns. Interesting dynamics are observed with respect to deterministically defined disease states and their dependence on noise intensity. Finally, our simulations show how sensitization effects quite naturally lead to a disease course which ends in irregular fluctuating disease patterns as observed in clinical data. Our findings indicate the usefulness of a computational approach as a way to understand and explain the complexity of temporal disease dynamics of mood disorders but also to procede to new experimental approaches for disease characterisation with the aim of better treatment options.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

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

Linear and nonlinear subspace analysis of hand movements during grasping.

PubMed

Cui, Phil Hengjun; Visell, Yon

2014-01-01

This study investigated nonlinear patterns of coordination, or synergies, underlying whole-hand grasping kinematics. Prior research has shed considerable light on roles played by such coordinated degrees-of-freedom (DOF), illuminating how motor control is facilitated by structural and functional specializations in the brain, peripheral nervous system, and musculoskeletal system. However, existing analyses suppose that the patterns of coordination can be captured by means of linear analyses, as linear combinations of nominally independent DOF. In contrast, hand kinematics is itself highly nonlinear in nature. To address this discrepancy, we sought to to determine whether nonlinear synergies might serve to more accurately and efficiently explain human grasping kinematics than is possible with linear analyses. We analyzed motion capture data acquired from the hands of individuals as they grasped an array of common objects, using four of the most widely used linear and nonlinear dimensionality reduction algorithms. We compared the results using a recently developed algorithm-agnostic quality measure, which enabled us to assess the quality of the dimensional reductions that resulted by assessing the extent to which local neighborhood information in the data was preserved. Although qualitative inspection of this data suggested that nonlinear correlations between kinematic variables were present, we found that linear modeling, in the form of Principle Components Analysis, could perform better than any of the nonlinear techniques we applied.

The Sap Flow Dynamics and Response of Hedysarum scoparium to Environmental Factors in Semiarid Northwestern China.

PubMed

Deng, Jifeng; Ding, Guodong; Gao, Guanglei; Wu, Bin; Zhang, Yuqing; Qin, Shugao; Fan, Wenhui

2015-01-01

Hedysarum scoparium is an important, fast-growing and drought-resistant shrub that has been extensively used for grassland restoration and preventing desertification in semiarid regions of northwestern China. The primary objective of this study was to investigate the diurnal and seasonal variations in stem sap flow (Js) and its relation to environmental factors. The stem heat balance method was applied to plants that were approximately 17 years old (with diameters of 25, 16, 13, and 9 mm at ground level and heights of 3.1, 1.8, 1.7 and 1.4 m) and growing under natural conditions. The vertical soil temperature profile (ST), soil surface heat flux (SoilG), volumetric soil moisture content (SWC) and meteorological variables such as solar radiation (Rn), air temperature (Ta), vapour pressure deficit (VPD), wind speed (Ws) relative humidity (RH) and precipitation (P) were simultaneously measured at a meteorological station on site. Results indicated that Js varied regularly during the diurnal and seasonal term. The nocturnal Js was substantial, with a seasonal variation similar to the patterns of daytime Js. The magnitude of Js changed considerably between sunny and rainy days. Redundancy (RDA) and Kendall's tau analysis suggested that daily Js in large plants was more sensitive to environmental factors, and the variation in daily Js during the growing season could be described by a multiple linear regression against environmental variables including Ta, VPD, Ws, RH, ST, and SoilG. While the nocturnal Js in smaller plants was more sensitive to meteorological factors. Ta, VPD, and Ws were significantly correlated with nighttime Js. The hourly nighttime sap flow rate of H. scoparium corresponded closely to Ta and VPD following a non-linear pattern. The results of this study can be used to estimate the transpiration of H. scoparium.

Nonlinear Insolation Forcing: A Physical Mechanism for Climate Change

NASA Technical Reports Server (NTRS)

Liu, H. S.

1998-01-01

This paper focuses on recent advances in the understanding of nonlinear insolation forcing for climate change. The amplitude-frequency resonances in the insolation variations induced by the Earth's changing obliquity are emergent and may provide a physical mechanism to drive the glaciation cycles. To establish the criterion that nonlinear insolation forcing is responsible for major climate changes, the cooperative phenomena between the frequency and amplitude of the insolation are defined as insolation pulsation. Coupling of the insolation frequency and amplitude variations has established an especially new and interesting series of insolation pulses. These pulses would modulate the insolation in such a way that the mode of insolation variations could be locked to generate the 100-kyr ice age cycle which is a long-time geophysical puzzle. The nonlinear behavior of insolation forcing is tested by energy balance and ice sheet climate models and the physical mechanism behind this forcing is explained in terms of pulse duration in the incoming solar radiation. Calculations of the solar energy flux at the top of the atmosphere show that the duration of the negative and positive insolation pulses is about 2 thousand years which is long enough to prolong glaciation into deep ice ages and cause rapid melting of large ice sheets in the high latitudes of the northern hemisphere. We have performed numerical simulations of climate response to nonlinear insolation forcing for the past 2 million years. Our calculated results of temperature fluctuations are in good agreement with the climate cycles as seen in the terrestrial biogenic silica (BDP-96-2) data as well as in the marine oxygen isotope (delta(sup 18)O) records.

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

Induced polarization: Simulation and inversion of nonlinear mineral electrodics

NASA Astrophysics Data System (ADS)

Agunloye, Olu

1983-02-01

Graph-theoretic representations are used to model nonlinear electrodics, while forward and inverse simulations are based on reaction rate theory. The electrodic responses are presented as distorted elliptical Lissajous shapes obtained from dynamic impedance over a full cycle. Simulations show that asymmetry in reaction energy barrier causes slight asymmetry in the shape of the response ellipse and hardly affects the phase angle of the complex electrode impedance. The charge transfer resistance and the diffusion constraints tend to have opposite effects. The former causes reduction in the phase angle, tending to make the impedance purely resistive. Both of these mechanisms show saturation effects. Charge transfer resistance at its limit forces a thin S-type symmetry on the Lissajous patterns, while with diffusion control the size of the Lissajous patterns begins to reduce after saturation. The fixed layer causes substantial increase in the phase angle and tends to “enlarge” the Lissajous patterns. It is responsible for the hysteresis-like shapes of the Lissajous patterns when superimposed on strong charge transfer resistance. This study shows that it is quite possible to deduce the mechanisms that control the electrodic processes by inverting electrodic parameters from “observed” distorted, nonelliptical Lissajous patterns characteristic of nonlinear electrodics. The results and qualities of the inversion technique are discussed.

Theoretical and Analog Studies of the Effects of Nonlinear Stability Derivatives on the Longitudinal Motions of an Aircraft in Response to Step Control Deflections and to the Influence of Proportional Automatic Control

NASA Technical Reports Server (NTRS)

Curfman, Howard J , Jr

1955-01-01

Through theoretical and analog results the effects of two nonlinear stability derivatives on the longitudinal motions of an aircraft have been investigated. Nonlinear functions of pitching-moment and lift coefficients with angle of attack were considered. Analog results of aircraft motions in response to step elevator deflections and to the action of the proportional control systems are presented. The occurrence of continuous hunting oscillations was predicted and demonstrated for the attitude stabilization system with proportional control for certain nonlinear pitching-moment variations and autopilot adjustments.

Some effects of nonlinear variation in the directional-stability and damping-in-yawing derivatives on the lateral stability of an airplane

NASA Technical Reports Server (NTRS)

Sternfield, Leonard

1951-01-01

A theoretical investigation has been made to determine the effect of nonlinear stability derivatives on the lateral stability of an airplane. Motions were calculated on the assumption that the directional-stability and the damping-in-yawing derivatives are functions of the angle of sideslip. The application of the Laplace transform to the calculation of an airplane motion when certain types of nonlinear derivatives are present is described in detail. The types of nonlinearities assumed correspond to the condition in which the values of the directional-stability and damping-in-yawing derivatives are zero for small angle of sideslip.

Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

Wakano, Joe Yuichiro; Komoto, Atsushi; Yamaguchi, Yukio

2004-05-01

Depending on the growth condition, bacterial colonies can exhibit different morphologies. Many previous studies have used reaction diffusion equations to reproduce spatial patterns. They have revealed that nonlinear reaction term can produce diverse patterns as well as nonlinear diffusion coefficient. Typical reaction term consists of nutrient consumption, bacterial reproduction, and sporulation. Among them, the functional form of sporulation rate has not been biologically investigated. Here we report experimentally measured sporulation rate. Then, based on the result, a reaction diffusion model is proposed. One-dimensional simulation showed the existence of traveling wave solution. We study the wave form as a function of the initial nutrient concentration and find two distinct types of solution. Moreover, transition between them is very sharp, which is analogous to phase transition. The velocity of traveling wave also shows sharp transition in nonlinear diffusion model, which is consistent with the previous experimental result. The phenomenon can be explained by separatrix in reaction term dynamics. Results of two-dimensional simulation are also shown and discussed.

The periodic structure of the natural record, and nonlinear dynamics.

USGS Publications Warehouse

Shaw, H.R.

1987-01-01

This paper addresses how nonlinear dynamics can contribute to interpretations of the geologic record and evolutionary processes. Background is given to explain why nonlinear concepts are important. A resume of personal research is offered to illustrate why I think nonlinear processes fit with observations on geological and cosmological time series data. The fabric of universal periodicity arrays generated by nonlinear processes is illustrated by means of a simple computer mode. I conclude with implications concerning patterns of evolution, stratigraphic boundary events, and close correlations of major geologically instantaneous events (such as impacts or massive volcanic episodes) with any sharply defined boundary in the geologic column. - from Author

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

Spectral Study of Measles Epidemics: The Dependence of Spectral Gradient on the Population Size of the Community

NASA Astrophysics Data System (ADS)

Sumi, Ayako; Olsen, Lars Folke; Ohtomo, Norio; Tanaka, Yukio; Sawamura, Sadashi

2003-02-01

We have carried out spectral analysis of measles notifications in several communities in Denmark, UK and USA. The results confirm that each power spectral density (PSD) shows exponential characteristics, which are universally observed in the PSD for time series generated from nonlinear dynamical system. The exponential gradient increases with the population size. For almost all communities, many spectral lines observed in each PSD can be fully assigned to linear combinations of several fundamental periods, suggesting that the measles data are substantially noise-free. The optimum least squares fitting curve calculated using these fundamental periods essentially reproduces an underlying variation of the measles data, and an extension of the curve can be used to predict measles epidemics. For the communities with large population sizes, some PSD patterns obtained from segment time series analysis show a close resemblance to the PSD patterns at the initial stages of a period-doubling bifurcation process for the so-called susceptible/exposed/infectious/recovered (SEIR) model with seasonal forcing. The meaning of the relationship between the exponential gradient and the population size is discussed.

Hele-Shaw scaling properties of low-contrast Saffman-Taylor flows

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

DiFrancesco, M. W.; Maher, J. V.

1989-07-01

We have measured variations of Saffman-Taylor flows by changingdimensionless surface tension /ital B/ alone and by changing /ital B/ inconjunction with changes in dimensionless viscosity contrast /ital A/. Ourlow-aspect-ratio cell permits close study of the linear- and earlynonlinear-flow regimes. Our critical binary-liquid sample allows study of verylow values of /ital A/. The predictions of linear stability analysis work wellfor predicting which length scales are important, but discrepancies areobserved for growth rates. We observe an empirical scaling law for growth ofthe Fourier modes of the patterns in the linear regime. The observed frontpropagation velocity for side-wall disturbances is constantly 2+-1in dimensionlessmore » units, a value consistent with the predictions of Langer andof van Saarloos. Patterns in both the linear and nonlinear regimes collapseimpressively under the scaling suggested by the Hele-Shaw equations. Violationsof scaling due to wetting phenomena are not evident here, presumably becausethe wetting properties of the two phases of the critical binary liquid are sosimilar; thus direct comparison with large-scale Hele-Shaw simulations shouldbe meaningful.« less

Streamflow prediction using multi-site rainfall obtained from hydroclimatic teleconnection

NASA Astrophysics Data System (ADS)

Kashid, S. S.; Ghosh, Subimal; Maity, Rajib

2010-12-01

SummarySimultaneous variations in weather and climate over widely separated regions are commonly known as "hydroclimatic teleconnections". Rainfall and runoff patterns, over continents, are found to be significantly teleconnected, with large-scale circulation patterns, through such hydroclimatic teleconnections. Though such teleconnections exist in nature, it is very difficult to model them, due to their inherent complexity. Statistical techniques and Artificial Intelligence (AI) tools gain popularity in modeling hydroclimatic teleconnection, based on their ability, in capturing the complicated relationship between the predictors (e.g. sea surface temperatures) and predictand (e.g., rainfall). Genetic Programming is such an AI tool, which is capable of capturing nonlinear relationship, between predictor and predictand, due to its flexible functional structure. In the present study, gridded multi-site weekly rainfall is predicted from El Niño Southern Oscillation (ENSO) indices, Equatorial Indian Ocean Oscillation (EQUINOO) indices, Outgoing Longwave Radiation (OLR) and lag rainfall at grid points, over the catchment, using Genetic Programming. The predicted rainfall is further used in a Genetic Programming model to predict streamflows. The model is applied for weekly forecasting of streamflow in Mahanadi River, India, and satisfactory performance is observed.

Comparison of line shortening assessed by aerial image and wafer measurements

NASA Astrophysics Data System (ADS)

Ziegler, Wolfram; Pforr, Rainer; Thiele, Joerg; Maurer, Wilhelm

1997-02-01

Increasing number of patterns per area and decreasing linewidth demand enhancement technologies for optical lithography. OPC, the correction of systematic non-linearity in the pattern transfer process by correction of design data is one possibility to tighten process control and to increase the lifetime of existing lithographic equipment. The two most prominent proximity effects to be corrected by OPC are CD variation and line shortening. Line shortening measured on a wafer is up to 2 times larger than full resist simulation results. Therefore, the influence of mask geometry to line shortening is a key item to parameterize lithography. The following paper discusses the effect of adding small serifs to line ends with 0.25 micrometer ground-rule design. For reticles produced on an ALTA 3000 with standard wet etch process, the corner rounding on them mask can be reduced by adding serifs of a certain size. The corner rounding was measured and the effect on line shortening on the wafer is determined. This was investigated by resist measurements on wafer, aerial image plus resist simulation and aerial image measurements on the AIMS microscope.

Temporal Gain Correction for X-Ray Calorimeter Spectrometers

NASA Technical Reports Server (NTRS)

Porter, F. S.; Chiao, M. P.; Eckart, M. E.; Fujimoto, R.; Ishisaki, Y.; Kelley, R. L.; Kilbourne, C. A.; Leutenegger, M. A.; McCammon, D.; Mitsuda, K.

2016-01-01

Calorimetric X-ray detectors are very sensitive to their environment. The boundary conditions can have a profound effect on the gain including heat sink temperature, the local radiation temperature, bias, and the temperature of the readout electronics. Any variation in the boundary conditions can cause temporal variations in the gain of the detector and compromise both the energy scale and the resolving power of the spectrometer. Most production X-ray calorimeter spectrometers, both on the ground and in space, have some means of tracking the gain as a function of time, often using a calibration spectral line. For small gain changes, a linear stretch correction is often sufficient. However, the detectors are intrinsically non-linear and often the event analysis, i.e., shaping, optimal filters etc., add additional non-linearity. Thus for large gain variations or when the best possible precision is required, a linear stretch correction is not sufficient. Here, we discuss a new correction technique based on non-linear interpolation of the energy-scale functions. Using Astro-HSXS calibration data, we demonstrate that the correction can recover the X-ray energy to better than 1 part in 104 over the entire spectral band to above 12 keV even for large-scale gain variations. This method will be used to correct any temporal drift of the on-orbit per-pixel gain using on-board calibration sources for the SXS instrument on the Astro-H observatory.

Demographic and spatiotemporal patterns of avian influenza infection at the continental scale, and in relation to annual life cycle of a migratory host

USGS Publications Warehouse

Nallar, Rodolfo; Papp, Zsuzsanna; Epp, Tasha; Leighton, Frederick A.; Swafford, Seth R.; DeLiberto, Thomas J.; Dusek, Robert J.; Ip, Hon S.; Hall, Jeffrey S.; Berhane, Yohannes; Gibbs, Samantha E.J.; Soos, Catherine

2015-01-01

Since the spread of highly pathogenic avian influenza (HPAI) H5N1 in the eastern hemisphere, numerous surveillance programs and studies have been undertaken to detect the occurrence, distribution, or spread of avian influenza viruses (AIV) in wild bird populations worldwide. To identify demographic determinants and spatiotemporal patterns of AIV infection in long distance migratory waterfowl in North America, we fitted generalized linear models with binominal distribution to analyze results from 13,574 blue-winged teal (Anas discors, BWTE) sampled in 2007 to 2010 year round during AIV surveillance programs in Canada and the United States. Our analyses revealed that during late summer staging (July-August) and fall migration (September-October), hatch year (HY) birds were more likely to be infected than after hatch year (AHY) birds, however there was no difference between age categories for the remainder of the year (winter, spring migration, and breeding period), likely due to maturing immune systems and newly acquired immunity of HY birds. Probability of infection increased non-linearly with latitude, and was highest in late summer prior to fall migration when densities of birds and the proportion of susceptible HY birds in the population are highest. Birds in the Central and Mississippi flyways were more likely to be infected compared to those in the Atlantic flyway. Seasonal cycles and spatial variation of AIV infection were largely driven by the dynamics of AIV infection in HY birds, which had more prominent cycles and spatial variation in infection compared to AHY birds. Our results demonstrate demographic as well as seasonal, latitudinal and flyway trends across Canada and the US, while illustrating the importance of migratory host life cycle and age in driving cyclical patterns of prevalence.

Reduced basis technique for evaluating the sensitivity coefficients of the nonlinear tire response

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Tanner, John A.; Peters, Jeanne M.

1992-01-01

An efficient reduced-basis technique is proposed for calculating the sensitivity of nonlinear tire response to variations in the design variables. The tire is modeled using a 2-D, moderate rotation, laminated anisotropic shell theory, including the effects of variation in material and geometric parameters. The vector of structural response and its first-order and second-order sensitivity coefficients are each expressed as a linear combination of a small number of basis vectors. The effectiveness of the basis vectors used in approximating the sensitivity coefficients is demonstrated by a numerical example involving the Space Shuttle nose-gear tire, which is subjected to uniform inflation pressure.

Global surface temperatures and the atmospheric electrical circuit

NASA Technical Reports Server (NTRS)

Price, Colin

1993-01-01

To monitor future global temperature trends, it would be extremely useful if parameters nonlinearly related to surface temperature could be found, thereby amplifying any warming signal that may exist. Evidence that global thunderstorm activity is nonlinearly related to diurnal, seasonal and interannual temperature variations is presented. Since global thunderstorm activity is also well correlated with the earth's ionospheric potential, it appears that variations of ionospheric potential, that can be measured at a single location, may be able to supply valuable information regarding global surface temperature fluctuations. The observations presented enable a prediction that a 1 percent increase in global surface temperatures may result in a 20 percent increase in ionospheric potential.

Unravelling variation in feeding, social interaction and growth patterns among pigs using an agent-based model.

PubMed

Boumans, Iris J M M; de Boer, Imke J M; Hofstede, Gert Jan; Bokkers, Eddie A M

2018-07-01

Domesticated pigs, Sus scrofa, vary considerably in feeding, social interaction and growth patterns. This variation originates partly from genetic variation that affects physiological factors and partly from behavioural strategies (avoid or approach) in competitive food resource situations. Currently, it is unknown how variation in physiological factors and in behavioural strategies among animals contributes to variation in feeding, social interaction and growth patterns in animals. The aim of this study was to unravel causation of variation in these patterns among pigs. We used an agent-based model to explore the effects of physiological factors and behavioural strategies in pigs on variation in feeding, social interaction and growth patterns. Model results show that variation in feeding, social interaction and growth patterns are caused partly by chance, such as time effects and coincidence of conflicts. Furthermore, results show that seemingly contradictory empirical findings in literature can be explained by variation in pig characteristics (i.e. growth potential, positive feedback, dominance, and coping style). Growth potential mainly affected feeding and growth patterns, whereas positive feedback, dominance and coping style affected feeding patterns, social interaction patterns, as well as growth patterns. Variation in behavioural strategies among pigs can reduce aggression at group level, but also make some pigs more susceptible to social constraints inhibiting them from feeding when they want to, especially low-ranking pigs and pigs with a passive coping style. Variation in feeding patterns, such as feeding rate or meal frequency, can indicate social constraints. Feeding patterns, however, can say something different about social constraints at group versus individual level. A combination of feeding patterns, such as a decreased feed intake, an increased feeding rate, and an increased meal frequency might, therefore, be needed to measure social constraints at individual level. Copyright © 2018 Elsevier Inc. All rights reserved.

Tidal Dissipation Within the Jupiter Moon Io - A Numerical Approach

NASA Astrophysics Data System (ADS)

Steinke, Teresa; van der Wal, Wouter; Hu, Haiyang; Vermeersen, Bert

2017-04-01

Satellite images and recent Earth-based observations of the innermost of the Galilean moons reveal a conspicuous pattern of volcanic hotspots and paterae on its surface. This pattern is associated with the heat flux originating from tidal dissipation in Io's mantle and asthenosphere. As shown by many analytical studies [e.g. Segatz et al. 1988], the local heat flux pattern depends on the rheology and structure of the satellite's interior and therefore could reveal constraints on Io's present interior. However, non-linear processes, different rheologies, and in particular lateral variations arising from the spatial heating pattern are difficult to incorporate in analytical 1D models but might be crucial. This motivates the development of a 3D finite element model of a layered body disturbed by a tidal potential. As a first step of this project we present a 3D finite element model of a spherically stratified body of linear viscoelastic rheology. For validation, we compare the resulting tidal deformation and local heating patterns with the results obtained by analytical models. Numerical errors increase with lower values of the asthenosphere viscosity. Currently, the numerical model allows realistic simulation down to viscosities of 1018 Pa s. Furthermore, we investigate an adequate way to deal with the relaxation of false modes that arise at the onset of the periodic tidal potential series in the numerical approach. Segatz, M., Spohn, T., Ross, M. N., Schubert, G. (1988). Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io. Icarus, 75(2), 187-206.

Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry.

PubMed

Tang, Chen; Lu, Wenjing; Chen, Song; Zhang, Zhen; Li, Botao; Wang, Wenping; Han, Lin

2007-10-20

We extend and refine previous work [Appl. Opt. 46, 2907 (2007)]. Combining the coupled nonlinear partial differential equations (PDEs) denoising model with the ordinary differential equations enhancement method, we propose the new denoising and enhancing model for electronic speckle pattern interferometry (ESPI) fringe patterns. Meanwhile, we propose the backpropagation neural networks (BPNN) method to obtain unwrapped phase values based on a skeleton map instead of traditional interpolations. We test the introduced methods on the computer-simulated speckle ESPI fringe patterns and experimentally obtained fringe pattern, respectively. The experimental results show that the coupled nonlinear PDEs denoising model is capable of effectively removing noise, and the unwrapped phase values obtained by the BPNN method are much more accurate than those obtained by the well-known traditional interpolation. In addition, the accuracy of the BPNN method is adjustable by changing the parameters of networks such as the number of neurons.

Strongly nonlinear parabolic variational inequalities

PubMed Central

Browder, Felix E.; Brézis, Haim

1980-01-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form ∂u/∂t + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications. PMID:16592776

Non-linear three dimensional spectral model of the Venusian thermosphere with super-rotation. I - Formulation and numerical technique. II - Temperature, composition and winds

NASA Technical Reports Server (NTRS)

Stevens-Rayburn, D. R.; Mengel, J. G.; Harris, I.; Mayr, H. G.

1989-01-01

A three-dimensional spectral model for the Venusion thermosphere is presented which uses spherical harmonics to represent the horizontal variations in longitude and latitude and which uses Fourier harmonics to represent the LT variations due to atmospheric rotation. A differencing scheme with tridiagonal block elimination is used to perform the height integration. Quadratic nonlinearities are taken into account. In the second part, numerical results obtained with the model are shown to reproduce the observed broad daytime maxima in CO2 and CO and the significantly larger values at dawn than at dusk. It is found that the diurnal variations in He are most sensitive to thermospheric superrotation, and that, given a globally uniform atmosphere as input, larger heating rates yield a larger temperature contrast between day and night.

Investigation on thermally-induced optical nonlinearity of alcohols

NASA Astrophysics Data System (ADS)

Zhang, Qian; Cheng, Xuemei; He, Bo; Ren, Zhaoyu; Zhang, Ying; Chen, Haowei; Bai, Jintao

2018-06-01

In this work, we studied the thermally-induced optical nonlinearity of alcohols by analyzing the far-filed diffraction rings patterns, which are generated when the alcohols are illuminated by a laser beam resonant to their overtones. We deduced the nonlinear refractive index coefficient n2 generated by thermal nonlinear optical effect to be - (20.53 ± 00.03) ×10-8cm2 /W , which is much higher than that of Kerr effect (7.7 ×10-16cm2 /W). The results also demonstrated that the thermally-induced optical nonlinearity increased with the laser power and sample concentration increasing. The notable nonlinearity suggests that thermal effect has potentials in many applications such as optical spatial modulation, and trapping and guiding of atoms.

Climate sensitivity to the lower stratospheric ozone variations

NASA Astrophysics Data System (ADS)

Kilifarska, N. A.

2012-12-01

The strong sensitivity of the Earth's radiation balance to variations in the lower stratospheric ozone—reported previously—is analysed here by the use of non-linear statistical methods. Our non-linear model of the land air temperature (T)—driven by the measured Arosa total ozone (TOZ)—explains 75% of total variability of Earth's T variations during the period 1926-2011. We have analysed also the factors which could influence the TOZ variability and found that the strongest impact belongs to the multi-decadal variations of galactic cosmic rays. Constructing a statistical model of the ozone variability, we have been able to predict the tendency in the land air T evolution till the end of the current decade. Results show that Earth is facing a weak cooling of the surface T by 0.05-0.25 K (depending on the ozone model) until the end of the current solar cycle. A new mechanism for O3 influence on climate is proposed.

Extended arrays for nonlinear susceptibility magnitude imaging

PubMed Central

Ficko, Bradley W.; Giacometti, Paolo; Diamond, Solomon G.

2016-01-01

This study implements nonlinear susceptibility magnitude imaging (SMI) with multifrequency intermodulation and phase encoding. An imaging grid was constructed of cylindrical wells of 3.5-mm diameter and 4.2-mm height on a hexagonal two-dimensional 61-voxel pattern with 5-mm spacing. Patterns of sample wells were filled with 40-μl volumes of Fe3O4 starch-coated magnetic nanoparticles (mNPs) with a hydrodynamic diameter of 100 nm and a concentration of 25 mg/ml. The imaging hardware was configured with three excitation coils and three detection coils in anticipation that a larger imaging system will have arrays of excitation and detection coils. Hexagonal and bar patterns of mNP were successfully imaged (R2 > 0.9) at several orientations. This SMI demonstration extends our prior work to feature a larger coil array, enlarged field-of-view, effective phase encoding scheme, reduced mNP sample size, and more complex imaging patterns to test the feasibility of extending the method beyond the pilot scale. The results presented in this study show that nonlinear SMI holds promise for further development into a practical imaging system for medical applications. PMID:26124044

Nonlinear Dielectric Properties of Yeast Cells Cultured in Different Environmental Conditions

NASA Astrophysics Data System (ADS)

Kawanishi, Gomon; Fukuda, Naoki; Muraji, Masafumi

The harmonics of the electric current through yeast suspensions, the nonlinear dielectric properties of yeast cells, have particular patterns according to the biological activity of the cells and the measurement of these patterns is a technique for determining the activity of living cells. The concentration of glucose and oxygen in yeast culture medium influences the manifestation of fermentation or respiration of yeast cells. Measurements were made with yeast cells (Saccharomyces cerevisiae) cultured aerobically and anaerobically in sufficient glucose concentration, aerobic fermentation and anaerobic fermentation, and aerobically in limited glucose concentration, respiration. The results showed that the harmonics were barely apparent for yeast cells in aerobic fermentation and respiratory; however, cells in the anaerobic fermentation displayed substantial third and fifth harmonics. We can say that environmental condition affects the yeast cells' nonlinear properties, from another viewpoint, the measurements of the nonlinear properties are available to determine the activity of yeast cells adjusted to the conditions of their cultivation.

Thermomagnetic instabilities in a vertical layer of ferrofluid: nonlinear analysis away from a critical point

NASA Astrophysics Data System (ADS)

Dey, Pinkee; Suslov, Sergey A.

2016-12-01

A finite amplitude instability has been analysed to discover the exact mechanism leading to the appearance of stationary magnetoconvection patterns in a vertical layer of a non-conducting ferrofluid heated from the side and placed in an external magnetic field perpendicular to the walls. The physical results have been obtained using a version of a weakly nonlinear analysis that is based on the disturbance amplitude expansion. It enables a low-dimensional reduction of a full nonlinear problem in supercritical regimes away from a bifurcation point. The details of the reduction are given in comparison with traditional small-parameter expansions. It is also demonstrated that Squire’s transformation can be introduced for higher-order nonlinear terms thus reducing the full three-dimensional problem to its equivalent two-dimensional counterpart and enabling significant computational savings. The full three-dimensional instability patterns are subsequently recovered using the inverse transforms The analysed stationary thermomagnetic instability is shown to occur as a result of a supercritical pitchfork bifurcation.

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.

Local control of globally competing patterns in coupled Swift-Hohenberg equations

NASA Astrophysics Data System (ADS)

Becker, Maximilian; Frenzel, Thomas; Niedermayer, Thomas; Reichelt, Sina; Mielke, Alexander; Bär, Markus

2018-04-01

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

Personality trait change across late childhood to young adulthood: Evidence for nonlinearity and sex differences in change.

PubMed

Durbin, C Emily; Hicks, Brian M; Blonigen, Daniel M; Johnson, Wendy; Iacono, William G; McGue, Matt

2016-01-01

We explored patterns of self-reported personality trait change across late childhood through young adulthood in a sample assessed up to 4 times on the lower-order facets of Positive Emotionality (PEM), Negative Emotionality (NEM), and Constraint (CON). Multilevel modeling analyses were used to describe both group- and individual-level change trajectories across this time span. There was evidence for nonlinear age-related change in most traits, and substantial individual differences in change for all traits. Gender differences were detected in the change trajectories for several facets of NEM and CON. Findings add to the literature on personality development by demonstrating robust nonlinear change in several traits across late childhood to young adulthood, as well as deviations from normative patterns of maturation at the earliest ages.

A nonlinear discriminant algorithm for feature extraction and data classification.

PubMed

Santa Cruz, C; Dorronsoro, J R

1998-01-01

This paper presents a nonlinear supervised feature extraction algorithm that combines Fisher's criterion function with a preliminary perceptron-like nonlinear projection of vectors in pattern space. Its main motivation is to combine the approximation properties of multilayer perceptrons (MLP's) with the target free nature of Fisher's classical discriminant analysis. In fact, although MLP's provide good classifiers for many problems, there may be some situations, such as unequal class sizes with a high degree of pattern mixing among them, that may make difficult the construction of good MLP classifiers. In these instances, the features extracted by our procedure could be more effective. After the description of its construction and the analysis of its complexity, we will illustrate its use over a synthetic problem with the above characteristics.

Short Time Impulse Response Function (STIRF) for automatic evaluation of the variation of the dynamic parameters of reinforced concrete framed structures during strong earthquakes.

NASA Astrophysics Data System (ADS)

Carlo Ponzo, Felice; Ditommaso, Rocco

2015-04-01

This study presents an innovative strategy for automatic evaluation of the variable fundamental frequency and related damping factor of nonlinear structures during strong motion phases. Most of methods for damage detection are based on the assessment of the variations of the dynamic parameters characterizing the monitored structure. A crucial aspect of these methods is the automatic and accurate estimation of both structural eigen-frequencies and related damping factors also during the nonlinear behaviour. A new method, named STIRF (Short-Time Impulse Response Function - STIRF), based on the nonlinear interferometric analysis combined with the Fourier Transform (FT) here is proposed in order to allow scientists and engineers to characterize frequencies and damping variations of a monitored structure. The STIRF approach helps to overcome some limitation derived from the use of techniques based on simple Fourier Transform. These latter techniques provide good results when the response of the monitored system is stationary, but fails when the system exhibits a non-stationary, time-varying behaviour: even non-stationary input, soil-foundation and/or adjacent structures interaction phenomena can show the inadequacy of classic techniques to analysing the nonlinear and/or non-stationary behaviour of structures. In fact, using this kind of approach it is possible to improve some of the existing methods for the automatic damage detection providing stable results also during the strong motion phase. Results are consistent with those expected if compared with other techniques. The main advantage derived from the use of the proposed approach (STIRF) for Structural Health Monitoring is based on the simplicity of the interpretation of the nonlinear variations of the fundamental frequency and the related equivalent viscous damping factor. The proposed methodology has been tested on both numerical and experimental models also using data retrieved from shaking table tests. Based on the results provided in this study, the methodology seems to be able to evaluate fast variations (over time) of dynamic parameters of a generic reinforced concrete framed structure. Further analyses are necessary to better calibrate the length of the moving time-window (in order to minimize the spurious frequency within each Interferometric Response Function evaluated on both weak and strong motion phases) and to verify the possibility to use the STIRF to analyse the nonlinear behaviour of general systems. Acknowledgements This study was partially funded by the Italian Civil Protection Department within the project DPC-RELUIS 2014 - RS4 ''Seismic observatory of structures and health monitoring''. References R. Ditommaso, F.C. Ponzo (2015). Automatic evaluation of the fundamental frequency variations and related damping factor of reinforced concrete framed structures using the Short Time Impulse Response Function (STIRF). Engineering Structures, 82 (2015), 104-112. http://dx.doi.org/10.1016/j.engstruct.2014.10.023.

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.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

PubMed

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

State-Dependent Riccati Equation Regulation of Systems with State and Control Nonlinearities

NASA Technical Reports Server (NTRS)

Beeler, Scott C.; Cox, David E. (Technical Monitor)

2004-01-01

The state-dependent Riccati equations (SDRE) is the basis of a technique for suboptimal feedback control of a nonlinear quadratic regulator (NQR) problem. It is an extension of the Riccati equation used for feedback control of linear problems, with the addition of nonlinearities in the state dynamics of the system resulting in a state-dependent gain matrix as the solution of the equation. In this paper several variations on the SDRE-based method will be considered for the feedback control problem with control nonlinearities. The control nonlinearities may result in complications in the numerical implementation of the control, which the different versions of the SDRE method must try to overcome. The control methods will be applied to three test problems and their resulting performance analyzed.

Water-energy dynamics, habitat heterogeneity, history, and broad-scale patterns of mammal diversity

NASA Astrophysics Data System (ADS)

Ferrer-Castán, Dolores; Morales-Barbero, Jennifer; Vetaas, Ole R.

2016-11-01

Numerous hypotheses on diversity patterns are often presented as if they were mutually exclusive. However, because of multicollinearity, correlational analyses are not able to distinguish the causal effects of different factors on these patterns. For this reason, we examine the interrelationships among current climate, habitat heterogeneity and evolutionary history by partitioning the variation in both total and non-volant mammal species richness in the Iberian Peninsula. Thus, it is possible to determine the variation accounted for by each one of these three components that is not shared by the others, and the respective overlaps. More specifically, we hypothesize that (H1) in warm temperate zones, a small increase in the available energy has strong negative effects on mammal richness if water availability is limiting; (H2) there are functional relationships between woody plant species richness (WOOD) and the richness of mammal species; (H3) there is a signal of evolutionary history in contemporary patterns of species richness, and (H4) mammal richness and the historical variable mean root distance (MRD) respond to the same driving forces. Additionally, we also test for spatial autocorrelation. We found a sharp nonlinear decrease in mammal richness with increasing energy and a monotonic increase with increasing water availability. Moreover, an interaction term between these two climate factors appeared to be statistically significant, so H1 could not be rejected. WOOD remained significant after partialling out both current climate and MRD at the family level (MRDf), supporting H2. The relationship between mammal diversity and MRD averaged by species richness was found to be spurious, but there appeared a significant historical signal using MRDf (this supports H3). The overlaps among these factors are consistent with H4 and suggest that water-energy dynamics have probably been active drivers throughout evolutionary history with habitat heterogeneity, and biotic interactions playing an important role.

Acoustic-radiation stress in solids. I - Theory

NASA Technical Reports Server (NTRS)

Cantrell, J. H., Jr.

1984-01-01

The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.

Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

NASA Astrophysics Data System (ADS)

Wang, Liming; Zheng, Shijie

2018-02-01

In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

Bioconvection in spatially extended domains

NASA Astrophysics Data System (ADS)

Karimi, A.; Paul, M. R.

2013-05-01

We numerically explore gyrotactic bioconvection in large spatially extended domains of finite depth using parameter values from available experiments with the unicellular alga Chlamydomonas nivalis. We numerically integrate the three-dimensional, time-dependent continuum model of Pedley [J. Fluid Mech.10.1017/S0022112088002393 195, 223 (1988)] using a high-order, parallel, spectral-element approach. We explore the long-time nonlinear patterns and dynamics found for layers with an aspect ratio of 10 over a range of Rayleigh numbers. Our results yield the pattern wavelength and pattern dynamics which we compare with available theory and experimental measurement. There is good agreement for the pattern wavelength at short times between numerics, experiment, and a linear stability analysis. At long times we find that the general sequence of patterns given by the nonlinear evolution of the governing equations correspond qualitatively to what has been described experimentally. However, at long times the patterns in numerics grow to larger wavelengths, in contrast to what is observed in experiment where the wavelength is found to decrease with time.

Growth rate and stable carbon and nitrogen isotope trophic discrimination factors of lion and leopard whiskers.

PubMed

Mutirwara, Ruwimbo; Radloff, Frans G T; Codron, Daryl

2018-01-15

Stable isotope analysis (SIA) of whiskers has been used to identify temporal feeding habits, intra-population diet variation, as well as individual dietary specialisation of marine and terrestrial carnivores. However, the potential of the method to disclose such dietary information for large wild felids is hampered by lack of information on species-specific whisker growth rates, whisker growth patterns and whisker-diet trophic discrimination factors (TDFs). Whisker growth rates and growth patterns were measured for four lions (Panthera leo) and one leopard (Panthera pardus) held at the National Zoological Gardens, Pretoria, South Africa. Actively growing whiskers of the felids were 'marked' four times over 185 days using 13 C-depleted, C 3 -based giraffe (Giraffa camelopardalis) meat. The periods with low δ 13 C values, identified following serial sectioning of the regrown whiskers at 1 mm intervals and isotopic analysis, were then correlated to specific giraffe meat feeding bouts and hence growth periods. δ 13 C and δ 15 N whisker-diet TDFs were estimated for five lions whose diet remained consistent over multiple years. The whisker growth rates of three lionesses and the leopard were similar (mean = 0.65 mm day -1 ), despite species, sex and age differences. There was a decrease in whisker growth rate over time, suggesting a non-linear whisker growth pattern. However, linear and non-linear growth simulations showed slight differences between the two growth patterns for the proximal ~50 mm of whiskers. δ 13 C and δ 15 N lion whisker-diet TDFs were also similar amongst individuals (mean = 2.7 ± 0.12 ‰ for δ 13 C values and 2.5 ± 0.08 ‰ for δ 15 N values), irrespective of age and sex. The whisker growth rate and δ 13 C and δ 15 N lion whisker-diet TDFs obtained in this study can be applied in future studies to assign dietary information contained in analysed felid whiskers to the correct time period and improve deductions of prey species consumed by wild felids. Copyright © 2017 John Wiley & Sons, Ltd.

Dynamics of localized structures in reaction-diffusion systems induced by delayed feedback

NASA Astrophysics Data System (ADS)

Gurevich, Svetlana V.

2013-05-01

We are interested in stability properties of a single localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to complex dynamical behavior of the system, including formation of target patterns, spontaneous motion, and spontaneous breathing as well as various complex structures, arising from combination of different oscillatory instabilities. In the case of spontaneous motion, we provide a bifurcation analysis of the delayed system and derive an order parameter equation for the position of the localized structure, explicitly describing its temporal evolution in the vicinity of the bifurcation point. This equation is a subject to a nonlinear delay differential equation, which can be transformed to the normal form of the pitchfork drift bifurcation.

Conic section function neural network circuitry for offline signature recognition.

PubMed

Erkmen, Burcu; Kahraman, Nihan; Vural, Revna A; Yildirim, Tulay

2010-04-01

In this brief, conic section function neural network (CSFNN) circuitry was designed for offline signature recognition. CSFNN is a unified framework for multilayer perceptron (MLP) and radial basis function (RBF) networks to make simultaneous use of advantages of both. The CSFNN circuitry architecture was developed using a mixed mode circuit implementation. The designed circuit system is problem independent. Hence, the general purpose neural network circuit system could be applied to various pattern recognition problems with different network sizes on condition with the maximum network size of 16-16-8. In this brief, CSFNN circuitry system has been applied to two different signature recognition problems. CSFNN circuitry was trained with chip-in-the-loop learning technique in order to compensate typical analog process variations. CSFNN hardware achieved highly comparable computational performances with CSFNN software for nonlinear signature recognition problems.

Fuzzy Temporal Logic Based Railway Passenger Flow Forecast Model

PubMed Central

Dou, Fei; Jia, Limin; Wang, Li; Xu, Jie; Huang, Yakun

2014-01-01

Passenger flow forecast is of essential importance to the organization of railway transportation and is one of the most important basics for the decision-making on transportation pattern and train operation planning. Passenger flow of high-speed railway features the quasi-periodic variations in a short time and complex nonlinear fluctuation because of existence of many influencing factors. In this study, a fuzzy temporal logic based passenger flow forecast model (FTLPFFM) is presented based on fuzzy logic relationship recognition techniques that predicts the short-term passenger flow for high-speed railway, and the forecast accuracy is also significantly improved. An applied case that uses the real-world data illustrates the precision and accuracy of FTLPFFM. For this applied case, the proposed model performs better than the k-nearest neighbor (KNN) and autoregressive integrated moving average (ARIMA) models. PMID:25431586

Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern.

PubMed

Bugaychuk, S; Conte, R

2012-08-01

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a "dark" dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a tanh function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope; at the same time, the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as retention of the pulse shape during the transmission of impulses in a long nonlinear cavity, and giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.

Light Diffraction by Large Amplitude Ultrasonic Waves in Liquids

NASA Technical Reports Server (NTRS)

Adler, Laszlo; Cantrell, John H.; Yost, William T.

2016-01-01

Light diffraction from ultrasound, which can be used to investigate nonlinear acoustic phenomena in liquids, is reported for wave amplitudes larger than that typically reported in the literature. Large amplitude waves result in waveform distortion due to the nonlinearity of the medium that generates harmonics and produces asymmetries in the light diffraction pattern. For standing waves with amplitudes above a threshold value, subharmonics are generated in addition to the harmonics and produce additional diffraction orders of the incident light. With increasing drive amplitude above the threshold a cascade of period-doubling subharmonics are generated, terminating in a region characterized by a random, incoherent (chaotic) diffraction pattern. To explain the experimental results a toy model is introduced, which is derived from traveling wave solutions of the nonlinear wave equation corresponding to the fundamental and second harmonic standing waves. The toy model reduces the nonlinear partial differential equation to a mathematically more tractable nonlinear ordinary differential equation. The model predicts the experimentally observed cascade of period-doubling subharmonics terminating in chaos that occurs with increasing drive amplitudes above the threshold value. The calculated threshold amplitude is consistent with the value estimated from the experimental data.

Analysis of the pattern of potential woody cover in Texas savanna

NASA Astrophysics Data System (ADS)

Yang, Xuebin; Crews, Kelley A.; Yan, Bowei

2016-10-01

While woody plant encroachment has been observed worldwide in savannas and adversely affected the ecosystem structure and function, a thorough understanding of the nature of this phenomenon is urgently required for savanna management and restoration. Among others, potential woody cover (the maximum realizable woody cover that a given site can support), especially its variation over environment has huge implication on the encroachment management in particular, and on tree-grass interactions in general. This project was designed to explore the pattern of potential woody cover in Texas savanna, an ecosystem with a large rainfall gradient in west-east direction. Substantial random pixels were sampled across the study area from MODIS Vegetation Continuous Fields (VCF) tree cover layer (250 m). Since potential woody cover is suggested to be limited by water availability, a nonlinear 99th quantile regression was performed between the observed woody cover and mean annual precipitation (MAP) to model the pattern of potential woody cover. Research result suggests a segmented relationship between potential woody cover and MAP at MODIS scale. Potential biases as well as the practical and theoretical implications were discussed. Through this study, the hypothesis about the primary role of water availability in determining savanna woody cover was further confirmed in a relatively understudied US-located savanna.

Body molt of male long-tailed ducks in the nearshore waters of the north slope, Alaska

USGS Publications Warehouse

Howell, M.D.; Grand, J.B.; Flint, Paul L.

2003-01-01

We examined the timing and intensity of body molt in relation to stage of remige growth for postbreeding adult male Long-tailed Ducks (Clangula hyemalis) off the coast of northern Alaska. During this period, remige and rectrix feathers are molted simultaneously with body feathers during the prebasic molt, which results in a period of increased energetic and nutritional demands. We collected birds from late July through mid-August and recorded intensity of molt in eight regions: head and neck, back and rump, greater coverts, lesser coverts, flank and sides, breast, belly, and tail. Using nonlinear regression, we estimated the peak intensity and variation for each region in relation to ninth primary length. We found little evidence of molt in the head and neck region. The greater and lesser coverts, and back and rump reached peak molt intensities earliest and were followed by tail, breast, and belly. Molt intensity in the flank and side region was highly variable and indicated a more prolonged molting pattern in relation to other regions. While body molt occurs simultaneously with wing molt, we found that molt among regions occurred in a staggered pattern. Long-tailed Ducks may employ this staggered molting pattern to minimize the energetic and nutritional requirements of molt.

Thermodynamic potentials in anisotropic and nonlinear dielectrics

NASA Astrophysics Data System (ADS)

Parravicini, Jacopo

2018-07-01

The variation of total energy, entropy, Helmoltz free energy due to the application of a static electric field is calculated and discussed, under suitable conditions, in the case of a dielectric with either anisotropic or nonlinear response. The proposed approach starts from Fröhlich's theory of dielectric thermodynamics and, by analyzing its assumptions, provides a method to generalize it. The obtained relationships can be employed for describing the thermodynamics of different classes of dielectric materials, also in experimental investigations. Specifically, the anisotropy and nonlinearity conditions are considered and relative examples are indicated and discussed.

Z-scan and optical limiting properties of Hibiscus Sabdariffa dye

NASA Astrophysics Data System (ADS)

Diallo, A.; Zongo, S.; Mthunzi, P.; Rehman, S.; Alqaradawi, S. Y.; Soboyejo, W.; Maaza, M.

2014-12-01

The intensity-dependent refractive index n 2 and the nonlinear susceptibility χ (3) of Hibiscus Sabdariffa dye solutions in the nanosecond regime at 532 nm are reported. More presicely, the variation of n 2, β, and real and imaginary parts of χ (3) versus the natural dye extract concentration has been carried out by z-scan and optical limiting techniques. The third-order nonlinearity of the Hibiscus Sabdariffa dye solutions was found to be dominated by nonlinear refraction, which leads to strong optical limiting of laser.

Computational Analyses of Synergism in Small Molecular Network Motifs

PubMed Central

Zhang, Yili; Smolen, Paul; Baxter, Douglas A.; Byrne, John H.

2014-01-01

Cellular functions and responses to stimuli are controlled by complex regulatory networks that comprise a large diversity of molecular components and their interactions. However, achieving an intuitive understanding of the dynamical properties and responses to stimuli of these networks is hampered by their large scale and complexity. To address this issue, analyses of regulatory networks often focus on reduced models that depict distinct, reoccurring connectivity patterns referred to as motifs. Previous modeling studies have begun to characterize the dynamics of small motifs, and to describe ways in which variations in parameters affect their responses to stimuli. The present study investigates how variations in pairs of parameters affect responses in a series of ten common network motifs, identifying concurrent variations that act synergistically (or antagonistically) to alter the responses of the motifs to stimuli. Synergism (or antagonism) was quantified using degrees of nonlinear blending and additive synergism. Simulations identified concurrent variations that maximized synergism, and examined the ways in which it was affected by stimulus protocols and the architecture of a motif. Only a subset of architectures exhibited synergism following paired changes in parameters. The approach was then applied to a model describing interlocked feedback loops governing the synthesis of the CREB1 and CREB2 transcription factors. The effects of motifs on synergism for this biologically realistic model were consistent with those for the abstract models of single motifs. These results have implications for the rational design of combination drug therapies with the potential for synergistic interactions. PMID:24651495

Identifying environmental correlates of intraspecific genetic variation.

PubMed

Harrisson, K A; Yen, J D L; Pavlova, A; Rourke, M L; Gilligan, D; Ingram, B A; Lyon, J; Tonkin, Z; Sunnucks, P

2016-09-01

Genetic variation is critical to the persistence of populations and their capacity to adapt to environmental change. The distribution of genetic variation across a species' range can reveal critical information that is not necessarily represented in species occurrence or abundance patterns. We identified environmental factors associated with the amount of intraspecific, individual-based genetic variation across the range of a widespread freshwater fish species, the Murray cod Maccullochella peelii. We used two different approaches to statistically quantify the relative importance of predictor variables, allowing for nonlinear relationships: a random forest model and a Bayesian approach. The latter also accounted for population history. Both approaches identified associations between homozygosity by locus and both disturbance to the natural flow regime and mean annual flow. Homozygosity by locus was negatively associated with disturbance to the natural flow regime, suggesting that river reaches with more disturbed flow regimes may support larger, more genetically diverse populations. Our findings are consistent with the hypothesis that artificially induced perennial flows in regulated channels may provide greater and more consistent habitat and reduce the frequency of population bottlenecks that can occur frequently under the highly variable and unpredictable natural flow regime of the system. Although extensive river regulation across eastern Australia has not had an overall positive effect on Murray cod numbers over the past century, regulation may not represent the primary threat to Murray cod survival. Instead, pressures other than flow regulation may be more critical to the persistence of Murray cod (for example, reduced frequency of large floods, overfishing and chemical pollution).

Variations in Ratio and Correlation of Solar Magnetic Fields in the Fe i 525.02 nm and Na i 589.59 nm Lines According to Mount Wilson Measurements During 2000 - 2012

NASA Astrophysics Data System (ADS)

Golubeva, Elena

2016-10-01

Variations in the solar magnetic-field ratio over 13 years are analyzed, relying on the comparison of simultaneous measurements in two spectral lines at the Mount Wilson Observatory (MWO). The ratio and correlation coefficient are calculated over the general working range of measured magnetic-field values and in various ranges of the field magnitudes. Variations in both parameters are considered. We found the following tendencies: i) the parameters show changes with the cycle of solar activity in the general case; ii) their dependence on magnetic-field magnitude is a nonlinear function of time, and this is especially pronounced in the ratio behavior; iii) several separate ranges of the field magnitudes can be distinguished based on the behavioral patterns of the ratio variations. Correspondences between these ranges and the known structural objects of the solar atmosphere are discussed. This permits us to reach the conclusion that the dependence of parameters considered on the magnetic-field magnitude and time is connected with the variety of magnetic structural components and their cyclic rearrangements. The results represented may be useful for solving interpretation problems of solar magnetic-field measurements and for the cross-calibration of applicable instruments. They can also be of interest for tasks related to the creation of a uniform long temporal series of solar magnetic-field data from various sources.

Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity

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

Lebedev, M. E., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Alfimov, G. L., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Malomed, Boris A., E-mail: malomed@post.tau.ac.il

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate thatmore » one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.« less

Coriolis effects on nonlinear oscillations of rotating cylinders and rings

NASA Technical Reports Server (NTRS)

Padovan, J.

1976-01-01

The effects which moderately large deflections have on the frequency spectrum of rotating rings and cylinders are considered. To develop the requisite solution, a variationally constrained version of the Lindstedt-Poincare procedure is employed. Based on the solution developed, in addition to considering the effects of displacement induced nonlinearity, the role of Coriolis forces is also given special consideration.

Joystick With Cable Springs Offers Better Feel

NASA Technical Reports Server (NTRS)

Kerley, James; Ecklund, Wayne

1992-01-01

Improved joystick allows motion in 6 degrees of freedom, biased toward central position and orientation by 16 segments of cable serving as springs. Improvement in feel and control results from nonlinear compliance of cable-spring assembly. Nonlinear variations accommodate natural reactions of hand and brain. Operator functions as part of feedback control loop. More comfortable, increases ability to exert control and reduces fatigue.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Nonlinear observation of internal states of fuel cell cathode utilizing a high-order sliding-mode algorithm

NASA Astrophysics Data System (ADS)

Xu, Liangfei; Hu, Junming; Cheng, Siliang; Fang, Chuan; Li, Jianqiu; Ouyang, Minggao; Lehnert, Werner

2017-07-01

A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (<1 s). Moreover, the nonlinear observer shows good robustness against variations in the initial values of the internal states, but less robustness against variations in system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.

Non-linear effects of drought under shade: reconciling physiological and ecological models in plant communities.

PubMed

Holmgren, Milena; Gómez-Aparicio, Lorena; Quero, José Luis; Valladares, Fernando

2012-06-01

The combined effects of shade and drought on plant performance and the implications for species interactions are highly debated in plant ecology. Empirical evidence for positive and negative effects of shade on the performance of plants under dry conditions supports two contrasting theoretical models about the role of shade under dry conditions: the trade-off and the facilitation hypotheses. We performed a meta-analysis of field and greenhouse studies evaluating the effects of drought at two or more irradiance levels on nine response variables describing plant physiological condition, growth, and survival. We explored differences in plant response across plant functional types, ecosystem types and methodological approaches. The data were best fit using quadratic models indicating a humped-back shape response to drought along an irradiance gradient for survival, whole plant biomass, maximum photosynthetic capacity, stomatal conductance and maximal photochemical efficiency. Drought effects were ameliorated at intermediate irradiance, becoming more severe at higher or lower light levels. This general pattern was maintained when controlling for potential variations in the strength of the drought treatment among light levels. Our quantitative meta-analysis indicates that dense shade ameliorates drought especially among drought-intolerant and shade-tolerant species. Wet tropical species showed larger negative effects of drought with increasing irradiance than semiarid and cold temperate species. Non-linear responses to irradiance were stronger under field conditions than under controlled greenhouse conditions. Non-linear responses to drought along the irradiance gradient reconciliate opposing views in plant ecology, indicating that facilitation is more likely within certain range of environmental conditions, fading under deep shade, especially for drought-tolerant species.

Modeling nonlinear responses of DOC transport in boreal catchments in Sweden

NASA Astrophysics Data System (ADS)

Kasurinen, Ville; Alfredsen, Knut; Ojala, Anne; Pumpanen, Jukka; Weyhenmeyer, Gesa A.; Futter, Martyn N.; Laudon, Hjalmar; Berninger, Frank

2016-07-01

Stream water dissolved organic carbon (DOC) concentrations display high spatial and temporal variation in boreal catchments. Understanding and predicting these patterns is a challenge with great implications for water quality projections and carbon balance estimates. Although several biogeochemical models have been used to estimate stream water DOC dynamics, model biases common during both rain and snow melt-driven events. The parsimonious DOC-model, K-DOC, with 10 calibrated parameters, uses a nonlinear discharge and catchment water storage relationship including soil temperature dependencies of DOC release and consumption. K-DOC was used to estimate the stream water DOC concentrations over 5 years for eighteen nested boreal catchments having total area of 68 km2 (varying from 0.04 to 67.9 km2). The model successfully simulated DOC concentrations during base flow conditions, as well as, hydrological events in catchments dominated by organic and mineral soils reaching NSEs from 0.46 to 0.76. Our semimechanistic model was parsimonious enough to have all parameters estimated using statistical methods. We did not find any clear differences between forest and mire-dominated catchments that could be explained by soil type or tree species composition. However, parameters controlling slow release and consumption of DOC from soil water behaved differently for small headwater catchments (less than 2 km2) than for those that integrate larger areas of different ecosystem types (10-68 km2). Our results emphasize that it is important to account for nonlinear dependencies of both, soil temperature, and catchment water storage, when simulating DOC dynamics of boreal catchments.

Self-Organization of Light in Optical Media with Competing Nonlinearities.

PubMed

Maucher, F; Pohl, T; Skupin, S; Krolikowski, W

2016-04-22

We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.

Quantum Associative Neural Network with Nonlinear Search Algorithm

NASA Astrophysics Data System (ADS)

Zhou, Rigui; Wang, Huian; Wu, Qian; Shi, Yang

2012-03-01

Based on analysis on properties of quantum linear superposition, to overcome the complexity of existing quantum associative memory which was proposed by Ventura, a new storage method for multiply patterns is proposed in this paper by constructing the quantum array with the binary decision diagrams. Also, the adoption of the nonlinear search algorithm increases the pattern recalling speed of this model which has multiply patterns to O( {log2}^{2^{n -t}} ) = O( n - t ) time complexity, where n is the number of quantum bit and t is the quantum information of the t quantum bit. Results of case analysis show that the associative neural network model proposed in this paper based on quantum learning is much better and optimized than other researchers' counterparts both in terms of avoiding the additional qubits or extraordinary initial operators, storing pattern and improving the recalling speed.

Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks.

PubMed

Gao, Zhongke; Jin, Ningde

2009-06-01

The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using complex network. Three unique network construction methods are proposed to build three types of networks, i.e., flow pattern complex network (FPCN), fluid dynamic complex network (FDCN), and fluid structure complex network (FSCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K -mean clustering, useful and interesting results are found which can be used for identifying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and demonstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time series in practice.

Turing instability in reaction-diffusion systems with nonlinear diffusion

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

Zemskov, E. P., E-mail: zemskov@ccas.ru

2013-10-15

The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.

Ferrofluid patterns in a radial magnetic field: linear stability, nonlinear dynamics, and exact solutions.

PubMed

Oliveira, Rafael M; Miranda, José A; Leandro, Eduardo S G

2008-01-01

The response of a ferrofluid droplet to a radial magnetic field is investigated, when the droplet is confined in a Hele-Shaw cell. We study how the stability properties of the interface and the shape of the emerging patterns react to the action of the magnetic field. At early linear stages, it is found that the radial field is destabilizing and determines the growth of fingering structures at the interface. In the weakly nonlinear regime, we have verified that the magnetic field favors the formation of peaked patterned structures that tend to become sharper and sharper as the magnitude of the magnetic effects is increased. A more detailed account of the pattern morphology is provided by the determination of nontrivial exact stationary solutions for the problem with finite surface tension. These solutions are obtained analytically and reveal the development of interesting polygon-shaped and starfishlike patterns. For sufficiently large applied fields or magnetic susceptibilities, pinch-off phenomena are detected, tending to occur near the fingertips. We have found that the morphological features obtained from the exact solutions are consistent with our linear and weakly nonlinear predictions. By contrasting the exact solutions for ferrofluids under radial field with those obtained for rotating Hele-Shaw flows with ordinary nonmagnetic fluids, we deduce that they coincide in the limit of very small susceptibilities.

Yearly and perhaps transyearly human natality patterns near the equator and at higher latitudes

PubMed Central

Cornélissen, G.; Halberg, F.; Mikulecky, M.; Florida, P.; Faraone, P.; Yamanaka, T.; Murakami, S.; Otsuka, K.; Bakken, E. E.

2008-01-01

Data on the daily numbers of births in Davao, Philippines, available from 1993 to 2003 are re-analyzed herein by linear–nonlinear rhythmometry, as are data from Italy and Japan. A transyear, characterizing the solar wind and other non-photic physical environmental factors, corresponds to a spectral peak of the near-equatorial natality series. This component with a period of about 1.3 years is found to have an amplitude larger than the calendar year, the amplitude ratio being 134%. Whereas the transyear is validated nonlinearly, the 95% confidence interval for the period extending from 1.21 to 1.38 years and the 95% confidence interval for the amplitude not overlapping zero (P < 0.05), the annual variation is only demonstrable by linear least squares analysis. The results bring added evidence for an influence of non-photic environmental effects on human physiology, in this case data collected near the equatorial region, Davao being situated at 7°N, 126°E. They are in keeping with some degree of generality of a rule of reciprocity among mutually supporting physical and biological periodicities. They do not detract from the fact that in other longer data sets at higher latitudes, the calendar year, presumably reflecting climatic influences, dominates the spectrum. PMID:16275480

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

PubMed

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

2017-11-01

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

Study of the effect of static/dynamic Coulomb friction variation at the tape-head interface of a spacecraft tape recorder by non-linear time response simulation

NASA Technical Reports Server (NTRS)

Mukhopadhyay, A. K.

1978-01-01

A description is presented of six simulation cases investigating the effect of the variation of static-dynamic Coulomb friction on servo system stability/performance. The upper and lower levels of dynamic Coulomb friction which allowed operation within requirements were determined roughly to be three times and 50% respectively of nominal values considered in a table. A useful application for the nonlinear time response simulation is the sensitivity analysis of final hardware design with respect to such system parameters as cannot be varied realistically or easily in the actual hardware. Parameters of the static/dynamic Coulomb friction fall in this category.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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.

Nonlinear permanent migration response to climatic variations but minimal response to disasters

PubMed Central

Bohra-Mishra, Pratikshya; Oppenheimer, Michael; Hsiang, Solomon M.

2014-01-01

We present a microlevel study to simultaneously investigate the effects of variations in temperature and precipitation along with sudden natural disasters to infer their relative influence on migration that is likely permanent. The study is made possible by the availability of household panel data from Indonesia with an exceptional tracking rate combined with frequent occurrence of natural disasters and significant climatic variations, thus providing a quasi-experiment to examine the influence of environment on migration. Using data on 7,185 households followed over 15 y, we analyze whole-household, province-to-province migration, which allows us to understand the effects of environmental factors on permanent moves that may differ from temporary migration. The results suggest that permanent migration is influenced by climatic variations, whereas episodic disasters tend to have much smaller or no impact on such migration. In particular, temperature has a nonlinear effect on migration such that above 25 °C, a rise in temperature is related to an increase in outmigration, potentially through its impact on economic conditions. We use these results to estimate the impact of projected temperature increases on future permanent migration. Though precipitation also has a similar nonlinear effect on migration, the effect is smaller than that of temperature, underscoring the importance of using an expanded set of climatic factors as predictors of migration. These findings on the minimal influence of natural disasters and precipitation on permanent moves supplement previous findings on the significant role of these variables in promoting temporary migration. PMID:24958887

Nonlinear permanent migration response to climatic variations but minimal response to disasters.

PubMed

Bohra-Mishra, Pratikshya; Oppenheimer, Michael; Hsiang, Solomon M

2014-07-08

We present a microlevel study to simultaneously investigate the effects of variations in temperature and precipitation along with sudden natural disasters to infer their relative influence on migration that is likely permanent. The study is made possible by the availability of household panel data from Indonesia with an exceptional tracking rate combined with frequent occurrence of natural disasters and significant climatic variations, thus providing a quasi-experiment to examine the influence of environment on migration. Using data on 7,185 households followed over 15 y, we analyze whole-household, province-to-province migration, which allows us to understand the effects of environmental factors on permanent moves that may differ from temporary migration. The results suggest that permanent migration is influenced by climatic variations, whereas episodic disasters tend to have much smaller or no impact on such migration. In particular, temperature has a nonlinear effect on migration such that above 25 °C, a rise in temperature is related to an increase in outmigration, potentially through its impact on economic conditions. We use these results to estimate the impact of projected temperature increases on future permanent migration. Though precipitation also has a similar nonlinear effect on migration, the effect is smaller than that of temperature, underscoring the importance of using an expanded set of climatic factors as predictors of migration. These findings on the minimal influence of natural disasters and precipitation on permanent moves supplement previous findings on the significant role of these variables in promoting temporary migration.

Gravitational Field as a Pressure Force from Logarithmic Lagrangians and Non-Standard Hamiltonians: The Case of Stellar Halo of Milky Way

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2018-03-01

Recently, the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations. Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties. One interesting form related to the inverse variational problem is the logarithmic Lagrangian, which has a number of motivating features related to the Liénard-type and Emden nonlinear differential equations. Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians. In this communication, we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians. One interesting consequence concerns the emergence of an extra pressure term, which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field. The case of the stellar halo of the Milky Way is considered.

The effect of high temperature on cause-specific mortality: A multi-county analysis in China.

PubMed

Ban, Jie; Xu, Dandan; He, Mike Z; Sun, Qinghua; Chen, Chen; Wang, Wentao; Zhu, Pengfei; Li, Tiantian

2017-09-01

Although existing studies have linked high temperature to mortality in a small number of regions, less evidence is available on the variation in the associations between high temperature exposure and cause-specific mortality of multiple regions in China. Our study focused on the use of time series analysis to quantify the association between high temperature and different cause-specific mortalities for susceptible populations for 43 counties in China. Two-stage analyses adopting a distributed lag non-linear model (DLNM) and a meta-analysis allowed us to obtain county-specific estimates and national-scale pooled estimates of the nonlinear temperature-mortality relationship. We also considered different populations stratified by age and sex, causes of death, absolute and relative temperature patterns, and potential confounding from air pollutants. All of the observed cause-specific mortalities are significantly associated with higher temperature. The estimated effects of high temperature on mortality varied by spatial distribution and temperature patterns. Compared with the 90th percentile temperature, the overall relative risk (RR) at the 99th percentile temperature for non-accidental mortality is 1.105 (95%CI: 1.089, 1.122), for circulatory disease is 1.107 (95%CI: 1.081, 1.133), for respiratory disease is 1.095 (95%CI: 1.050, 1.142), for coronary heart disease is 1.073 (95%CI: 1.047, 1.099), for acute myocardial infarction is 1.072 (95%CI: 1.042, 1.104), and for stroke is 1.095 (95%CI: 1.052, 1.138). Based on our findings, we believe that heat-related health effect in China is a significant issue that requires more attention and allocation of existing resources. Copyright © 2017 Elsevier Ltd. All rights reserved.

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

On the pressure field of nonlinear standing water waves

NASA Technical Reports Server (NTRS)

Schwartz, L. W.

1980-01-01

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

Non-linear dielectric spectroscopy of microbiological suspensions

PubMed Central

Treo, Ernesto F; Felice, Carmelo J

2009-01-01

Background Non-linear dielectric spectroscopy (NLDS) of microorganism was characterized by the generation of harmonics in the polarization current when a microorganism suspension was exposed to a sinusoidal electric field. The biological nonlinear response initially described was not well verified by other authors and the results were susceptible to ambiguous interpretation. In this paper NLDS was performed to yeast suspension in tripolar and tetrapolar configuration with a recently developed analyzer. Methods Tripolar analysis was carried out by applying sinusoidal voltages up to 1 V at the electrode interface. Tetrapolar analysis was carried on with sinusoidal field strengths from 0.1 V cm-1 to 70 V cm-1. Both analyses were performed within a frequency range from 1 Hz through 100 Hz. The harmonic amplitudes were Fourier-analyzed and expressed in dB. The third harmonic, as reported previously, was investigated. Statistical analysis (ANOVA) was used to test the effect of inhibitor an activator of the plasma membrane enzyme in the measured response. Results No significant non-linearities were observed in tetrapolar analysis, and no observable changes occurred when inhibitor and activator were added to the suspension. Statistical analysis confirmed these results. When a pure sinus voltage was applied to an electrode-yeast suspension interface, variations higher than 25 dB for the 3rd harmonic were observed. Variation higher than 20 dB in the 3rd harmonics has also been found when adding an inhibitor or activator of the membrane-bounded enzymes. These variations did not occur when the suspension was boiled. Discussion The lack of result in tetrapolar cells suggest that there is no, if any, harmonic generation in microbiological bulk suspension. The non-linear response observed was originated in the electrode-electrolyte interface. The frequency and voltage windows observed in previous tetrapolar analysis were repeated in the tripolar measurements, but maximum were not observed at the same values. Conclusion Contrary to previous assertions, no repeatable dielectric non-linearity was exhibited in the bulk suspensions tested under the field and frequency condition reported with this recently designed analyzer. Indeed, interface related harmonics were observed and monitored during biochemical stimuli. The changes were coherent with the expected biological response. PMID:19772595

A variational approach to probing extreme events in turbulent dynamical systems

PubMed Central

Farazmand, Mohammad; Sapsis, Themistoklis P.

2017-01-01

Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large-scale networks, and biological systems. We propose a variational framework for probing conditions that trigger intermittent extreme events in high-dimensional nonlinear dynamical systems. We seek the triggers as the probabilistically feasible solutions of an appropriately constrained optimization problem, where the function to be maximized is a system observable exhibiting intermittent extreme bursts. The constraints are imposed to ensure the physical admissibility of the optimal solutions, that is, significant probability for their occurrence under the natural flow of the dynamical system. We apply the method to a body-forced incompressible Navier-Stokes equation, known as the Kolmogorov flow. We find that the intermittent bursts of the energy dissipation are independent of the external forcing and are instead caused by the spontaneous transfer of energy from large scales to the mean flow via nonlinear triad interactions. The global maximizer of the corresponding variational problem identifies the responsible triad, hence providing a precursor for the occurrence of extreme dissipation events. Specifically, monitoring the energy transfers within this triad allows us to develop a data-driven short-term predictor for the intermittent bursts of energy dissipation. We assess the performance of this predictor through direct numerical simulations. PMID:28948226

Comparing Models of Spontaneous Variations, Maneuvers and Indexes to Assess Dynamic Cerebral Autoregulation.

PubMed

Chacón, Max; Noh, Sun-Ho; Landerretche, Jean; Jara, José L

2018-01-01

We analyzed the performance of linear and nonlinear models to assess dynamic cerebral autoregulation (dCA) from spontaneous variations in healthy subjects and compared it with the use of two known maneuvers to abruptly change arterial blood pressure (BP): thigh cuffs and sit-to-stand. Cerebral blood flow velocity and BP were measured simultaneously at rest and while the maneuvers were performed in 20 healthy subjects. To analyze the spontaneous variations, we implemented two types of models using support vector machine (SVM): linear and nonlinear finite impulse response models. The classic autoregulation index (ARI) and the more recently proposed model-free ARI (mfARI) were used as measures of dCA. An ANOVA analysis was applied to compare the different methods and the coefficient of variation was calculated to evaluate their variability. There are differences between indexes, but not between models and maneuvers. The mfARI index with the sit-to-stand maneuver shows the least variability. Support vector machine modeling of spontaneous variation with the mfARI index could be used for the assessment of dCA as an alternative to maneuvers to introduce large BP fluctuations.

Closing the Loop for Memory Prostheses: Detecting the Role of Hippocampal Neural Ensembles Using Nonlinear Models

PubMed Central

Hampson, Robert E.; Song, Dong; Chan, Rosa H.M.; Sweatt, Andrew J.; Riley, Mitchell R.; Goonawardena, Anushka V.; Marmarelis, Vasilis Z.; Gerhardt, Greg A.; Berger, Theodore W.; Deadwyler, Sam A.

2012-01-01

A major factor involved in providing closed loop feedback for control of neural function is to understand how neural ensembles encode online information critical to the final behavioral endpoint. This issue was directly assessed in rats performing a short-term delay memory task in which successful encoding of task information is dependent upon specific spatiotemporal firing patterns recorded from ensembles of CA3 and CA1 hippocampal neurons. Such patterns, extracted by a specially designed nonlinear multi-input multi-output (MIMO) nonlinear mathematical model, were used to predict successful performance online via a closed loop paradigm which regulated trial difficulty (time of retention) as a function of the “strength” of stimulus encoding. The significance of the MIMO model as a neural prosthesis has been demonstrated by substituting trains of electrical stimulation pulses to mimic these same ensemble firing patterns. This feature was used repeatedly to vary “normal” encoding as a means of understanding how neural ensembles can be “tuned” to mimic the inherent process of selecting codes of different strength and functional specificity. The capacity to enhance and tune hippocampal encoding via MIMO model detection and insertion of critical ensemble firing patterns shown here provides the basis for possible extension to other disrupted brain circuitry. PMID:22498704

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.

PubMed

El-Shamy, E F

2015-03-01

The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.

Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch.

PubMed

Bache, Morten; Nielsen, Hanne; Laegsgaard, Jesper; Bang, Ole

2006-06-01

We consider an index-guiding silica photonic crystal fiber with a triangular hole pattern and a periodically poled quadratic nonlinearity. By tuning the pitch and the relative hole size, second-harmonic generation with zero group-velocity mismatch is found for any fundamental wavelength above 780 nm. The nonlinear strength is optimized when the fundamental has maximum confinement in the core. The conversion bandwidth allows for femtosecond-pulse conversion, and 4%-180%W(-1)cm(-2) relative efficiencies were found.

A biometric latent curve analysis of memory decline in older men of the NAS-NRC twin registry.

PubMed

McArdle, John J; Plassman, Brenda L

2009-09-01

Previous research has shown cognitive abilities to have different biometric patterns of age-changes. We examined the variation in episodic memory (word recall task) for over 6,000 twin pairs who were initially aged 59-75, and were subsequently re-assessed up to three more times over 12 years. In cross-sectional analyses, variation in the number of words recalled independent of age was explained largely by non-shared influences (65-72%), with clear additive genetic influences (12-32%), and marginal shared family influences (1-18%). The longitudinal phenotypic analysis of the word recall task showed systematic linear declines over age, but several nonlinear models with more dramatic changes at later ages, improved the overall fit. A two-part spline model for the longitudinal twin data with an optimal turning point at age 74 led to: (a) a separation of non-shared environmental influences and transient measurement error (~50%); (b) strong additive genetic components of this latent curve (~44% at age 60) with increases (over 50%) up to age 74, but with no additional genetic variation after age 74; (c) the smaller influences of shared family environment (~15% at age 74) were constant over all ages; (d) non-shared effects play an important role over most of the life-span but diminish after age 74.

A comparative study between nonlinear regression and artificial neural network approaches for modelling wild oat (Avena fatua) field emergence

USDA-ARS?s Scientific Manuscript database

Non-linear regression techniques are used widely to fit weed field emergence patterns to soil microclimatic indices using S-type functions. Artificial neural networks present interesting and alternative features for such modeling purposes. In this work, a univariate hydrothermal-time based Weibull m...

The nonlocal elastomagnetoelectrostatics of disordered micropolar media

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

Kabychenkov, A. F.; Lisiovskii, F. V., E-mail: lisf@rambler.ru

The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2003-01-01

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Predicting seizures in untreated temporal lobe epilepsy using point-process nonlinear models of heartbeat dynamics.

PubMed

Valenza, G; Romigi, A; Citi, L; Placidi, F; Izzi, F; Albanese, M; Scilingo, E P; Marciani, M G; Duggento, A; Guerrisi, M; Toschi, N; Barbieri, R

2016-08-01

Symptoms of temporal lobe epilepsy (TLE) are frequently associated with autonomic dysregulation, whose underlying biological processes are thought to strongly contribute to sudden unexpected death in epilepsy (SUDEP). While abnormal cardiovascular patterns commonly occur during ictal events, putative patterns of autonomic cardiac effects during pre-ictal (PRE) periods (i.e. periods preceding seizures) are still unknown. In this study, we investigated TLE-related heart rate variability (HRV) through instantaneous, nonlinear estimates of cardiovascular oscillations during inter-ictal (INT) and PRE periods. ECG recordings from 12 patients with TLE were processed to extract standard HRV indices, as well as indices of instantaneous HRV complexity (dominant Lyapunov exponent and entropy) and higher-order statistics (bispectra) obtained through definition of inhomogeneous point-process nonlinear models, employing Volterra-Laguerre expansions of linear, quadratic, and cubic kernels. Experimental results demonstrate that the best INT vs. PRE classification performance (balanced accuracy: 73.91%) was achieved only when retaining the time-varying, nonlinear, and non-stationary structure of heartbeat dynamical features. The proposed approach opens novel important avenues in predicting ictal events using information gathered from cardiovascular signals exclusively.

Discrimination of nonlinear frequency glides.

PubMed

Thyer, Nick; Mahar, Doug

2006-05-01

Discrimination thresholds for short duration nonlinear tone glides that differed in glide rate were measured in order to determine whether cues related to rate of frequency change alone were sufficient for discrimination. Thresholds for rising and falling nonlinear glides of 50-ms and 400-ms duration, spanning three frequency excursions (0.5, 1, and 2 ERBs) at three center frequencies (0.5, 2.0, and 6.0 kHz) were measured. Results showed that glide discrimination was possible when duration and initial and final frequencies were identical. Thresholds were of a different order to those found in previous studies using linear frequency glides where endpoint frequency or duration information is available as added cues. The pattern of results was suggestive of a mechanism sensitive to spectral changes in time. Thresholds increased as the rate of transition span increased, particularly above spans of 1 ERB. The Weber fraction associated with these changes was 0.6-0.7. Overall, the results were consistent with an excitation pattern model of nonlinear glide detection that has difficulty in tracking signals with rapid frequency changes that exceed the width of an auditory filter and are of short duration.

Coexistence of Multiple Nonlinear States in a Tristable Passive Kerr Resonator

NASA Astrophysics Data System (ADS)

Anderson, Miles; Wang, Yadong; Leo, François; Coen, Stéphane; Erkintalo, Miro; Murdoch, Stuart G.

2017-07-01

Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localized dissipative structures (solitons). Their conceptual simplicity has for several decades offered an unprecedented window into nonlinear cavity dynamics, providing insights into numerous systems and applications ranging from all-optical memory devices to microresonator frequency combs. Yet despite the decades of study, a recent theoretical work has surprisingly alluded to an entirely new and unexplored paradigm in the regime where nonlinearly tilted cavity resonances overlap with one another [T. Hansson and S. Wabnitz, J. Opt. Soc. Am. B 32, 1259 (2015), 10.1364/JOSAB.32.001259]. We use synchronously driven fiber ring resonators to experimentally access this regime and observe the rise of new nonlinear dissipative states. Specifically, we observe, for the first time to the best of our knowledge, the stable coexistence of temporal Kerr cavity solitons and extended modulation instability (Turing) patterns, and perform real-time measurements that unveil the dynamics of the ensuing nonlinear structure. When operating in the regime of continuous wave tristability, we further observe the coexistence of two distinct cavity soliton states, one of which can be identified as a "super" cavity soliton, as predicted by Hansson and Wabnitz. Our experimental findings are in excellent agreement with theoretical analyses and numerical simulations of the infinite-dimensional Ikeda map that governs the cavity dynamics. The results from our work reveal that experimental systems can support complex combinations of distinct nonlinear states, and they could have practical implications to future microresonator-based frequency comb sources.

Inbreeding Depression and Male Survivorship in Drosophila: Implications for Senescence Theory

PubMed Central

Swindell, William R.; Bouzat, Juan L.

2006-01-01

The extent to which inbreeding depression affects longevity and patterns of survivorship is an important issue from several research perspectives, including evolutionary biology, conservation biology, and the genetic analysis of quantitative traits. However, few previous inbreeding depression studies have considered longevity as a focal life-history trait. We maintained laboratory populations of Drosophila melanogaster at census population sizes of 2 and 10 male-female pairs for up to 66 generations and performed repeated assays of male survivorship throughout this time period. On average, significant levels of inbreeding depression were observed for median life span and age-specific mortality. For age-specific mortality, the severity of inbreeding depression increased over the life span. We found that a baseline inbreeding load of 0.307 lethal equivalents per gamete affected age-specific mortality, and that this value increased at a rate of 0.046 per day of the life span. With respect to some survivorship parameters, the differentiation of lineages was nonlinear with respect to the inbreeding coefficient, which suggested that nonadditive genetic variation contributed to variation among lineages. These findings provide insights into the genetic basis of longevity as a quantitative trait and have implications regarding the mutation-accumulation evolutionary explanation of senescence. PMID:16204222

Modifiers: Increasing Richness and Nuance of Design Pattern Languages

NASA Astrophysics Data System (ADS)

Kolfschoten, Gwendolyn L.; Briggs, Robert O.; Lukosch, Stephan

One of the challenges when establishing and maintaining a pattern language is to balance richness with simplicity. On the one hand, designers need a variety of useful design patterns to increase the speed of their design efforts and to reduce design risk. On the other hand, the greater the variety of design patterns in a language, the higher the cognitive load to remember and select among them. One solution to this problem is the concept of a modifier design pattern, a design pattern for pattern languages. A modifier pattern is a named, documented variation that can be applied to some set of other design patterns. They create similar, useful changes and refinements to the solutions derived from any pattern to which they are applied. The modifier concept, described in this paper emerged in a relatively new design pattern language for collaborative work practices in which the design patterns are called thinkLets. When analyzing the thinkLet pattern language, we found that many of the patterns we knew were variations and refinements of other patterns. However, we also found patterns in these variations; we found variations that could be applied to different patterns, with similar effects. We document these variations as modifiers. In this paper, we introduce the concept of modifier design patterns and illustrate the use of modifiers with two case studies.

The effects of surface evaporation parameterizations on climate sensitivity to solar constant variations

NASA Technical Reports Server (NTRS)

Chou, S.-H.; Curran, R. J.; Ohring, G.

1981-01-01

The effects of two different evaporation parameterizations on the sensitivity of simulated climate to solar constant variations are investigated by using a zonally averaged climate model. One parameterization is a nonlinear formulation in which the evaporation is nonlinearly proportional to the sensible heat flux, with the Bowen ratio determined by the predicted vertical temperature and humidity gradients near the earth's surface (model A). The other is the formulation of Saltzman (1968) with the evaporation linearly proportional to the sensible heat flux (model B). The computed climates of models A and B are in good agreement except for the energy partition between sensible and latent heat at the earth's surface. The difference in evaporation parameterizations causes a difference in the response of temperature lapse rate to solar constant variations and a difference in the sensitivity of longwave radiation to surface temperature which leads to a smaller sensitivity of surface temperature to solar constant variations in model A than in model B. The results of model A are qualitatively in agreement with those of the general circulation model calculations of Wetherald and Manabe (1975).

Pattern Formation in Complex Fluids

NASA Astrophysics Data System (ADS)

Shelley, Michael

2000-03-01

Classical fluid instabilities -- such as the Saffman-Taylor instability in a Hele-Shaw cell -- are dramatically modified by using complex fluids. For example, polymeric liquids driven in a Hele-Shaw cell yield "dendritic" patterns with an apparent directional anisotropy. The dynamics of complex liquids can also lead to new instabilities and patterns, such as space-filling patterns formed by successive bucklings of growing "elastica" seen in the phase transition of a liquid crystalline material. Understanding such problems requires an interplay between physical modeling, mathematical analysis, and sophisticated nonlinear simulation. For the first problem, I will discuss a non-Newtonian version of Darcy's law for Hele-Shaw flow. This yields a free-boundary problem for the pattern formation, and requires the solution of a nonlinear elliptic equation in a time-dependent domain. This is pushing the development of adaptive grid methods that represent the geometry accurately and efficiently. Our simulations yield insight into how shear-thinning, as is evinced by polymeric liquids, can produce patterns reminiscent of experiment, with "dendritic fingers", side-branching, and reduced tip-splitting. In the second problem, a long filament in a smectic-A phase grows within an isotropic fluid. The splay deformation of the material gives this filament an elastic response. The macroscopic model describes the dynamics of a growing, elastic filament immersed in a Stokesian fluid. The model marries filament elasticity and tensile forces with a numerically tractable nonlocal slender-body theory. Analysis shows that growth of the filament, despite fluid drag, produces a buckling instability. When coupled to a nonlocal hydrodynamic self-interaction, our fully nonlinear simulations show that such instabilities iterate along the filament, and give "space-filling" patterns.

A mixed-order nonlinear diffusion compressed sensing MR image reconstruction.

PubMed

Joy, Ajin; Paul, Joseph Suresh

2018-03-07

Avoid formation of staircase artifacts in nonlinear diffusion-based MR image reconstruction without compromising computational speed. Whereas second-order diffusion encourages the evolution of pixel neighborhood with uniform intensities, fourth-order diffusion considers smooth region to be not necessarily a uniform intensity region but also a planar region. Therefore, a controlled application of fourth-order diffusivity function is used to encourage second-order diffusion to reconstruct the smooth regions of the image as a plane rather than a group of blocks, while not being strong enough to introduce the undesirable speckle effect. Proposed method is compared with second- and fourth-order nonlinear diffusion reconstruction, total variation (TV), total generalized variation, and higher degree TV using in vivo data sets for different undersampling levels with application to dictionary learning-based reconstruction. It is observed that the proposed technique preserves sharp boundaries in the image while preventing the formation of staircase artifacts in the regions of smoothly varying pixel intensities. It also shows reduced error measures compared with second-order nonlinear diffusion reconstruction or TV and converges faster than TV-based methods. Because nonlinear diffusion is known to be an effective alternative to TV for edge-preserving reconstruction, the crucial aspect of staircase artifact removal is addressed. Reconstruction is found to be stable for the experimentally determined range of fourth-order regularization parameter, and therefore not does not introduce a parameter search. Hence, the computational simplicity of second-order diffusion is retained. © 2018 International Society for Magnetic Resonance in Medicine.

Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity.

PubMed

Merkel, A; Tournat, V; Gusev, V

2014-08-01

We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.

What is more important for national well-being: money or autonomy? A meta-analysis of well-being, burnout, and anxiety across 63 societies.

PubMed

Fischer, Ronald; Boer, Diana

2011-07-01

What is more important: to provide citizens with more money or with more autonomy for their subjective well-being? In the current meta-analysis, the authors examined national levels of well-being on the basis of lack of psychological health, anxiety, and stress measures. Data are available for 63 countries, with a total sample of 420,599 individuals. Using a 3-level variance-known model, the authors found that individualism was a consistently better predictor than wealth, after controlling for measurement, sample, and temporal variations. Despite some emerging nonlinear trends and interactions between wealth and individualism, the overall pattern strongly suggests that greater individualism is consistently associated with more well-being. Wealth may influence well-being only via its effect on individualism. Implications of the findings for well-being research and applications are outlined. PsycINFO Database Record (c) 2011 APA, all rights reserved.

Estimating monthly streamflow values by cokriging

USGS Publications Warehouse

Solow, A.R.; Gorelick, S.M.

1986-01-01

Cokriging is applied to estimation of missing monthly streamflow values in three records from gaging stations in west central Virginia. Missing values are estimated from optimal consideration of the pattern of auto- and cross-correlation among standardized residual log-flow records. Investigation of the sensitivity of estimation to data configuration showed that when observations are available within two months of a missing value, estimation is improved by accounting for correlation. Concurrent and lag-one observations tend to screen the influence of other available observations. Three models of covariance structure in residual log-flow records are compared using cross-validation. Models differ in how much monthly variation they allow in covariance. Precision of estimation, reflected in mean squared error (MSE), proved to be insensitive to this choice. Cross-validation is suggested as a tool for choosing an inverse transformation when an initial nonlinear transformation is applied to flow values. ?? 1986 Plenum Publishing Corporation.

Phase-selective entrainment of nonlinear oscillator ensembles

DOE PAGES

Zlotnik, Anatoly V.; Nagao, Raphael; Kiss, Istvan Z.; ...

2016-03-18

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups intomore » spatiotemporal patterns with multiple phase clusters. As a result, the experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.« less

Bi-dimensional empirical mode decomposition based fringe-like pattern suppression in polarization interference imaging spectrometer

NASA Astrophysics Data System (ADS)

Ren, Wenyi; Cao, Qizhi; Wu, Dan; Jiang, Jiangang; Yang, Guoan; Xie, Yingge; Wang, Guodong; Zhang, Sheqi

2018-01-01

Many observers using interference imaging spectrometer were plagued by the fringe-like pattern(FP) that occurs for optical wavelengths in red and near-infrared region. It brings us more difficulties in the data processing such as the spectrum calibration, information retrieval, and so on. An adaptive method based on the bi-dimensional empirical mode decomposition was developed to suppress the nonlinear FP in polarization interference imaging spectrometer. The FP and corrected interferogram were separated effectively. Meanwhile, the stripes introduced by CCD mosaic was suppressed. The nonlinear interferogram background removal and the spectrum distortion correction were implemented as well. It provides us an alternative method to adaptively suppress the nonlinear FP without prior experimental data and knowledge. This approach potentially is a powerful tool in the fields of Fourier transform spectroscopy, holographic imaging, optical measurement based on moire fringe, etc.

Phase-selective entrainment of nonlinear oscillator ensembles

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

Zlotnik, Anatoly V.; Nagao, Raphael; Kiss, Istvan Z.

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups intomore » spatiotemporal patterns with multiple phase clusters. As a result, the experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.« less

Phase-selective entrainment of nonlinear oscillator ensembles

NASA Astrophysics Data System (ADS)

Zlotnik, Anatoly; Nagao, Raphael; Kiss, István Z.; Li-Shin, Jr.

2016-03-01

The ability to organize and finely manipulate the hierarchy and timing of dynamic processes is important for understanding and influencing brain functions, sleep and metabolic cycles, and many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles is a challenging task that requires controlling large collections of complex nonlinear dynamical units. In this report, we present a method to design entrainment signals that create stable phase patterns in ensembles of heterogeneous nonlinear oscillators without using state feedback information. We demonstrate the approach using experiments with electrochemical reactions on multielectrode arrays, in which we selectively assign ensemble subgroups into spatiotemporal patterns with multiple phase clusters. The experimentally confirmed mechanism elucidates the connection between the phases and natural frequencies of a collection of dynamical elements, the spatial and temporal information that is encoded within this ensemble, and how external signals can be used to retrieve this information.

Sum-Frequency Generation from a Thin Cylindrical Layer

NASA Astrophysics Data System (ADS)

Shamyna, A. A.; Kapshai, V. N.

2018-01-01

In the Rayleigh-Gans-Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.

Modelling Nonlinear Dynamic Textures using Hybrid DWT-DCT and Kernel PCA with GPU

NASA Astrophysics Data System (ADS)

Ghadekar, Premanand Pralhad; Chopade, Nilkanth Bhikaji

2016-12-01

Most of the real-world dynamic textures are nonlinear, non-stationary, and irregular. Nonlinear motion also has some repetition of motion, but it exhibits high variation, stochasticity, and randomness. Hybrid DWT-DCT and Kernel Principal Component Analysis (KPCA) with YCbCr/YIQ colour coding using the Dynamic Texture Unit (DTU) approach is proposed to model a nonlinear dynamic texture, which provides better results than state-of-art methods in terms of PSNR, compression ratio, model coefficients, and model size. Dynamic texture is decomposed into DTUs as they help to extract temporal self-similarity. Hybrid DWT-DCT is used to extract spatial redundancy. YCbCr/YIQ colour encoding is performed to capture chromatic correlation. KPCA is applied to capture nonlinear motion. Further, the proposed algorithm is implemented on Graphics Processing Unit (GPU), which comprise of hundreds of small processors to decrease time complexity and to achieve parallelism.

Analysis of Nonlinear Dynamics in Linear Compressors Driven by Linear Motors

NASA Astrophysics Data System (ADS)

Chen, Liangyuan

2018-03-01

The analysis of dynamic characteristics of the mechatronics system is of great significance for the linear motor design and control. Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically based on the linearized and nonlinear models. First, the influence factors considering the nonlinear gas force load were analyzed. Then, a simple linearized model was set up to analyze the influence on the stroke and resonance frequency. Finally, the nonlinear model was set up to analyze the effects of piston mass, spring stiffness, driving force as an example of design parameter variation. The simulating results show that the stroke can be obtained by adjusting the excitation amplitude, frequency and other adjustments, the equilibrium position can be adjusted by adjusting the DC input, and to make the more efficient operation, the operating frequency must always equal to the resonance frequency.

Nonlinear engine model for idle speed control

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

Livshiz, M.; Sanvido, D.J.; Stiles, S.D.

1994-12-31

This paper describes a nonlinear model of an engine used for the design of idle speed control and prediction in a broad range of idle speeds and operational conditions. Idle speed control systems make use of both spark advance and the idle air actuator to control engine speed for improved response relative to variations in the target idle speed due to load disturbances. The control system at idle can be presented by a multiple input multiple output (MIMO) nonlinear model. Information of nonlinearities helps to improve performance of the system over the whole range of engine speeds. A proposed simplemore » nonlinear model of the engine at idle was applied for design of optimal controllers and predictors for improved steady state, load rejection and transition from and to idle. This paper describes vehicle results of engine speed prediction based on the described model.« less

Effective Desynchronization by Nonlinear Delayed Feedback

NASA Astrophysics Data System (ADS)

Popovych, Oleksandr V.; Hauptmann, Christian; Tass, Peter A.

2005-04-01

We show that nonlinear delayed feedback opens up novel means for the control of synchronization. In particular, we propose a demand-controlled method for powerful desynchronization, which does not require any time-consuming calibration. Our technique distinguishes itself by its robustness against variations of system parameters, even in strongly coupled ensembles of oscillators. We suggest our method for mild and effective deep brain stimulation in neurological diseases characterized by pathological cerebral synchronization.

Dynamics of Nonlinear Excitation of the High-Order Mode in a Single-Mode Step-Index Optical Fiber

NASA Astrophysics Data System (ADS)

Burdin, V.; Bourdine, A.

2018-04-01

This work is concerned with approximate model of higher-order mode nonlinear excitation in a singlemode silica optical fiber. We present some results of simulation for step-index optical fiber under femtosecond optical pulse launching, which confirm ability of relatively stable higher-order mode excitation in such singlemode optical fiber over sufficiently narrow range of launched optical power variation.

Numerical simulations to the nonlinear model of interpersonal relationships with time fractional derivative

NASA Astrophysics Data System (ADS)

Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan

2017-01-01

The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.

A regime-switching cointegration approach for removing environmental and operational variations in structural health monitoring

NASA Astrophysics Data System (ADS)

Shi, Haichen; Worden, Keith; Cross, Elizabeth J.

2018-03-01

Cointegration is now extensively used to model the long term common trends among economic variables in the field of econometrics. Recently, cointegration has been successfully implemented in the context of structural health monitoring (SHM), where it has been used to remove the confounding influences of environmental and operational variations (EOVs) that can often mask the signature of structural damage. However, restrained by its linear nature, the conventional cointegration approach has limited power in modelling systems where measurands are nonlinearly related; this occurs, for example, in the benchmark study of the Z24 Bridge, where nonlinear relationships between natural frequencies were induced during a period of very cold temperatures. To allow the removal of EOVs from SHM data with nonlinear relationships like this, this paper extends the well-established cointegration method to a nonlinear context, which is to allow a breakpoint in the cointegrating vector. In a novel approach, the augmented Dickey-Fuller (ADF) statistic is used to find which position is most appropriate for inserting a breakpoint, the Johansen procedure is then utilised for the estimation of cointegrating vectors. The proposed approach is examined with a simulated case and real SHM data from the Z24 Bridge, demonstrating that the EOVs can be neatly eliminated.

Least squares reconstruction of non-linear RF phase encoded MR data.

PubMed

Salajeghe, Somaie; Babyn, Paul; Sharp, Jonathan C; Sarty, Gordon E

2016-09-01

The numerical feasibility of reconstructing MRI signals generated by RF coils that produce B1 fields with a non-linearly varying spatial phase is explored. A global linear spatial phase variation of B1 is difficult to produce from current confined to RF coils. Here we use regularized least squares inversion, in place of the usual Fourier transform, to reconstruct signals generated in B1 fields with non-linear phase variation. RF encoded signals were simulated for three RF coil configurations: ideal linear, parallel conductors and, circular coil pairs. The simulated signals were reconstructed by Fourier transform and by regularized least squares. The Fourier reconstruction of simulated RF encoded signals from the parallel conductor coil set showed minor distortions over the reconstruction of signals from the ideal linear coil set but the Fourier reconstruction of signals from the circular coil set produced severe geometric distortion. Least squares inversion in all cases produced reconstruction errors comparable to the Fourier reconstruction of the simulated signal from the ideal linear coil set. MRI signals encoded in B1 fields with non-linearly varying spatial phase may be accurately reconstructed using regularized least squares thus pointing the way to the use of simple RF coil designs for RF encoded MRI. Crown Copyright © 2016. Published by Elsevier Inc. All rights reserved.

The optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

NASA Astrophysics Data System (ADS)

Singh, Randhir; Das, Nilima; Kumar, Jitendra

2017-06-01

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

Feature extraction via KPCA for classification of gait patterns.

PubMed

Wu, Jianning; Wang, Jue; Liu, Li

2007-06-01

Automated recognition of gait pattern change is important in medical diagnostics as well as in the early identification of at-risk gait in the elderly. We evaluated the use of Kernel-based Principal Component Analysis (KPCA) to extract more gait features (i.e., to obtain more significant amounts of information about human movement) and thus to improve the classification of gait patterns. 3D gait data of 24 young and 24 elderly participants were acquired using an OPTOTRAK 3020 motion analysis system during normal walking, and a total of 36 gait spatio-temporal and kinematic variables were extracted from the recorded data. KPCA was used first for nonlinear feature extraction to then evaluate its effect on a subsequent classification in combination with learning algorithms such as support vector machines (SVMs). Cross-validation test results indicated that the proposed technique could allow spreading the information about the gait's kinematic structure into more nonlinear principal components, thus providing additional discriminatory information for the improvement of gait classification performance. The feature extraction ability of KPCA was affected slightly with different kernel functions as polynomial and radial basis function. The combination of KPCA and SVM could identify young-elderly gait patterns with 91% accuracy, resulting in a markedly improved performance compared to the combination of PCA and SVM. These results suggest that nonlinear feature extraction by KPCA improves the classification of young-elderly gait patterns, and holds considerable potential for future applications in direct dimensionality reduction and interpretation of multiple gait signals.

Stratification Pattern of Static and Scale-Invariant Dynamic Measures of Heartbeat Fluctuations Across Sleep Stages in Young and Elderly

PubMed Central

Schmitt, Daniel T.; Stein, Phyllis K.; Ivanov, Plamen Ch.

2010-01-01

Cardiac dynamics exhibit complex variability characterized by scale-invariant and nonlinear temporal organization related to the mechanism of neuroautonomic control, which changes with physiologic states and pathologic conditions. Changes in sleep regulation during sleep stages are also related to fluctuations in autonomic nervous activity. However, the interaction between sleep regulation and cardiac autonomic control remains not well understood. Even less is known how this interaction changes with age, as aspects of both cardiac dynamics and sleep regulation differ in healthy elderly compared to young subjects. We hypothesize that because of the neuroautonomic responsiveness in young subjects, fractal and nonlinear features of cardiac dynamics exhibit a pronounced stratification pattern across sleep stages, while in elderly these features will remain unchanged due to age-related loss of cardiac variability and decline of neuroautonomic responsiveness. We analyze the variability and the temporal fractal organization of heartbeat fluctuations across sleep stages in both young and elderly. We find that independent linear and nonlinear measures of cardiac control consistently exhibit the same ordering in their values across sleep stages, forming a robust stratification pattern. Despite changes in sleep architecture and reduced heart rate variability in elderly subjects, this stratification surprisingly does not break down with advanced age. Moreover, the difference between sleep stages for some linear, fractal, and nonlinear measures exceeds the difference between young and elderly, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. Quantifying changes in this stratification pattern may provide insights into how alterations in sleep regulation contribute to increased cardiac risk. PMID:19203874

Annual variation in the atmospheric radon concentration in Japan.

PubMed

Kobayashi, Yuka; Yasuoka, Yumi; Omori, Yasutaka; Nagahama, Hiroyuki; Sanada, Tetsuya; Muto, Jun; Suzuki, Toshiyuki; Homma, Yoshimi; Ihara, Hayato; Kubota, Kazuhito; Mukai, Takahiro

2015-08-01

Anomalous atmospheric variations in radon related to earthquakes have been observed in hourly exhaust-monitoring data from radioisotope institutes in Japan. The extraction of seismic anomalous radon variations would be greatly aided by understanding the normal pattern of variation in radon concentrations. Using atmospheric daily minimum radon concentration data from five sampling sites, we show that a sinusoidal regression curve can be fitted to the data. In addition, we identify areas where the atmospheric radon variation is significantly affected by the variation in atmospheric turbulence and the onshore-offshore pattern of Asian monsoons. Furthermore, by comparing the sinusoidal regression curve for the normal annual (seasonal) variations at the five sites to the sinusoidal regression curve for a previously published dataset of radon values at the five Japanese prefectures, we can estimate the normal annual variation pattern. By fitting sinusoidal regression curves to the previously published dataset containing sites in all Japanese prefectures, we find that 72% of the Japanese prefectures satisfy the requirements of the sinusoidal regression curve pattern. Using the normal annual variation pattern of atmospheric daily minimum radon concentration data, these prefectures are suitable areas for obtaining anomalous radon variations related to earthquakes. Copyright © 2015 Elsevier Ltd. All rights reserved.

Optical Pattern Formation in Cold Atoms: Explaining the Red-Blue Asymmetry

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie; Gauthier, Daniel

2013-05-01

The study of pattern formation in atomic systems has provided new insight into fundamental many-body physics and low-light-level nonlinear optics. Pattern formation in cold atoms in particular is of great interest in condensed matter physics and quantum information science because atoms undergo self-organization at ultralow input powers. We recently reported the first observation of pattern formation in cold atoms but found that our results were not accurately described by any existing theoretical model of pattern formation. Previous models describing pattern formation in cold atoms predict that pattern formation should occur using both red and blue-detuned pump beams, favoring a lower threshold for blue detunings. This disagrees with our recent work, in which we only observed pattern formation with red-detuned pump beams. Previous models also assume a two-level atom, which cannot account for the cooling processes that arise when beams counterpropagate through a cold atomic vapor. We describe a new model for pattern formation that accounts for Sisyphus cooling in multi-level atoms, which gives rise to a new nonlinearity via spatial organization of the atoms. This spatial organization causes a sharp red-blue detuning asymmetry, which agrees well with our experimental observations. We gratefully acknowledge the financial support of the NSF through Grant #PHY-1206040.

Connections Among the Spatial and Temporal Structures in Tidal Currents, Internal Bores, and Surficial Sediment Distributions Over the Shelf off Palos Verdes, California

USGS Publications Warehouse

Noble, Marlene A.; Rosenberger, Kurt J.; Xu, Jingping; Signell, Richard P.; Steele, Alex

2009-01-01

The topography of the Continental Shelf in the central portion of the Southern California Bight has rapid variations over relatively small spatial scales. The width of the shelf off the Palos Verdes peninsula, just northwest of Los Angeles, California, is only 1 to 3 km. About 7 km southeast of the peninsula, the shelf within San Pedro Bay widens to about 20 km. In 2000, the Los Angeles County Sanitation District began deploying a dense array of moorings in this complex region of the central Southern California Bight to monitor local circulation patterns. Moorings were deployed at 13 sites on the Palos Verdes shelf and within the northwestern portion of San Pedro Bay. At each site, a mooring supported a string of thermistors and an adjacent bottom platform housed an Acoustic Doppler Current Profiler. These instruments collected vertical profiles of current and temperature data continuously for one to two years. The variable bathymetry in the region causes rapid changes in the amplitudes and spatial structures of barotropic tidal currents, internal tidal currents, and in the associated nonlinear baroclinic currents that occur at approximate tidal frequencies. The largest barotropic tidal constituent is M2, the principal semidiurnal tide. The amplitude of this tidal current changes over fairly short along-shelf length scales. Tidal-current amplitudes are largest in the transition region between the two shelves; they increase from about 5 cm/s over the northern San Pedro shelf to nearly 10 cm/s on the southern portion of the Palos Verdes Shelf. Tidal-current amplitudes are then reduced to less than 2 cm/s over the very narrow section of the northern Palos Verdes shelf that lies just 6 km upcoast of the southern sites. Models suggest that the amplitude of the barotropic M2 tidal currents, which propagate toward the northwest primarily as a Kelvin wave, is adjusting to the short topographic length scales in the region. Semidiurnal sea-level oscillations are, as expected, independent of these topographic variations; they have a uniform amplitude and phase structure over the entire region. Because the cross-shelf angle of the seabed over most of the Palos Verdes shelf is 1 to 3 degrees, which is critical for the local generation and/or enhancement of nonlinear characteristics in semidiurnal internal tides, some internal tidal-current events have strong asymmetric current oscillations that are enhanced near the seabed. Near-bottom currents in these events are directed primarily offshore with amplitudes that exceed 30 cm/s. The spatial patterns in these energetic near-bottom currents have fairly short-length scales. They are largest over the inner shelf and in the transition region between the Palos Verdes and San Pedro shelves. This spatial pattern is similar to that found in the barotropic tidal currents. Because these baroclinic currents have an approximate tidal frequency, an asymmetric vertical structure, and a somewhat stable phase, they can produce a non-zero depth-mean flow for periods of a few months. These baroclinic currents can interact with the barotropic tidal current and cause an apparent increase (or decrease) in the estimated barotropic tidal-current amplitude. The apparent amplitude of the barotropic tidal current may change by 30 to 80 percent or more in a current record that is less than three months long. The currents and surficial sediments in this region are in dynamic equilibrium in that the spatial patterns in bottom stresses generated by near-bed currents from surface tides, internal tides, and internal bores partly control the spatial patterns in the local sediments. Coarser sediments are found in the regions with enhanced bottom stresses (that is, over the inner shelf and in the region between the Palos Verdes and San Pedro shelves). Finer sediments are found over the northwestern portion of the Palos Verdes shelf, where near-bottom currents are relatively weak. The nonlinear asymmetries in the i

Weak variations of Lipschitz graphs and stability of phase boundaries

NASA Astrophysics Data System (ADS)

Grabovsky, Yury; Kucher, Vladislav A.; Truskinovsky, Lev

2011-03-01

In the case of Lipschitz extremals of vectorial variational problems, an important class of strong variations originates from smooth deformations of the corresponding non-smooth graphs. These seemingly singular variations, which can be viewed as combinations of weak inner and outer variations, produce directions of differentiability of the functional and lead to singularity-centered necessary conditions on strong local minima: an equality, arising from stationarity, and an inequality, implying configurational stability of the singularity set. To illustrate the underlying coupling between inner and outer variations, we study in detail the case of smooth surfaces of gradient discontinuity representing, for instance, martensitic phase boundaries in non-linear elasticity.

The role of ferroelectric domain structure in second harmonic generation in random quadratic media.

PubMed

Roppo, Vito; Wang, W; Kalinowski, K; Kong, Y; Cojocaru, C; Trull, J; Vilaseca, R; Scalora, M; Krolikowski, W; Kivshar, Yu

2010-03-01

We study theoretically and numerically the second harmonic generation in a nonlinear crystal with random distribution of ferroelectric domains. We show that the specific features of disordered domain structure greatly affect the emission pattern of the generated harmonics. This phenomena can be used to characterize the degree of disorder in nonlinear photonic structures.

Nonlinear dynamics of Aeolian sand ripples.

PubMed

Prigozhin, L

1999-07-01

We study the initial instability of flat sand surface and further nonlinear dynamics of wind ripples. The proposed continuous model of ripple formation allowed us to simulate the development of a typical asymmetric ripple shape and the evolution of a sand ripple pattern. We suggest that this evolution occurs via ripple merger preceded by several soliton-like interaction of ripples.

Identifying Complex Dynamics in Social Systems: A New Methodological Approach Applied to Study School Segregation

ERIC Educational Resources Information Center

Spaiser, Viktoria; Hedström, Peter; Ranganathan, Shyam; Jansson, Kim; Nordvik, Monica K.; Sumpter, David J. T.

2018-01-01

It is widely recognized that segregation processes are often the result of complex nonlinear dynamics. Empirical analyses of complex dynamics are however rare, because there is a lack of appropriate empirical modeling techniques that are capable of capturing complex patterns and nonlinearities. At the same time, we know that many social phenomena…

Spatiotemporal Dynamics of a Network of Coupled Time-Delay Digital Tanlock Loops

NASA Astrophysics Data System (ADS)

Paul, Bishwajit; Banerjee, Tanmoy; Sarkar, B. C.

The time-delay digital tanlock loop (TDTLs) is an important class of phase-locked loop that is widely used in electronic communication systems. Although nonlinear dynamics of an isolated TDTL has been studied in the past but the collective behavior of TDTLs in a network is an important topic of research and deserves special attention as in practical communication systems separate entities are rarely isolated. In this paper, we carry out the detailed analysis and numerical simulations to explore the spatiotemporal dynamics of a network of a one-dimensional ring of coupled TDTLs with nearest neighbor coupling. The equation representing the network is derived and we carry out analytical calculations using the circulant matrix formalism to obtain the stability criteria. An extensive numerical simulation reveals that with the variation of gain parameter and coupling strength the network shows a variety of spatiotemporal dynamics such as frozen random pattern, pattern selection, spatiotemporal intermittency and fully developed spatiotemporal chaos. We map the distinct dynamical regions of the system in two-parameter space. Finally, we quantify the spatiotemporal dynamics by using quantitative measures like Lyapunov exponent and the average quadratic deviation of the full network.

Influence of polymer additive on flow past a hydrofoil: A numerical study

NASA Astrophysics Data System (ADS)

Xiong, Yongliang; Peng, Sai; Yang, Dan; Duan, Juan; Wang, Limin

2018-01-01

Flows of dilute polymer solutions past a hydrofoil (NACA0012) are examined by direct numerical simulation to investigate the modification of the wake pattern due to the addition of polymer. The influence of polymer additive is modeled by the FENE-P model in order to simulate a non-linear modulus of elasticity and a finite extendibility of the polymer macromolecules. Simulations were carried out at a Reynolds number of 1000 with the angle of attack varying from 0° to 20°. The results show that the influence of polymer on the flow behavior of the flow past a hydrofoil exhibits different flow regimes. In general, the addition of polymer modifies the wake patterns for all angles of attack in this study. Consequently, both drag and lift forces are changed as the Weissenberg number increases while the drag of the hydrofoil is enhanced at small angles of attack and reduced at large angles of attack. As the Weissenberg number increases, two attached recirculation bubbles or two columns of shedding vortices downstream tend to be symmetric, and the polymer tends to make the flow less sensitive to the variation of the angle of attack.

Noise-induced effects on multicellular biopacemaker spontaneous activity: Differences between weak and strong pacemaker cells

NASA Astrophysics Data System (ADS)

Aghighi, Alireza; Comtois, Philippe

2017-09-01

Self-organization of spontaneous activity of a network of active elements is important to the general theory of reaction-diffusion systems as well as for pacemaking activity to initiate beating of the heart. Monolayer cultures of neonatal rat ventricular myocytes, consisting of resting and pacemaker cells, exhibit spontaneous activation of their electrical activity. Similarly, one proposed approach to the development of biopacemakers as an alternative to electronic pacemakers for cardiac therapy is based on heterogeneous cardiac cells with resting and spontaneously beating phenotypes. However, the combined effect of pacemaker characteristics, density, and spatial distribution of the pacemaker cells on spontaneous activity is unknown. Using a simple stochastic pattern formation algorithm, we previously showed a clear nonlinear dependency of spontaneous activity (occurrence and amplitude of spontaneous period) on the spatial patterns of pacemaker cells. In this study, we show that this behavior is dependent on the pacemaker cell characteristics, with weaker pacemaker cells requiring higher density and larger clusters to sustain multicellular activity. These multicellular structures also demonstrated an increased sensitivity to voltage noise that favored spontaneous activity at lower density while increasing temporal variation in the period of activity. This information will help researchers overcome the current limitations of biopacemakers.

Nonlinear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.

1972-01-01

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

Evaluating the utility of vegetation indices to monitoring forests in South America, Western & Central Africa, and Southeast Asia

NASA Astrophysics Data System (ADS)

Cherrington, E. A.; Vincent, G.; Barbier, N.; Pélissier, R.; Sabatier, D.; Berger, U.

2017-12-01

In recent years, there has been controversy regarding applying vegetation indices (VIs) for monitoring tropical forests because of data artefacts related to sun-sensor geometry issues. One means of addressing the issue is comparing the VI variation of tropical forests in similar latitudes. That is, if intra-annual variation in VIs is not driven by real structural and biological changes in the vegetation, then one would expect that forests on the same latitudes should display similar patterns of VI variation. Data from multiple vegetation indices (from MODIS and SPOT VEGETATION) were analyzed over three ten degree by ten degree tiles covering the Guianas, western-central Africa, and northern Borneo in Southeast Asia. In addition to comparing the intra-annual trends across the three regions, the trends were also compared with intra-annual patterns of temporal variation, to see if these explained the VI variation. Those analyses showed that not only did the VI variation across the three regions differ significantly, but the patterns in VI variation for at least two of the three regions were largely correlated with intra-annual variation in environmental factors such as rainfall or light availability. For the Guianas, the pattern of VI variation was largely correlated with the variation in solar radiation, while for western-central Africa, the pattern of variation was more correlated to the variation in rainfall. In contrast, for northern Borneo, the pattern of VI variation did not correlate well with either variation in solar elevation or with intra-annual variation in environmental factors. Firstly, the data would seem to suggest that the patterns of variation in VI data for tropical forests are not strongly biased by artefacts related to sun-sensor geometry effects. More importantly, however, the results also suggest that the phenological of forests in both the Guianas and in western-central Africa are governed by different environmental regimes. That is to say, the forests in the Guianas appear to be light-limited, whereas in contrast, the forests in western-central Africa appear to be moisture-limited. This research suggests that vegetation index data - when corrected for artefacts related to bi-directional effects - can indeed be used to study patterns of temporal variation of forests in the tropics.

Nonlinear Poisson Equation for Heterogeneous Media

PubMed Central

Hu, Langhua; Wei, Guo-Wei

2012-01-01

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. PMID:22947937

Finite stretching of a circular plate of neo-Hookean material.

NASA Technical Reports Server (NTRS)

Biricikoglu, V.

1971-01-01

The analytical solution presented is based on the assumption that the deformed thickness of the plate is approximately constant. The nonlinear equations governing finite axisymmetric deformations of a circular plate made of neo-Hookean material are used in the analysis. The variation of circumferential extension ratio and the variation of deformed thickness are shown in graphs.

Decoupling nonclassical nonlinear behavior of elastic wave types

DOE PAGES

Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cedric; ...

2016-03-01

In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. As a result, this could lead to furthermore » understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.« less

Signatures of Nonlinear Waves in Coronal Plumes and Holes

NASA Technical Reports Server (NTRS)

Ofman, Leon

1999-01-01

In recent Ultraviolet Coronagraph Spectrometer/Solar and Heliospheric Observatory (UVCS/SOHO) White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9-2.45 solar radii. The motivation for the observation is the 2.5D Magnetohydrodynamics (MHD) model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. To help identify the waves observed with the UVCS/WLC we model the propagation and dissipation of slow magnetosonic waves in polar plumes using 1D MHD code in spherical geometry, We find that the slow waves nonlinearly steepen in the gravitationally stratified plumes. The nonlinear steepening of the waves leads to enhanced dissipation due to compressive viscosity at the wave-fronts.

Pulsational mode fluctuations and their basic conservation laws

NASA Astrophysics Data System (ADS)

Borah, B.; Karmakar, P. K.

2015-01-01

We propose a theoretical hydrodynamic model for investigating the basic features of nonlinear pulsational mode stability in a partially charged dust molecular cloud within the framework of the Jeans homogenization assumption. The inhomogeneous cloud is modeled as a quasi-neutral multifluid consisting of the warm electrons, warm ions, and identical inertial cold dust grains with partial ionization in a neutral gaseous background. The grain-charge is assumed not to vary in the fluctuation evolution time scale. The active inertial roles of the thermal species are included. We apply a standard multiple scaling technique centered on the gravito-electrostatic equilibrium to understand the fluctuations on the astrophysical scales of space and time. This is found that electrostatic and self-gravitational eigenmodes co-exist as diverse solitary spectral patterns governed by a pair of Korteweg-de Vries (KdV) equations. In addition, all the relevant classical conserved quantities associated with the KdV system under translational invariance are methodologically derived and numerically analyzed. A full numerical shape-analysis of the fluctuations, scale lengths and perturbed densities with multi-parameter variation of judicious plasma conditions is carried out. A correlation of the perturbed densities and gravito-electrostatic spectral patterns is also graphically indicated. It is demonstrated that the solitary mass, momentum and energy densities also evolve like solitary spectral patterns which remain conserved throughout the spatiotemporal scales of the fluctuation dynamics. Astrophysical and space environments significant to our results are briefly highlighted.

Distribution pattern of reptiles along an eastern Himalayan elevation gradient, India

NASA Astrophysics Data System (ADS)

Chettri, Basundhara; Bhupathy, Subramanian; Acharya, Bhoj Kumar

2010-01-01

We examined the spatial distribution pattern of reptiles in an eastern Himalayan elevation gradient. The factors governing the distribution have been assessed with emphasis on the mid-domain effect. We surveyed reptiles along the elevation gradient (300-4800 m) of the Teesta valley in Sikkim, Eastern Himalaya, India using time constrained visual encounter survey. A total of 42 species of reptiles were observed during the study, and the species richness peaked at 500-1000 m with no species beyond 3000 m. The observed pattern was consistent with estimated richness, both showing significant negative relation with elevation. Lizards showed a linear decline with elevation, whereas snakes followed a non-linear relation with peak at 500-1000 m. Observed species richness deviated significantly from that predicted by a mid-domain null model. The regression between empirical and simulated richness was not significant for total reptiles as well as lizards and snakes separately. Most species distributed in the high elevation extended towards lower elevation, but low elevation species (around 50%) were restricted below 1000 m. Deviation of empirical from predicted richness indicates that the distributions of reptile species were least governed by geographic hard boundaries. Climatic factors especially temperature explained much variation of reptiles along the Himalayan elevation gradient. Most reptiles were narrowly distributed, especially those found in low elevation indicating the importance of tropical low-land forests in the conservation of reptiles in Eastern Himalayas.

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Variations in Developmental Patterns across Pragmatic Features

ERIC Educational Resources Information Center

Li, Qiong

2016-01-01

Drawing on the findings of longitudinal studies in uninstructed contexts over the last two decades, this synthesis explores variations in developmental patterns across second language (L2) pragmatic features. Two synthesis questions were addressed: (a) What are the variations in developmental patterns across pragmatic features?, and (b) What are…

Assessing Spontaneous Combustion Instability with Recurrence Quantification Analysis

NASA Technical Reports Server (NTRS)

Eberhart, Chad J.; Casiano, Matthew J.

2016-01-01

Spontaneous instabilities can pose a significant challenge to verification of combustion stability, and characterizing its onset is an important avenue of improvement for stability assessments of liquid propellant rocket engines. Recurrence Quantification Analysis (RQA) is used here to explore nonlinear combustion dynamics that might give insight into instability. Multiple types of patterns representative of different dynamical states are identified within fluctuating chamber pressure data, and markers for impending instability are found. A class of metrics which describe these patterns is also calculated. RQA metrics are compared with and interpreted against another metric from nonlinear time series analysis, the Hurst exponent, to help better distinguish between stable and unstable operation.

Linking actin networks and cell membrane via a reaction-diffusion-elastic description of nonlinear filopodia initiation.

PubMed

Ben Isaac, Eyal; Manor, Uri; Kachar, Bechara; Yochelis, Arik; Gov, Nir S

2013-08-01

Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations.

Probabilistic model of nonlinear penalties due to collision-induced timing jitter for calculation of the bit error ratio in wavelength-division-multiplexed return-to-zero systems

NASA Astrophysics Data System (ADS)

Sinkin, Oleg V.; Grigoryan, Vladimir S.; Menyuk, Curtis R.

2006-12-01

We introduce a fully deterministic, computationally efficient method for characterizing the effect of nonlinearity in optical fiber transmission systems that utilize wavelength-division multiplexing and return-to-zero modulation. The method accurately accounts for bit-pattern-dependent nonlinear distortion due to collision-induced timing jitter and for amplifier noise. We apply this method to calculate the error probability as a function of channel spacing in a prototypical multichannel return-to-zero undersea system.

Fourier series expansion for nonlinear Hamiltonian oscillators.

PubMed

Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac

2010-06-01

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.

Temperature dependence of nonlinear optical properties in Li doped nano-carbon bowl material

NASA Astrophysics Data System (ADS)

Li, Wei-qi; Zhou, Xin; Chang, Ying; Quan Tian, Wei; Sun, Xiu-Dong

2013-04-01

The mechanism for change of nonlinear optical (NLO) properties with temperature is proposed for a nonlinear optical material, Li doped curved nano-carbon bowl. Four stable conformations of Li doped corannulene were located and their electronic properties were investigated in detail. The NLO response of those Li doped conformations varies with relative position of doping agent on the curved carbon surface of corannulene. Conversion among those Li doped conformations, which could be controlled by temperature, changes the NLO response of bulk material. Thus, conformation change of alkali metal doped carbon nano-material with temperature rationalizes the variation of NLO properties of those materials.

General methodology for simultaneous representation and discrimination of multiple object classes

NASA Astrophysics Data System (ADS)

Talukder, Ashit; Casasent, David P.

1998-03-01

We address a new general method for linear and nonlinear feature extraction for simultaneous representation and classification. We call this approach the maximum representation and discrimination feature (MRDF) method. We develop a novel nonlinear eigenfeature extraction technique to represent data with closed-form solutions and use it to derive a nonlinear MRDF algorithm. Results of the MRDF method on synthetic databases are shown and compared with results from standard Fukunaga-Koontz transform and Fisher discriminant function methods. The method is also applied to an automated product inspection problem and for classification and pose estimation of two similar objects under 3D aspect angle variations.

Non-linear effects in bunch compressor of TARLA

NASA Astrophysics Data System (ADS)

Yildiz, Hüseyin; Aksoy, Avni; Arikan, Pervin

2016-03-01

Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects on bunch compressor of TARLA.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing

PubMed Central

Yang, Changju; Kim, Hyongsuk

2016-01-01

A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model. PMID:27548186

Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space

NASA Astrophysics Data System (ADS)

Ruggeri, Michele; Moroni, Saverio; Holzmann, Markus

2018-05-01

We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid 4He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values. For two dimensional 4He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form—a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid 3He in three dimensions, improving previous variational and fixed-node energies.

An inverse method for determining the spatially resolved properties of viscoelastic–viscoplastic three-dimensional printed materials

PubMed Central

Chen, X.; Ashcroft, I. A.; Wildman, R. D.; Tuck, C. J.

2015-01-01

A method using experimental nanoindentation and inverse finite-element analysis (FEA) has been developed that enables the spatial variation of material constitutive properties to be accurately determined. The method was used to measure property variation in a three-dimensional printed (3DP) polymeric material. The accuracy of the method is dependent on the applicability of the constitutive model used in the inverse FEA, hence four potential material models: viscoelastic, viscoelastic–viscoplastic, nonlinear viscoelastic and nonlinear viscoelastic–viscoplastic were evaluated, with the latter enabling the best fit to experimental data. Significant changes in material properties were seen in the depth direction of the 3DP sample, which could be linked to the degree of cross-linking within the material, a feature inherent in a UV-cured layer-by-layer construction method. It is proposed that the method is a powerful tool in the analysis of manufacturing processes with potential spatial property variation that will also enable the accurate prediction of final manufactured part performance. PMID:26730216

Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing.

PubMed

Yang, Changju; Kim, Hyongsuk

2016-08-19

A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model.

An inverse method for determining the spatially resolved properties of viscoelastic-viscoplastic three-dimensional printed materials.

PubMed

Chen, X; Ashcroft, I A; Wildman, R D; Tuck, C J

2015-11-08

A method using experimental nanoindentation and inverse finite-element analysis (FEA) has been developed that enables the spatial variation of material constitutive properties to be accurately determined. The method was used to measure property variation in a three-dimensional printed (3DP) polymeric material. The accuracy of the method is dependent on the applicability of the constitutive model used in the inverse FEA, hence four potential material models: viscoelastic, viscoelastic-viscoplastic, nonlinear viscoelastic and nonlinear viscoelastic-viscoplastic were evaluated, with the latter enabling the best fit to experimental data. Significant changes in material properties were seen in the depth direction of the 3DP sample, which could be linked to the degree of cross-linking within the material, a feature inherent in a UV-cured layer-by-layer construction method. It is proposed that the method is a powerful tool in the analysis of manufacturing processes with potential spatial property variation that will also enable the accurate prediction of final manufactured part performance.

Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties

PubMed Central

Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon

2014-01-01

Purpose The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency during anterior-posterior stretching. Method Three materially linear and three materially nonlinear models were created and stretched up to 10 mm in 1 mm increments. Phonation onset pressure (Pon) and fundamental frequency (F0) at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1 mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Results Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Conclusions Nonlinear synthetic models appear to more accurately represent the human vocal folds than linear models, especially with respect to F0 response. PMID:22271874

Frequency response of synthetic vocal fold models with linear and nonlinear material properties.

PubMed

Shaw, Stephanie M; Thomson, Scott L; Dromey, Christopher; Smith, Simeon

2012-10-01

The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F0) during anterior-posterior stretching. Three materially linear and 3 materially nonlinear models were created and stretched up to 10 mm in 1-mm increments. Phonation onset pressure (Pon) and F0 at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1-mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Nonlinear synthetic models appear to more accurately represent the human vocal folds than do linear models, especially with respect to F0 response.

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow.

PubMed

Heise, M; Hoffmann, Ch; Abshagen, J; Pinter, A; Pfister, G; Lücke, M

2008-02-15

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.

Non-linear Growth Models in Mplus and SAS

PubMed Central

Grimm, Kevin J.; Ram, Nilam

2013-01-01

Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134

Modulation stability analysis of exact multidimensional solutions to the generalized nonlinear Schrödinger equation and the Gross-Pitaevskii equation using a variational approach.

PubMed

Petrović, Nikola Z; Aleksić, Najdan B; Belić, Milivoj

2015-04-20

We analyze the modulation stability of spatiotemporal solitary and traveling wave solutions to the multidimensional nonlinear Schrödinger equation and the Gross-Pitaevskii equation with variable coefficients that were obtained using Jacobi elliptic functions. For all the solutions we obtain either unconditional stability, or a conditional stability that can be furnished through the use of dispersion management.

An Astronomical Test of CCD Photometric Precision

NASA Technical Reports Server (NTRS)

Koch, David; Dunham, Edward; Borucki, William; Jenkins, Jon; DeVingenzi, D. (Technical Monitor)

1998-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Irreversibility and entropy production in transport phenomena, III—Principle of minimum integrated entropy production including nonlinear responses

NASA Astrophysics Data System (ADS)

Suzuki, Masuo

2013-01-01

A new variational principle of steady states is found by introducing an integrated type of energy dissipation (or entropy production) instead of instantaneous energy dissipation. This new principle is valid both in linear and nonlinear transport phenomena. Prigogine’s dream has now been realized by this new general principle of minimum “integrated” entropy production (or energy dissipation). This new principle does not contradict with the Onsager-Prigogine principle of minimum instantaneous entropy production in the linear regime, but it is conceptually different from the latter which does not hold in the nonlinear regime. Applications of this theory to electric conduction, heat conduction, particle diffusion and chemical reactions are presented. The irreversibility (or positive entropy production) and long time tail problem in Kubo’s formula are also discussed in the Introduction and last section. This constitutes the complementary explanation of our theory of entropy production given in the previous papers (M. Suzuki, Physica A 390 (2011) 1904 and M. Suzuki, Physica A 391 (2012) 1074) and has given the motivation of the present investigation of variational principle.

A real-time recursive filter for the attitude determination of the Spacelab instrument pointing subsystem

NASA Technical Reports Server (NTRS)

West, M. E.

1992-01-01

A real-time estimation filter which reduces sensitivity to system variations and reduces the amount of preflight computation is developed for the instrument pointing subsystem (IPS). The IPS is a three-axis stabilized platform developed to point various astronomical observation instruments aboard the shuttle. Currently, the IPS utilizes a linearized Kalman filter (LKF), with premission defined gains, to compensate for system drifts and accumulated attitude errors. Since the a priori gains are generated for an expected system, variations result in a suboptimal estimation process. This report compares the performance of three real-time estimation filters with the current LKF implementation. An extended Kalman filter and a second-order Kalman filter are developed to account for the system nonlinearities, while a linear Kalman filter implementation assumes that the nonlinearities are negligible. The performance of each of the four estimation filters are compared with respect to accuracy, stability, settling time, robustness, and computational requirements. It is shown, that for the current IPS pointing requirements, the linear Kalman filter provides improved robustness over the LKF with less computational requirements than the two real-time nonlinear estimation filters.

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

Zhang, Hailong; Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042; Zhang, Ning

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phasemore » trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.« less

Analysis of Classes of Superlinear Semipositone Problems with Nonlinear Boundary Conditions

NASA Astrophysics Data System (ADS)

Morris, Quinn A.

We study positive radial solutions for classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We consider p-Laplacian problems (p > 1) with reaction terms which are superlinear at infinity and semipositone. In the case p = 2, using variational methods, we establish the existence of a solution, and via detailed analysis of the Green's function, we prove the positivity of the solution. In the case p ≠ 2, we again use variational methods to establish the existence of a solution, but the positivity of the solution is achieved via sophisticated a priori estimates. In the case p ≠ 2, the Green's function analysis is no longer available. Our results significantly enhance the literature on superlinear semipositone problems. Finally, we provide algorithms for the numerical generation of exact bifurcation curves for one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and using nonlinear solvers in Mathematica, generate bifurcation curves. In the nonautonomous case, we employ shooting methods in Mathematica to generate bifurcation curves.

Polarizabilities of Impurity Doped Quantum Dots Under Pulsed Field: Role of Multiplicative White Noise

NASA Astrophysics Data System (ADS)

Saha, Surajit; Ghosh, Manas

2016-02-01

We perform a rigorous analysis of the profiles of a few diagonal and off-diagonal components of linear ( α xx , α yy , α xy , and α yx ), first nonlinear ( β xxx , β yyy , β xyy , and β yxx ), and second nonlinear ( γ xxxx , γ yyyy , γ xxyy , and γ yyxx ) polarizabilities of quantum dots exposed to an external pulsed field. Simultaneous presence of multiplicative white noise has also been taken into account. The quantum dot contains a dopant represented by a Gaussian potential. The number of pulse and the dopant location have been found to fabricate the said profiles through their interplay. Moreover, a variation in the noise strength also contributes evidently in designing the profiles of above polarizability components. In general, the off-diagonal components have been found to be somewhat more responsive to a variation of noise strength. However, we have found some exception to the above fact for the off-diagonal β yxx component. The study projects some pathways of achieving stable, enhanced, and often maximized output of linear and nonlinear polarizabilities of doped quantum dots driven by multiplicative noise.

Quantitative thickness measurement of polarity-inverted piezoelectric thin-film layer by scanning nonlinear dielectric microscopy

NASA Astrophysics Data System (ADS)

Odagawa, Hiroyuki; Terada, Koshiro; Tanaka, Yohei; Nishikawa, Hiroaki; Yanagitani, Takahiko; Cho, Yasuo

2017-10-01

A quantitative measurement method for a polarity-inverted layer in ferroelectric or piezoelectric thin film is proposed. It is performed nondestructively by scanning nonlinear dielectric microscopy (SNDM). In SNDM, linear and nonlinear dielectric constants are measured using a probe that converts the variation of capacitance related to these constants into the variation of electrical oscillation frequency. In this paper, we describe a principle for determining the layer thickness and some calculation results of the output signal, which are related to the radius of the probe tip and the thickness of the inverted layer. Moreover, we derive an equation that represents the relationship between the output signal and the oscillation frequency of the probe and explain how to determine the thickness from the measured frequency. Experimental results in Sc-doped AlN piezoelectric thin films that have a polarity-inverted layer with a thickness of 1.5 µm fabricated by radio frequency magnetron sputtering showed a fairly good value of 1.38 µm for the thickness of the polarity-inverted layer.

Analysis of Composite Panels Subjected to Thermo-Mechanical Loads

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Peters, Jeanne M.

1999-01-01

The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.

Spectra of Baroclinic Inertia-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, Roman E.

1996-01-01

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

On the interannual oscillations in the northern temperate total ozone

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

Krzyscin, J.W.

1994-07-01

The interannual variations in total ozone are studied using revised Dobson total ozone records (1961-1990) from 17 stations located within the latitude band 30 deg N - 60 deg N. To obtain the quasi-biennial oscillation (QBO), El Nino-Southern Oscillation (ENSO), and 11-year solar cycle manifestation in the `northern temperate` total ozone data, various multiple regression models are constructed by the least squares fitting to the observed ozone. The statistical relationships between the selected indices of the atmospheric variabilities and total ozone are described in the linear and nonlinear regression models. Nonlinear relationships to the predictor variables are found. That is,more » the total ozone variations are statistically modeled by nonlinear terms accounting for the coupling between QBO and ENSO, QBO and solar activity, and ENSO and solar activity. It is suggested that large reduction of total ozone values over the `northern temperate` region occurs in cold season when a strong ENSO warm event meets the west phase of the QBO during the period of high solar activity.« less

Theory of multiple quantum dot formation in strained-layer heteroepitaxy

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

Du, Lin; Maroudas, Dimitrios, E-mail: maroudas@ecs.umass.edu

2016-07-11

We develop a theory for the experimentally observed formation of multiple quantum dots (QDs) in strained-layer heteroepitaxy based on surface morphological stability analysis of a coherently strained epitaxial thin film on a crystalline substrate. Using a fully nonlinear model of surface morphological evolution that accounts for a wetting potential contribution to the epitaxial film's free energy as well as surface diffusional anisotropy, we demonstrate the formation of multiple QD patterns in self-consistent dynamical simulations of the evolution of the epitaxial film surface perturbed from its planar state. The simulation predictions are supported by weakly nonlinear analysis of the epitaxial filmmore » surface morphological stability. We find that, in addition to the Stranski-Krastanow instability, long-wavelength perturbations from the planar film surface morphology can trigger a nonlinear instability, resulting in the splitting of a single QD into multiple QDs of smaller sizes, and predict the critical wavelength of the film surface perturbation for the onset of the nonlinear tip-splitting instability. The theory provides a fundamental interpretation for the observations of “QD pairs” or “double QDs” and other multiple QDs reported in experimental studies of epitaxial growth of semiconductor strained layers and sets the stage for precise engineering of tunable-size nanoscale surface features in strained-layer heteroepitaxy by exploiting film surface nonlinear, pattern forming phenomena.« less

Roles of dispersal, stochasticity, and nonlinear dynamics in the spatial structuring of seasonal natural enemy-victim populations

Treesearch

Patrick C. Tobin; Ottar N. Bjornstad

2005-01-01

Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...

Bryan's effect and anisotropic nonlinear damping

NASA Astrophysics Data System (ADS)

Joubert, Stephan V.; Shatalov, Michael Y.; Fay, Temple H.; Manzhirov, Alexander V.

2018-03-01

In 1890, G. H. Bryan discovered the following: "The vibration pattern of a revolving cylinder or bell revolves at a rate proportional to the inertial rotation rate of the cylinder or bell." We call this phenomenon Bryan's law or Bryan's effect. It is well known that any imperfections in a vibratory gyroscope (VG) affect Bryan's law and this affects the accuracy of the VG. Consequently, in this paper, we assume that all such imperfections are either minimised or eliminated by some known control method and that only damping is present within the VG. If the damping is isotropic (linear or nonlinear), then it has been recently demonstrated in this journal, using symbolic analysis, that Bryan's law remains invariant. However, it is known that linear anisotropic damping does affect Bryan's law. In this paper, we generalise Rayleigh's dissipation function so that anisotropic nonlinear damping may be introduced into the equations of motion. Using a mixture of numeric and symbolic analysis on the ODEs of motion of the VG, for anisotropic light nonlinear damping, we demonstrate (up to an approximate average), that Bryan's law is affected by any form of such damping, causing pattern drift, compromising the accuracy of the VG.

The frequency response of a coupled ice sheet-ice shelf-ocean system to climate forcing variability

NASA Astrophysics Data System (ADS)

Goldberg, D.; Snow, K.; Jordan, J. R.; Holland, P.; Arthern, R. J.

2017-12-01

Changes at the West Antarctic ice-ocean boundary in recent decades has triggered significant increases in the regions contribution to global sea-level rise, coincident with large scale, and in some cases potentially unstable, grounding line retreat. Much of the induced change is thought to be driven by fluctuations in the oceanic heat available at the ice-ocean boundary, transported on-shelf via warm Circumpolar Deep Water (CDW). However, the processes in which ocean heat drives ice-sheet loss remains poorly understood, with observational studies routinely hindered by the extreme environment notorious to the Antarctic region. In this study we apply a novel synchronous coupled ice-ocean model, developed within the MITgcm, and are thus able to provide detailed insight into the impacts of short time scale (interannual to decadal) climate variability and feedbacks within the ice-ocean system. Feedbacks and response are assessed in an idealised ice-sheet/ocean-cavity configuration in which the far field ocean condition is adjusted to emulate periodic climate variability patterns. We reveal a non-linear response of the ice-sheet to periodic variations in thermocline depth. These non-linearities illustrate the heightened sensitivity of fast flowing ice-shelves to periodic perturbations in heat fluxes occurring at interannual and decadal time scales. The results thus highlight how small perturbations in variable climate forcing, like that of ENSO, may trigger large changes in ice-sheet response.

An interative solution of an integral equation for radiative transfer by using variational technique

NASA Technical Reports Server (NTRS)

Yoshikawa, K. K.

1973-01-01

An effective iterative technique is introduced to solve a nonlinear integral equation frequently associated with radiative transfer problems. The problem is formulated in such a way that each step of an iterative sequence requires the solution of a linear integral equation. The advantage of a previously introduced variational technique which utilizes a stepwise constant trial function is exploited to cope with the nonlinear problem. The method is simple and straightforward. Rapid convergence is obtained by employing a linear interpolation of the iterative solutions. Using absorption coefficients of the Milne-Eddington type, which are applicable to some planetary atmospheric radiation problems. Solutions are found in terms of temperature and radiative flux. These solutions are presented numerically and show excellent agreement with other numerical solutions.

The relaxed-polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3D-EBSD experiments

NASA Astrophysics Data System (ADS)

Fischle, Andreas; Neff, Patrizio; Raabe, Dierk

2017-08-01

The rotation {{polar}}(F) \\in {{SO}}(3) arises as the unique orthogonal factor of the right polar decomposition F = {{polar}}(F) U of a given invertible matrix F \\in {{GL}}^+(3). In the context of nonlinear elasticity Grioli (Boll Un Math Ital 2:252-255, 1940) discovered a geometric variational characterization of {{polar}}(F) as a unique energy-minimizing rotation. In preceding works, we have analyzed a generalization of Grioli's variational approach with weights (material parameters) μ > 0 and μ _c ≥ 0 (Grioli: μ = μ _c). The energy subject to minimization coincides with the Cosserat shear-stretch contribution arising in any geometrically nonlinear, isotropic and quadratic Cosserat continuum model formulated in the deformation gradient field F :=\

Solar activity indices as a proxy for the variation of ionospheric Total Electron Content (TEC) over Bahir Dar, Ethiopia during the year 2010-2014

NASA Astrophysics Data System (ADS)

Kassa, Tsegaye; Tilahun, Samson; Damtie, Baylie

2017-09-01

This paper was aimed at investigating the solar variations of vTEC as a function of solar activity parameters, EUV and F10.7 radio flux. The daily values of ionospheric vertical Total Electron Content (vTEC) were observed using a dual frequency GPS receiver deployed at Bahir Dar (11.6°N and 37.36°E), Ethiopia. Measurements were taken during the period of 2010-2014 for successive five years and analysis was done on only quiet day observations. A quadratic fit was used as a model to describe the daily variation of vTEC in relation to solar parameters. Linear and non-linear coefficients of the vTEC variations were calculated in order to capture the trend of the variation. The variation of vTEC have showed good agreement with the trend of solar parameters in almost all of the days we consider during the period of our observations. We have explicitly observed days with insignificant TECU deviation (eg. modeling with respect to EUV, DOY = 49 in 2010 and modeling with respect to F10.7, DOY = 125 in 2012 and the like) and days with maximum deviation (about 50 TECU). A maximum deviation were observed, on average, during months of equinox whereas minimum during solstice months. This implies that there is a need to consider more parameters, including EUV and F10.7, that can affect the variation of vTEC during equinox seasons. Relatively, small deviations was observed in modeling vTEC as a function of EUV compared to that of the variation due to F10.7 cm flux. This may also tell us that EUV can be more suitable in modeling the solar variation of vTEC especially for longterm trends. Even though, the linear trend of solar variations of vTEC was frequently observed, significant saturation and amplification trends of the solar variations of vTEC were also observed to some extent across the months of the years we have analyzed. This mixed trend of the solar variation of vTEC implies the need for thorough investigation on the effect of solar parameters on TEC. However, based on long-term dataset, we came to conclude that the solar variations of vTEC is dominated by its linear pattern.

Temporal and nonlinear dispersal patterns of Ludwigia hexapetala in a regulated river

USDA-ARS?s Scientific Manuscript database

Rivers are vulnerable to biological invasion due to hydrologic connectivity, which facilitates post-entry movement of aquatic plant propagules by water currents. Ecological and watershed factors may influence spatial and temporal dispersal patterns. Field-based data on dispersal could improve risk...

Nonlinear analysis of human physical activity patterns in health and disease.

PubMed

Paraschiv-Ionescu, A; Buchser, E; Rutschmann, B; Aminian, K

2008-02-01

The reliable and objective assessment of chronic disease state has been and still is a very significant challenge in clinical medicine. An essential feature of human behavior related to the health status, the functional capacity, and the quality of life is the physical activity during daily life. A common way to assess physical activity is to measure the quantity of body movement. Since human activity is controlled by various factors both extrinsic and intrinsic to the body, quantitative parameters only provide a partial assessment and do not allow for a clear distinction between normal and abnormal activity. In this paper, we propose a methodology for the analysis of human activity pattern based on the definition of different physical activity time series with the appropriate analysis methods. The temporal pattern of postures, movements, and transitions between postures was quantified using fractal analysis and symbolic dynamics statistics. The derived nonlinear metrics were able to discriminate patterns of daily activity generated from healthy and chronic pain states.

Thermal motion of a nonlinear localized pattern in a quasi-one-dimensional system.

PubMed

Dessup, Tommy; Coste, Christophe; Saint Jean, Michel

2016-07-01

We study the dynamics of localized nonlinear patterns in a quasi-one-dimensional many-particle system near a subcritical pitchfork bifurcation. The normal form at the bifurcation is given and we show that these patterns can be described as solitary-wave envelopes. They are stable in a large temperature range and can diffuse along the chain of interacting particles. During their displacements the particles are continually redistributed on the envelope. This change of particle location induces a small modulation of the potential energy of the system, with an amplitude that depends on the transverse confinement. At high temperature, this modulation is irrelevant and the thermal motion of the localized patterns displays all the characteristics of a free quasiparticle diffusion with a diffusion coefficient that may be deduced from the normal form. At low temperature, significant physical effects are induced by the modulated potential. In particular, the localized pattern may be trapped at very low temperature. We also exhibit a series of confinement values for which the modulation amplitudes vanishes. For these peculiar confinements, the mean-square displacement of the localized patterns also evidences free-diffusion behavior at low temperature.

Variational approach to studying solitary waves in the nonlinear Schrödinger equation with complex potentials

DOE PAGES

Mertens, Franz G.; Cooper, Fred; Arevalo, Edward; ...

2016-09-15

Here in this paper, we discuss the behavior of solitary wave solutions of the nonlinear Schrödinger equation (NLSE) as they interact with complex potentials, using a four-parameter variational approximation based on a dissipation functional formulation of the dynamics. We concentrate on spatially periodic potentials with the periods of the real and imaginary part being either the same or different. Our results for the time evolution of the collective coordinates of our variational ansatz are in good agreement with direct numerical simulation of the NLSE. We compare our method with a collective coordinate approach of Kominis and give examples where themore » two methods give qualitatively different answers. In our variational approach, we are able to give analytic results for the small oscillation frequency of the solitary wave oscillating parameters which agree with the numerical solution of the collective coordinate equations. We also verify that instabilities set in when the slope dp(t)/dv(t) becomes negative when plotted parametrically as a function of time, where p(t) is the momentum of the solitary wave and v(t) the velocity.« less

Variational approach to studying solitary waves in the nonlinear Schrödinger equation with complex potentials

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

Mertens, Franz G.; Cooper, Fred; Arevalo, Edward

Here in this paper, we discuss the behavior of solitary wave solutions of the nonlinear Schrödinger equation (NLSE) as they interact with complex potentials, using a four-parameter variational approximation based on a dissipation functional formulation of the dynamics. We concentrate on spatially periodic potentials with the periods of the real and imaginary part being either the same or different. Our results for the time evolution of the collective coordinates of our variational ansatz are in good agreement with direct numerical simulation of the NLSE. We compare our method with a collective coordinate approach of Kominis and give examples where themore » two methods give qualitatively different answers. In our variational approach, we are able to give analytic results for the small oscillation frequency of the solitary wave oscillating parameters which agree with the numerical solution of the collective coordinate equations. We also verify that instabilities set in when the slope dp(t)/dv(t) becomes negative when plotted parametrically as a function of time, where p(t) is the momentum of the solitary wave and v(t) the velocity.« less

Workpiece Temperature Variations During Flat Peripheral Grinding

NASA Astrophysics Data System (ADS)

Smirnov, Vitalii A.; Repko, Aleksandr V.

2018-06-01

The paper presents the results of researches of temperature variations during flat peripheral grinding. It is shown that the temperature variations of the workpiece can reach 25...30% of the average values, which can lead to some thermal defects. A nonlinear two-dimensional thermophysical grinding model is suggested. It takes into account local changes in the cutting conditions: the fluctuation of the cut layer and the cutting force, the thermal impact of the cutting grains, and the presence of surface cavities in the intermittent wheel. For the numerical solution of the problem, the method of finite differences is adapted. Researches of the method stability and convergence are made, taking into account the specific nature of the problem. A high accuracy of the approximation of the boundary conditions and the nonlinear heat equation is provided. An experimental verification of the proposed thermophysical model was carried out with the use of installation for simultaneous measurement of the grinding force and temperature. It is shown that the discrepancy between the theoretical and experimental values of the grinding temperature does not exceed 5%. The proposed thermophysical model makes it possible to predict with high accuracy the temperature variations during grinding by the wheel periphery.

Variability in Regularity: Mining Temporal Mobility Patterns in London, Singapore and Beijing Using Smart-Card Data

PubMed Central

Zhong, Chen; Batty, Michael; Manley, Ed; Wang, Jiaqiu; Wang, Zijia; Chen, Feng; Schmitt, Gerhard

2016-01-01

To discover regularities in human mobility is of fundamental importance to our understanding of urban dynamics, and essential to city and transport planning, urban management and policymaking. Previous research has revealed universal regularities at mainly aggregated spatio-temporal scales but when we zoom into finer scales, considerable heterogeneity and diversity is observed instead. The fundamental question we address in this paper is at what scales are the regularities we detect stable, explicable, and sustainable. This paper thus proposes a basic measure of variability to assess the stability of such regularities focusing mainly on changes over a range of temporal scales. We demonstrate this by comparing regularities in the urban mobility patterns in three world cities, namely London, Singapore and Beijing using one-week of smart-card data. The results show that variations in regularity scale as non-linear functions of the temporal resolution, which we measure over a scale from 1 minute to 24 hours thus reflecting the diurnal cycle of human mobility. A particularly dramatic increase in variability occurs up to the temporal scale of about 15 minutes in all three cities and this implies that limits exist when we look forward or backward with respect to making short-term predictions. The degree of regularity varies in fact from city to city with Beijing and Singapore showing higher regularity in comparison to London across all temporal scales. A detailed discussion is provided, which relates the analysis to various characteristics of the three cities. In summary, this work contributes to a deeper understanding of regularities in patterns of transit use from variations in volumes of travellers entering subway stations, it establishes a generic analytical framework for comparative studies using urban mobility data, and it provides key points for the management of variability by policy-makers intent on for making the travel experience more amenable. PMID:26872333

Variability in Regularity: Mining Temporal Mobility Patterns in London, Singapore and Beijing Using Smart-Card Data.

PubMed

Zhong, Chen; Batty, Michael; Manley, Ed; Wang, Jiaqiu; Wang, Zijia; Chen, Feng; Schmitt, Gerhard

2016-01-01

To discover regularities in human mobility is of fundamental importance to our understanding of urban dynamics, and essential to city and transport planning, urban management and policymaking. Previous research has revealed universal regularities at mainly aggregated spatio-temporal scales but when we zoom into finer scales, considerable heterogeneity and diversity is observed instead. The fundamental question we address in this paper is at what scales are the regularities we detect stable, explicable, and sustainable. This paper thus proposes a basic measure of variability to assess the stability of such regularities focusing mainly on changes over a range of temporal scales. We demonstrate this by comparing regularities in the urban mobility patterns in three world cities, namely London, Singapore and Beijing using one-week of smart-card data. The results show that variations in regularity scale as non-linear functions of the temporal resolution, which we measure over a scale from 1 minute to 24 hours thus reflecting the diurnal cycle of human mobility. A particularly dramatic increase in variability occurs up to the temporal scale of about 15 minutes in all three cities and this implies that limits exist when we look forward or backward with respect to making short-term predictions. The degree of regularity varies in fact from city to city with Beijing and Singapore showing higher regularity in comparison to London across all temporal scales. A detailed discussion is provided, which relates the analysis to various characteristics of the three cities. In summary, this work contributes to a deeper understanding of regularities in patterns of transit use from variations in volumes of travellers entering subway stations, it establishes a generic analytical framework for comparative studies using urban mobility data, and it provides key points for the management of variability by policy-makers intent on for making the travel experience more amenable.

Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades

NASA Technical Reports Server (NTRS)

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

1986-01-01

The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation.

PubMed

Brito, Carlos S N; Gerstner, Wulfram

2016-09-01

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation

PubMed Central

Gerstner, Wulfram

2016-01-01

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. PMID:27690349

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

NASA Technical Reports Server (NTRS)

Larson, Mats G.; Barth, Timothy J.

1999-01-01

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Linear control of a boiler-turbine unit: analysis and design.

PubMed

Tan, Wen; Fang, Fang; Tian, Liang; Fu, Caifen; Liu, Jizhen

2008-04-01

Linear control of a boiler-turbine unit is discussed in this paper. Based on the nonlinear model of the unit, this paper analyzes the nonlinearity of the unit, and selects the appropriate operating points so that the linear controller can achieve wide-range performance. Simulation and experimental results at the No. 4 Unit at the Dalate Power Plant show that the linear controller can achieve the desired performance under a specific range of load variations.

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

NASA Astrophysics Data System (ADS)

Jiang, Fei

2018-04-01

We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations.

PubMed

Schüler, D; Alonso, S; Torcini, A; Bär, M

2014-12-01

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.

Nonlinear Poisson equation for heterogeneous media.

PubMed

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Nonlinear growth responses of Douglas-fir in the Pacific Northwest to summer temperatures in the past decade

EPA Science Inventory

Altered seasonal climate patterns resulting from global climate change could affect the productivity of coniferous forests in the Pacific Northwest region of North America. This study examined seasonal patterns of temperature, precipitation, relative humidity and plant available...

Applying landscape genomic tools to forest management and restoration of Hawaiian koa (Acacia koa) in a changing environment.

PubMed

Gugger, Paul F; Liang, Christina T; Sork, Victoria L; Hodgskiss, Paul; Wright, Jessica W

2018-02-01

Identifying and quantifying the importance of environmental variables in structuring population genetic variation can help inform management decisions for conservation, restoration, or reforestation purposes, in both current and future environmental conditions. Landscape genomics offers a powerful approach for understanding the environmental factors that currently associate with genetic variation, and given those associations, where populations may be most vulnerable under future environmental change. Here, we applied genotyping by sequencing to generate over 11,000 single nucleotide polymorphisms from 311 trees and then used nonlinear, multivariate environmental association methods to examine spatial genetic structure and its association with environmental variation in an ecologically and economically important tree species endemic to Hawaii, Acacia koa . Admixture and principal components analyses showed that trees from different islands are genetically distinct in general, with the exception of some genotypes that match other islands, likely as the result of recent translocations. Gradient forest and generalized dissimilarity models both revealed a strong association between genetic structure and mean annual rainfall. Utilizing a model for projected future climate on the island of Hawaii, we show that predicted changes in rainfall patterns may result in genetic offset, such that trees no longer may be genetically matched to their environment. These findings indicate that knowledge of current and future rainfall gradients can provide valuable information for the conservation of existing populations and also help refine seed transfer guidelines for reforestation or replanting of koa throughout the state.

The amazing evolutionary dynamics of non-linear optical systems with feedback

NASA Astrophysics Data System (ADS)

Yaroslavsky, Leonid

2013-09-01

Optical systems with feedback are, generally, non-linear dynamic systems. As such, they exhibit evolutionary behavior. In the paper we present results of experimental investigation of evolutionary dynamics of several models of such systems. The models are modifications of the famous mathematical "Game of Life". The modifications are two-fold: "Game of Life" rules are made stochastic and mutual influence of cells is made spatially non-uniform. A number of new phenomena in the evolutionary dynamics of the models are revealed: - "Ordering of chaos". Formation, from seed patterns, of stable maze-like patterns with chaotic "dislocations" that resemble natural patterns, such as skin patterns of some animals and fishes, see shell, fingerprints, magnetic domain patterns and alike, which one can frequently find in the nature. These patterns and their fragments exhibit a remarkable capability of unlimited growth. - "Self-controlled growth" of chaotic "live" formations into "communities" bounded, depending on the model, by a square, hexagon or octagon, until they reach a certain critical size, after which the growth stops. - "Eternal life in a bounded space" of "communities" after reaching a certain size and shape. - "Coherent shrinkage" of "mature", after reaching a certain size, "communities" into one of stable or oscillating patterns preserving in this process isomorphism of their bounding shapes until the very end.

A simultaneous all-optical half/full-subtraction strategy using cascaded highly nonlinear fibers

NASA Astrophysics Data System (ADS)

Singh, Karamdeep; Kaur, Gurmeet; Singh, Maninder Lal

2018-02-01

Using non-linear effects such as cross-gain modulation (XGM) and cross-phase modulation (XPM) inside two highly non-linear fibres (HNLF) arranged in cascaded configuration, a simultaneous half/full-subtracter is proposed. The proposed simultaneous half/full-subtracter design is attractive due to several features such as input data pattern independence and usage of minimal number of non-linear elements i.e. HNLFs. Proof of concept simulations have been conducted at 100 Gbps rate, indicating fine performance, as extinction ratio (dB) > 6.28 dB and eye opening factors (EO) > 77.1072% are recorded for each implemented output. The proposed simultaneous half/full-subtracter can be used as a key component in all-optical information processing circuits.

A novel encryption scheme for high-contrast image data in the Fresnelet domain

PubMed Central

Bibi, Nargis; Farwa, Shabieh; Jahngir, Adnan; Usman, Muhammad

2018-01-01

In this paper, a unique and more distinctive encryption algorithm is proposed. This is based on the complexity of highly nonlinear S box in Flesnelet domain. The nonlinear pattern is transformed further to enhance the confusion in the dummy data using Fresnelet technique. The security level of the encrypted image boosts using the algebra of Galois field in Fresnelet domain. At first level, the Fresnelet transform is used to propagate the given information with desired wavelength at specified distance. It decomposes given secret data into four complex subbands. These complex sub-bands are separated into two components of real subband data and imaginary subband data. At second level, the net subband data, produced at the first level, is deteriorated to non-linear diffused pattern using the unique S-box defined on the Galois field F28. In the diffusion process, the permuted image is substituted via dynamic algebraic S-box substitution. We prove through various analysis techniques that the proposed scheme enhances the cipher security level, extensively. PMID:29608609

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

PubMed

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

2016-07-11

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

Non-Linear Acoustic Concealed Weapons Detector

DTIC Science & Technology

2006-05-01

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

Inferring Instantaneous, Multivariate and Nonlinear Sensitivities for the Analysis of Feedback Processes in a Dynamical System: Lorenz Model Case Study

NASA Technical Reports Server (NTRS)

Aires, Filipe; Rossow, William B.; Hansen, James E. (Technical Monitor)

2001-01-01

A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.

Non-linear effects in bunch compressor of TARLA

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

Yildiz, Hüseyin, E-mail: huseyinyildiz006@gmail.com, E-mail: huseyinyildiz@gazi.edu.tr; Aksoy, Avni; Arikan, Pervin

2016-03-25

Transport of a beam through an accelerator beamline is affected by high order and non-linear effects such as space charge, coherent synchrotron radiation, wakefield, etc. These effects damage form of the beam, and they lead particle loss, emittance growth, bunch length variation, beam halo formation, etc. One of the known non-linear effects on low energy machine is space charge effect. In this study we focus on space charge effect for Turkish Accelerator and Radiation Laboratory in Ankara (TARLA) machine which is designed to drive InfraRed Free Electron Laser covering the range of 3-250 µm. Moreover, we discuss second order effects onmore » bunch compressor of TARLA.« less

Inverse halftoning via robust nonlinear filtering

NASA Astrophysics Data System (ADS)

Shen, Mei-Yin; Kuo, C.-C. Jay

1999-10-01

A new blind inverse halftoning algorithm based on a nonlinear filtering technique of low computational complexity and low memory requirement is proposed in this research. It is called blind since we do not require the knowledge of the halftone kernel. The proposed scheme performs nonlinear filtering in conjunction with edge enhancement to improve the quality of an inverse halftoned image. Distinct features of the proposed approach include: efficiently smoothing halftone patterns in large homogeneous areas, additional edge enhancement capability to recover the edge quality and an excellent PSNR performance with only local integer operations and a small memory buffer.

Nonlinear optical characterization of ZnS thin film synthesized by chemical spray pyrolysis method

NASA Astrophysics Data System (ADS)

G, Sreeja V.; V, Sabitha P.; Anila, E. I.; R, Reshmi; John, Manu Punnan; Radhakrishnan, P.

2014-10-01

ZnS thin film was prepared by Chemical Spray Pyrolysis (CSP) method. The sample was characterized by X-ray diffraction method and Z scan technique. XRD pattern showed that ZnS thin film has hexagonal structure with an average size of about 5.6nm. The nonlinear optical properties of ZnS thin film was studied by open aperture Z-Scan technique using Q-switched Nd-Yag Laser at 532nm. The Z-scan plot showed that the investigated ZnS thin film has saturable absorption behavior. The nonlinear absorption coefficient and saturation intensity were also estimated.

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2006-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

Variation of ecosystem services and human activities: A case study in the Yanhe Watershed of China

NASA Astrophysics Data System (ADS)

Su, Chang-hong; Fu, Bo-Jie; He, Chan-Sheng; Lü, Yi-He

2012-10-01

The concept of 'ecosystem service' provides cohesive views on mechanisms by which nature contributes to human well-being. Fast social and economic development calls for research on interactions between human and natural systems. We took the Yanhe Watershed as our study area, and valued the variation of ecosystem services and human activities of 2000 and 2008. Five ecosystem services were selected i.e. net primary production (NPP), carbon sequestration and oxygen production (CSOP), water conservation, soil conservation, and grain production. Human activity was represented by a composite human activity index (HAI) that integrates human population density, farmland ratio, influence of residential sites and road network. Analysis results of the five ecosystem services and human activity (HAI) are as follows: (i) NPP, CSOP, water conservation, and soil conservation increased from 2000 to 2008, while grain production declined. HAI decreased from 2000 to 2008. Spatially, NPP, CSOP, and water conservation in 2000 and 2008 roughly demonstrated a pattern of decline from south to north, while grain production shows an endocentric increasing spatial pattern. Soil conservation showed a spatial pattern of high in the south and low in the north in 2000 and a different pattern of high in the west and low in the east in 2008 respectively. HAI is proportional to the administrative level and economic development. Variation of NPP/CSOP between 2000 and 2008 show an increasing spatial pattern from northwest to southeast. In contrast, the variation of soil conservation shows an increasing pattern from southeast to northwest. Variation of water conservation shows a fanning out decreasing pattern. Variation of grain production doesn't show conspicuous spatial pattern. (ii) Variation of water conservation and of soil conservation is significantly positively correlated at 0.01 level. Both variations of water conservation and soil conservation are negatively correlated with variation of HAI at 0.01 level. Variations of NPP/CSOP are negatively correlated with variations of soil conservation and grain production at 0.05 level. (iii) Strong tradeoffs exist between regulation services and provision service, while synergies exist within regulation services. Driving effect of human activities on ecosystem services and tradeoffs and synergies among ecosystem service are also discussed.

CDU improvement technology of etching pattern using photo lithography

NASA Astrophysics Data System (ADS)

Tadokoro, Masahide; Shinozuka, Shinichi; Jyousaka, Megumi; Ogata, Kunie; Morimoto, Tamotsu; Konishi, Yoshitaka

2008-03-01

Semiconductor manufacturing technology has shifted towards finer design rules, and demands for critical dimension uniformity (CDU) of resist patterns have become greater than ever. One of the methods for improving Resist Pattern CDU is to control post-exposure bake (PEB) temperature. When ArF resist is used, there is a certain relationship between critical dimension (CD) and PEB temperature. By utilizing this relationship, Resist Pattern CDU can be improved through control of within-wafer temperature distribution in the PEB process. Resist Pattern CDU improvement contributes to Etching Pattern CDU improvement to a certain degree. To further improve Etching Pattern CDU, etcher-specific CD variation needs to be controlled. In this evaluation, 1. We verified whether etcher-specific CD variation can be controlled and consequently Etching Pattern CDU can be further improved by controlling resist patterns through PEB control. 2. Verifying whether Etching Pattern CDU improvement through has any effect on the reduction in wiring resistance variation. The evaluation procedure is as follows.1. Wafers with base film of Doped Poly-Si (D-Poly) were prepared. 2. Resist patterns were created on them. 3. To determine etcher-specific characteristics, the first etching was performed, and after cleaning off the resist and BARC, CD of etched D-Poly was measured. 4. Using the obtained within-wafer CD distribution of the etching patterns, within-wafer temperature distribution in the PEB process was modified. 5. Resist patterns were created again, followed by the second etching and cleaning, which was followed by CD measurement. We used Optical CD Measurement (OCD) for measurement of resist patterns and etching patterns as OCD is minimally affected by Line Edge Roughness (LER). As a result, 1. We confirmed the effect of Resist Pattern CD control through PEB control on the reduction in etcher-specific CD variation and the improvement in Etching Pattern CDU. 2. The improvement in Etching Pattern CDU has an effect on the reduction in wiring resistance variation. The method for Etching Pattern CDU improvement through PEB control reduces within-wafer variation of MOS transistor's gate length. Therefore, with this method, we can expect to observe uniform within-wafer MOS transistor characteristics.

Pattern formation in diffusive excitable systems under magnetic flow effects

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Takembo, Clovis N.; Ekobena Fouda, H. P.; Kofané, Timoléon C.

2017-07-01

We study the spatiotemporal formation of patterns in a diffusive FitzHugh-Nagumo network where the effect of electromagnetic induction has been introduced in the standard mathematical model by using magnetic flux, and the modulation of magnetic flux on membrane potential is realized by using memristor coupling. We use the multi-scale expansion to show that the system equations can be reduced to a single differential-difference nonlinear equation. The linear stability analysis is performed and discussed with emphasis on the impact of magnetic flux. It is observed that the effect of memristor coupling importantly modifies the features of modulational instability. Our analytical results are supported by the numerical experiments, which reveal that the improved model can lead to nonlinear quasi-periodic spatiotemporal patterns with some features of synchronization. It is observed also the generation of pulses and rhythmics behaviors like breathing or swimming which are important in brain researches.

Bench-marking effects in the blaming of professionals for incidents of aggression and assault.

PubMed

Carifio, J; Lanza, M

1994-01-01

This study compared all possible orders of responding to three vignettes describing incidents between a male patient and a female nurse in which the nurse is mildly assaulted, severely assaulted, or verbally abused by the patient (the control condition). Subjects were 32 female senior-year nursing students and 28 practicing nurses. It was found that response levels to a given vignette could predict a respondent's response to the other vignettes. Also, a significant "bench-marking" effect was found: if a subject responded to the mild assault vignette first, the subject's overall response pattern best fit the general nonlinear assignment-of-blame pattern observed, but if the subject responded to the severe assault or control vignette first, this vignette set a bench mark for responding from which the subject's subsequent responses did not deviate greatly, which slightly distorted the subject's V-shaped nonlinear response pattern.

Model of an axially strained weakly guiding optical fiber modal pattern

NASA Technical Reports Server (NTRS)

Egalon, Claudio O.; Rogowski, Robert S.

1992-01-01

Axial strain can be determined by monitoring the modal pattern variation of an optical fiber. The results of a numerical model developed to calculate the modal pattern variation at the end of a weakly guiding optical fiber under axial strain is presented. Whenever an optical fiber is under stress, the optical path length, the index of refraction, and the propagation constants of each fiber mode change. In consequence, the modal phase term for the fields and the fiber output pattern are also modified. For multimode fibers, very complicated patterns result. The predicted patterns are presented, and an expression for the phase variation with strain is derived.

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.

Racing against Time: Using Technology To Explore Distance, Rate, and Time.

ERIC Educational Resources Information Center

Essex, N. Kathryn; Lambdin, Diana V.; McGraw, Rebecca H.

2002-01-01

Investigates ways to analyze change in various contexts. Focuses on computer technology providing contexts for children's investigations of patterns of change and helping to develop foundational ideas of algebra and calculus. Discusses relationships between patterns of change, fundamental algebraic notions as linear and nonlinear functions, and…

Wrinkle-to-fold transition in soft layers under equi-biaxial strain: A weakly nonlinear analysis

NASA Astrophysics Data System (ADS)

Ciarletta, P.

2014-12-01

Soft materials can experience a mechanical instability when subjected to a finite compression, developing wrinkles which may eventually evolve into folds or creases. The possibility to control the wrinkling network morphology has recently found several applications in many developing fields, such as scaffolds for biomaterials, stretchable electronics and surface micro-fabrication. Albeit much is known of the pattern initiation at the linear stability order, the nonlinear effects driving the pattern selection in soft materials are still unknown. This work aims at investigating the nature of the elastic bifurcation undertaken by a growing soft layer subjected to a equi-biaxial strain. Considering a skin effect at the free surface, the instability thresholds are found to be controlled by a characteristic length, defined by the ratio between capillary energy and bulk elasticity. For the first time, a weakly nonlinear analysis of the wrinkling instability is performed here using the multiple-scale perturbation method applied to the incremental theory in finite elasticity. The Ginzburg-Landau equations are derived for different superposing linear modes. This study proves that a subcritical pitchfork bifurcation drives the observed wrinkle-to-fold transition in swelling gels experiments, favoring the emergence of hexagonal creased patterns, albeit quasi-hexagonal patterns might later emerge because of an expected symmetry break. Moreover, if the surface energy is somewhat comparable to the bulk elastic energy, it has the same stabilizing effect as for fluid instabilities, driving the formation of stable wrinkles, as observed in elastic bi-layered materials.

The evolution of phenotypic correlations and ‘developmental memory’

PubMed Central

Watson, Richard A.; Wagner, Günter P.; Pavlicev, Mihaela; Weinreich, Daniel M.; Mills, Rob

2014-01-01

Development introduces structured correlations among traits that may constrain or bias the distribution of phenotypes produced. Moreover, when suitable heritable variation exists, natural selection may alter such constraints and correlations, affecting the phenotypic variation available to subsequent selection. However, exactly how the distribution of phenotypes produced by complex developmental systems can be shaped by past selective environments is poorly understood. Here we investigate the evolution of a network of recurrent non-linear ontogenetic interactions, such as a gene regulation network, in various selective scenarios. We find that evolved networks of this type can exhibit several phenomena that are familiar in cognitive learning systems. These include formation of a distributed associative memory that can ‘store’ and ‘recall’ multiple phenotypes that have been selected in the past, recreate complete adult phenotypic patterns accurately from partial or corrupted embryonic phenotypes, and ‘generalise’ (by exploiting evolved developmental modules) to produce new combinations of phenotypic features. We show that these surprising behaviours follow from an equivalence between the action of natural selection on phenotypic correlations and associative learning, well-understood in the context of neural networks. This helps to explain how development facilitates the evolution of high-fitness phenotypes and how this ability changes over evolutionary time. PMID:24351058

What Can Causal Networks Tell Us about Metabolic Pathways?

PubMed Central

Blair, Rachael Hageman; Kliebenstein, Daniel J.; Churchill, Gary A.

2012-01-01

Graphical models describe the linear correlation structure of data and have been used to establish causal relationships among phenotypes in genetic mapping populations. Data are typically collected at a single point in time. Biological processes on the other hand are often non-linear and display time varying dynamics. The extent to which graphical models can recapitulate the architecture of an underlying biological processes is not well understood. We consider metabolic networks with known stoichiometry to address the fundamental question: “What can causal networks tell us about metabolic pathways?”. Using data from an Arabidopsis BaySha population and simulated data from dynamic models of pathway motifs, we assess our ability to reconstruct metabolic pathways using graphical models. Our results highlight the necessity of non-genetic residual biological variation for reliable inference. Recovery of the ordering within a pathway is possible, but should not be expected. Causal inference is sensitive to subtle patterns in the correlation structure that may be driven by a variety of factors, which may not emphasize the substrate-product relationship. We illustrate the effects of metabolic pathway architecture, epistasis and stochastic variation on correlation structure and graphical model-derived networks. We conclude that graphical models should be interpreted cautiously, especially if the implied causal relationships are to be used in the design of intervention strategies. PMID:22496633

The cross wavelet analysis of dengue fever variability influenced by meteorological conditions

NASA Astrophysics Data System (ADS)

Lin, Yuan-Chien; Yu, Hwa-Lung; Lee, Chieh-Han

2015-04-01

The multiyear variation of meteorological conditions induced by climate change causes the changing diffusion pattern of infectious disease and serious epidemic situation. Among them, dengue fever is one of the most serious vector-borne diseases distributed in tropical and sub-tropical regions. Dengue virus is transmitted by several species of mosquito and causing lots amount of human deaths every year around the world. The objective of this study is to investigate the impact of meteorological variables to the temporal variation of dengue fever epidemic in southern Taiwan. Several extreme and average indices of meteorological variables, i.e. temperature and humidity, were used for this analysis, including averaged, maximum and minimum temperature, and average rainfall, maximum 1-hr rainfall, and maximum 24-hr rainfall. This study plans to identify and quantify the nonlinear relationship of meteorological variables and dengue fever epidemic, finding the non-stationary time-frequency relationship and phase lag effects of those time series from 1998-2011 by using cross wavelet method. Results show that meteorological variables all have a significant time-frequency correlation region to dengue fever epidemic in frequency about one year (52 weeks). The associated phases can range from 0 to 90 degrees (0-13 weeks lag from meteorological factors to dengue incidences). Keywords: dengue fever, cross wavelet analysis, meteorological factor

Parametric Study of Flow Patterns behind the Standing Accretion Shock Wave for Core-Collapse Supernovae

NASA Astrophysics Data System (ADS)

Iwakami, Wakana; Nagakura, Hiroki; Yamada, Shoichi

2014-05-01

In this study, we conduct three-dimensional hydrodynamic simulations systematically to investigate the flow patterns behind the accretion shock waves that are commonly formed in the post-bounce phase of core-collapse supernovae. Adding small perturbations to spherically symmetric, steady, shocked accretion flows, we compute the subsequent evolutions to find what flow pattern emerges as a consequence of hydrodynamical instabilities such as convection and standing accretion shock instability for different neutrino luminosities and mass accretion rates. Depending on these two controlling parameters, various flow patterns are indeed realized. We classify them into three basic patterns and two intermediate ones; the former includes sloshing motion (SL), spiral motion (SP), and multiple buoyant bubble formation (BB); the latter consists of spiral motion with buoyant-bubble formation (SPB) and spiral motion with pulsationally changing rotational velocities (SPP). Although the post-shock flow is highly chaotic, there is a clear trend in the pattern realization. The sloshing and spiral motions tend to be dominant for high accretion rates and low neutrino luminosities, and multiple buoyant bubbles prevail for low accretion rates and high neutrino luminosities. It is interesting that the dominant pattern is not always identical between the semi-nonlinear and nonlinear phases near the critical luminosity; the intermediate cases are realized in the latter case. Running several simulations with different random perturbations, we confirm that the realization of flow pattern is robust in most cases.

Nonlinear behaviour of reflectivity of gallium - Silica interface & its applications

NASA Astrophysics Data System (ADS)

Naruka, Preeti; Bissa, Shivangi

2018-05-01

In this paper Optical properties and nonlinear behaviour of Gallium-Silica Interface is studied. Change in reflectivity of gallium film is explained as a function of thickness of metallic layer and intensity of incident light by using non-thermal mechanism. Here variation of dielectric constant of gallium with temperature is also explained on considering Binary nanoshell model of gallium nanoparticles of spherical shape. In the present paper application of structural phase transformation of gallium is explained as a Grating assisted coupler.

Quantum morphogenesis: A variation on Thom's catastrophe theory

NASA Astrophysics Data System (ADS)

Aerts, Dirk; Czachor, Marek; Gabora, Liane; Kuna, Maciej; Posiewnik, Andrzej; Pykacz, Jarosław; Syty, Monika

2003-05-01

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including “birth and death of an organism” and “development of complementary properties.”

Variational Theory of Motion of Curved, Twisted and Extensible Elastic Rods

DTIC Science & Technology

1993-01-18

nonlinear theory such as questions of existence of solutions and global behavior have been carried out by Antman (1976). His basic work entitled "The...Aerosp. Ens. Q017/018 16 REFERENCES Antman , S.S., "Ordinary Differential Equations of Non-Linear ElastIcity 1: Foundatious of the Theories of Non-Linearly...Elutic rods and Shells," A.R.M.A. 61 (1976), 307-351. Antman , S.S., "The Theory of Rods", Handbuch der Physik, Vol. Vla/2, Springer-Verlq, Berlin

Modeling dynamic acousto-elastic testing experiments: validation and perspectives.

PubMed

Gliozzi, A S; Scalerandi, M

2014-10-01

Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.

Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1986-01-01

The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.

Electromechanical, acoustical and thermodynamical characterization of a low-frequency sonotrode-type transducer in a small sonoreactor at different excitation levels and loading conditions.

PubMed

Petošić, Antonio; Horvat, Marko; Režek Jambrak, Anet

2017-11-01

The paper reports and compares the results of the electromechanical, acoustical and thermodynamical characterization of a low-frequency sonotrode-type ultrasonic device inside a small sonoreactor, immersed in three different loading media, namely, water, juice and milk, excited at different excitation levels, both below and above the cavitation threshold. The electroacoustic efficiency factor determined at system resonance through electromechanical characterization in degassed water as the reference medium is 88.7% for the device in question. This efficiency can be reduced up to three times due to the existence of a complex sound field in the reactor in linear driving conditions below the cavitation threshold. The behaviour of the system is more stable at higher excitation levels than in linear operating conditions. During acoustical characterization, acoustic pressure is spatially averaged, both below and above the cavitation threshold. The standing wave patterns inside the sonoreactor have a stronger influence on the variation of the spatially distributed RMS pressure in linear operating conditions. For these conditions, the variation of ±1.7dB was obtained, compared to ±1.4dB obtained in highly nonlinear regime. The acoustic power in the sonoreactor was estimated from the magnitude of the averaged RMS pressure, and from the reverberation time of the sonoreactor as the representation of the losses. The electroacoustic efficiency factors obtained through acoustical and electromechanical characterization are in a very good agreement at low excitation levels. The irradiated acoustic power estimated in nonlinear conditions differs from the dissipated acoustic power determined with the calorimetric method by several orders of magnitude. The number of negative pressure peaks that represent transient cavitation decreases over time during longer treatments of a medium with high-power ultrasound. The number of negative peaks decreases faster when the medium and the vessel are allowed to heat up. Copyright © 2017 Elsevier B.V. All rights reserved.

Temperature in lowland Danish streams: contemporary patterns, empirical models and future scenarios

NASA Astrophysics Data System (ADS)

Lagergaard Pedersen, Niels; Sand-Jensen, Kaj

2007-01-01

Continuous temperature measurements at 11 stream sites in small lowland streams of North Zealand, Denmark over a year showed much higher summer temperatures and lower winter temperatures along the course of the stream with artificial lakes than in the stream without lakes. The influence of lakes was even more prominent in the comparisons of colder lake inlets and warmer outlets and led to the decline of cold-water and oxygen-demanding brown trout. Seasonal and daily temperature variations were, as anticipated, dampened by forest cover, groundwater input, input from sewage plants and high downstream discharges. Seasonal variations in daily water temperature could be predicted with high accuracy at all sites by a linear air-water regression model (r2: 0.903-0.947). The predictions improved in all instances (r2: 0.927-0.964) by a non-linear logistic regression according to which water temperatures do not fall below freezing and they increase less steeply than air temperatures at high temperatures because of enhanced heat loss from the stream by evaporation and back radiation. The predictions improved slightly (r2: 0.933-0.969) by a multiple regression model which, in addition to air temperature as the main predictor, included solar radiation at un-shaded sites, relative humidity, precipitation and discharge. Application of the non-linear logistic model for a warming scenario of 4-5 °C higher air temperatures in Denmark in 2070-2100 yielded predictions of temperatures rising 1.6-3.0 °C during winter and summer and 4.4-6.0 °C during spring in un-shaded streams with low groundwater input. Groundwater-fed springs are expected to follow the increase of mean air temperatures for the region. Great caution should be exercised in these temperature projections because global and regional climate scenarios remain open to discussion. Copyright

Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach

NASA Astrophysics Data System (ADS)

Neicu, Toni

2002-09-01

An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were observed in a strongly nonlinear, dissipative granular system of vertically vibrated rods. Above a critical packing fraction, moving domains of nearly vertical rods were seen to coexist with horizontal rods. The vertical domains coarsen to form several large vortices, which were driven by the anisotropy and inclination of the rods.

Erosion by an Alpine glacier.

PubMed

Herman, Frédéric; Beyssac, Olivier; Brughelli, Mattia; Lane, Stuart N; Leprince, Sébastien; Adatte, Thierry; Lin, Jiao Y Y; Avouac, Jean-Philippe; Cox, Simon C

2015-10-09

Assessing the impact of glaciation on Earth's surface requires understanding glacial erosion processes. Developing erosion theories is challenging because of the complex nature of the erosion processes and the difficulty of examining the ice/bedrock interface of contemporary glaciers. We demonstrate that the glacial erosion rate is proportional to the ice-sliding velocity squared, by quantifying spatial variations in ice-sliding velocity and the erosion rate of a fast-flowing Alpine glacier. The nonlinear behavior implies a high erosion sensitivity to small variations in topographic slope and precipitation. A nonlinear rate law suggests that abrasion may dominate over other erosion processes in fast-flowing glaciers. It may also explain the wide range of observed glacial erosion rates and, in part, the impact of glaciation on mountainous landscapes during the past few million years. Copyright © 2015, American Association for the Advancement of Science.

Body Temperature Patterns and Rhythmicity in Free-Ranging Subterranean Damaraland Mole-Rats, Fukomys damarensis

PubMed Central

Streicher, Sonja; Boyles, Justin G.; Oosthuizen, Maria K.; Bennett, Nigel C.

2011-01-01

Body temperature (Tb) is an important physiological component that affects endotherms from the cellular to whole organism level, but measurements of Tb in the field have been noticeably skewed towards heterothermic species and seasonal comparisons are largely lacking. Thus, we investigated patterns of Tb patterns in a homeothermic, free-ranging small mammal, the Damaraland mole-rat (Fukomys damarensis) during both the summer and winter. Variation in Tb was significantly greater during winter than summer, and greater among males than females. Interestingly, body mass had only a small effect on variation in Tb and there was no consistent pattern relating ambient temperature to variation in Tb. Generally speaking, it appears that variation in Tb patterns varies between seasons in much the same way as in heterothermic species, just to a lesser degree. Both cosinor analysis and Fast Fourier Transform analysis revealed substantial individual variation in Tb rhythms, even within a single colony. Some individuals had no Tb rhythms, while others appeared to exhibit multiple rhythms. These data corroborate previous laboratory work showing multiplicity of rhythms in mole-rats and suggest the variation seen in the laboratory is a true indicator of the variation seen in the wild. PMID:22028861