Nonlinear Aspects Research Articles

A non-linear Granger-causality framework to investigate climate–vegetation dynamics

Abstract. Satellite Earth observation has led to the creation of global climate data records of many important environmental and climatic variables. These come in the form of multivariate time series with different spatial and temporal resolutions. Data of this kind provide new means to further unravel the influence of climate on vegetation dynamics. However, as advocated in this article, commonly used statistical methods are often too simplistic to represent complex climate–vegetation relationships due to linearity assumptions. Therefore, as an extension of linear Granger-causality analysis, we present a novel non-linear framework consisting of several components, such as data collection from various databases, time series decomposition techniques, feature construction methods, and predictive modelling by means of random forests. Experimental results on global data sets indicate that, with this framework, it is possible to detect non-linear patterns that are much less visible with traditional Granger-causality methods. In addition, we discuss extensive experimental results that highlight the importance of considering non-linear aspects of climate–vegetation dynamics.

Cosmic ray transport in the Galaxy: A review

The physics of energetic particle propagation in magnetized environments plays a crucial role in both the processes of acceleration and transport of cosmic rays. Recent theoretical developments in the field of cosmic ray research have been mainly in the direction of exploring non-linear aspects of the processes in which these particles are involved, namely the action of cosmic rays on the environment in which the transport and/or acceleration take place. When cosmic rays propagate outside of the acceleration region, such action is mainly in two forms: (1) they generate hydromagnetic waves, through streaming instabilities, leading to a dependence of the scattering properties of the medium on the spectrum and spatial distribution of the energetic particles, and (2) they exert a dynamical action on the plasma, which may cause the launching of cosmic ray driven Galactic winds. In this article we discuss these and other recent developments and how they compare with the bulk of new observations on the spectra of primary nuclei (mainly H and He) and secondary to primary ratios, such as the B/C ratio and the p¯/p ratio, and the positrons ratio e+/(e-+e+). We also comment on some radically new models of the origin of CRs, in which the physical meaning of the secondary to primary ratios is not the same as in the standard model.

From Pipelines to Tasting Lemonade: Reconceptualizing College Access

Pipeline metaphors are ubiquitous in theorizing and interpreting college access processes. In this conceptual article, we explore how a lemonade metaphor can open new possibilities to reimagining higher education access and going processes. We argue that using food metaphors, particularly the processes of mixing, tasting, and digesting lemonade, may help constitute new meanings of college going. Rather than focus on production, mechanization, and ignoring social justice, a lemonade metaphor emphasizes the nonlinear aspects of college-going processes, foregrounds power relations within these processes, and humanizes educational purposes and journeys. We encourage educational researchers to take up taste as a heuristic device to reveal something different about educational phenomena that will, in turn, have material consequences.

High intensity laser beam propagation through a relativistic warm magnetoplasma

In this work, nonlinear aspects of a circularly polarized high intensity Gaussian laser beam propagating in a relativistic warm magnetized plasma are studied, taking into account the relativistic ponderomotive force. The differential equation governing the dimensionless beam width parameter is achieved and numerically solved by introducing the dielectric permittivity of such plasma and using the paraxial ray approximation. The effects of entrance laser intensity and its polarization state, external magnetic field, and electron temperature on the laser spot size evolution are studied. It is found that for both right and left-handed polarization states increasing initial laser intensity deteriorates the self-focusing mechanism while rising electron temperature improves it. It is also observed that enhancing magnetic field leads to faster and stronger self-focusing in the case of right-handed polarization and an attenuation in the self-focusing process in the case of left-handed one. In addition, the spatial distribution of normalized modified electron density as well as laser intensity profiles as a function of plasma length and beam radius is plotted and discussed for three self-focusing, self-trapping, and defocusing regimes.

Nonlinear assessment of motor variability during practice and competition for individuals with different motivational orientations

The aim of the present study was to document how differing motivational orientation profiles, situated within environmental constraints (i.e., a competitive and practice environments) influence the nonlinear variability of performance and subsequent retention of a visual motor tracking skill. Myriad research associates atypical nonlinear aspects of motor variability with pathology; however, few empirical efforts have explored the influence of individual differences and environmental factors on nonlinear aspects of motor output and skill retention. Participants performed an isometric force-tracking task, matching the force indicated by a target line displayed across a computer screen. Dependent variables were performance outcome (root mean squared error) and the complexity of the produced signal (Sample Entropy) across practice, competition, and retention. Participants with high task orientation, regardless of high or low levels of ego orientation, exhibited the greatest visual motor tracking improvement as well as the greatest increases in irregularity of force variability from practice to competition and retention. We conclude that individual differences play a key role in the structure of continuous behavior, and that this structure influences the learning of continuous motor skills.

Gender differences in nonlinear motor performance following concussion

PurposeTo quantify differences in nonlinear aspects of performance on a seated visual-motor tracking task between clinically asymptomatic males and females with and without a self-reported mild traumatic brain injury history. MethodsSeventy-three individuals with a self-reported concussion history (age: 21.40 ± 2.25 years, mean ± SD) and 75 without completed the visual-motor tracking task (age: 21.50 ± 2.00 years). Participants pressed an index finger against a force sensor, tracing a line across a computer screen (visual-motor tracking). The produced signal's root-mean-square error (RMSE), sample entropy (SampEn, a measure of regularity), and average power (AvP) between 0 and 12 Hz were calculated. ResultsMales with a history of 0 or 1 concussion had greater RMSE (worse performance) than females with 0 (p< 0.0001) and 1 concussion (p = 0.052). Additionally, females with 2+ concussions exhibited lower SampEn than females with no history (p = 0.001) or a history of 1 concussion (p = 0.026). Finally, females with 2+ concussions had lower 8–12 Hz AvP than males with 2+ concussions (p = 0.031). Few differences were observed in the male participants. ConclusionFemales with a self-reported history of multiple concussions exhibited lower SampEn in the visual-motor tracking-task force output structure as compared to those with no reported history of concussion and their male counterparts. Lower SampEn and lower power between 8 and 12 Hz indicated persistent impairment in visual processing and feed-forward or predictive motor control systems.

Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control

The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson’s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity.

Chaotic dynamics of a magnetic particle at finite temperature

In this work, we study nonlinear aspects of the deterministic spin dynamics of an anisotropic single-domain magnetic particle at finite temperature modeled by the Landau-Lifshitz-Bloch equation. The magnetic field has two components: a constant term and a term involving a harmonic time modulation. The dynamical behavior of the system is characterized with the Lyapunov exponents and by means of bifurcation diagrams and Fourier spectra. In particular, we explore the effects of the magnitude and frequency of the applied magnetic field, finding that the system presents multiple transitions between regular and chaotic states when varying the control parameters. We also address the temperature dependence and evidence that it plays an important role in these transitions, almost suppressing the chaotic behavior close to the Curie temperature. Finally, we find that the system has hyperchaotic states for specific values of field and temperature.

A review of the most important failure, reliability and nonlinearity aspects in the development of microelectromechanical systems (MEMS)

PurposeThe purpose of this paper is to provide an overview of the major reliability issues of microelectromechanical systems (MEMS) under mechanical and environmental loading conditions. Furthermore, a comprehensive study on the nonlinear behavior of silicon MEMS devices is presented and different aspects of this phenomenon are discussed.Design/methodology/approachRegarding the reliability investigations, the most important failure aspects affecting the proper operation of the MEMS components with focus on those caused by environmental and mechanical loads are reviewed. These studies include failures due to fatigue loads, mechanical vibration, mechanical shock, humidity, temperature and particulate contamination. In addition, the influence of squeeze film air damping on the dynamic response of MEMS devices is briefly discussed. A further subject of this paper is discussion of studies on the nonlinearity of silicon MEMS. For this purpose, after a description of the basic principles of nonlinearity, the consequences of nonlinear phenomena such as frequency shift, hysteresis and harmonic generation and their effects on the device performance are reviewed. Special attention is paid to the mode coupling effect between the resonant modes as a result of energy transfer because of the nonlinearity of silicon. For a better understanding of these effects, the nonlinear behavior of silicon is demonstrated by using the example of Si cantilever beams.FindingsIt is shown that environmental and mechanical loads can influence on proper operation of the MEMS components and lead to early fracture. In addition, it is demonstrated that nonlinearity modifies dynamic response and leads to new phenomena such as frequency shift and mode coupling. Finally, some ideas are given as possible future areas of research works.Originality/valueThis is a review paper and aimed to review the latest manuscripts published in the field of reliability and nonlinearity of the MEMS structures.

Non-linear aspects of Görtler instability in boundary layers with pressure gradient

The laminar flow over a concave surface may undergo transition to a turbulent state driven by secondary instabilities initiated by the longitudinal vortices known as Görtler vortices. These vortices distort the boundary layer structure by modifying the streamwise velocity component in both spanwise and wall-normal directions. Numerical simulations have been conducted to identify the role of the external pressure gradients in the development and saturation of the vortices. The results show that flows with adverse pressure gradients reach saturation upstream from the saturation location for neutral and favorable pressure gradients. In the transition region, the mean spanwise shear stress is about three times larger than in the flow without the vortices.

Network Receptive Field Modeling Reveals Extensive Integration and Multi-feature Selectivity in Auditory Cortical Neurons.

Cortical sensory neurons are commonly characterized using the receptive field, the linear dependence of their response on the stimulus. In primary auditory cortex neurons can be characterized by their spectrotemporal receptive fields, the spectral and temporal features of a sound that linearly drive a neuron. However, receptive fields do not capture the fact that the response of a cortical neuron results from the complex nonlinear network in which it is embedded. By fitting a nonlinear feedforward network model (a network receptive field) to cortical responses to natural sounds, we reveal that primary auditory cortical neurons are sensitive over a substantially larger spectrotemporal domain than is seen in their standard spectrotemporal receptive fields. Furthermore, the network receptive field, a parsimonious network consisting of 1–7 sub-receptive fields that interact nonlinearly, consistently better predicts neural responses to auditory stimuli than the standard receptive fields. The network receptive field reveals separate excitatory and inhibitory sub-fields with different nonlinear properties, and interaction of the sub-fields gives rise to important operations such as gain control and conjunctive feature detection. The conjunctive effects, where neurons respond only if several specific features are present together, enable increased selectivity for particular complex spectrotemporal structures, and may constitute an important stage in sound recognition. In conclusion, we demonstrate that fitting auditory cortical neural responses with feedforward network models expands on simple linear receptive field models in a manner that yields substantially improved predictive power and reveals key nonlinear aspects of cortical processing, while remaining easy to interpret in a physiological context.

Giant Kerr response of ultrathin gold films from quantum size effect.

With the size of plasmonic devices entering into the nanoscale region, the impact of quantum physics needs to be considered. In the past, the quantum size effect on linear material properties has been studied extensively. However, the nonlinear aspects have not been explored much so far. On the other hand, much effort has been put into the field of integrated nonlinear optics and a medium with large nonlinearity is desirable. Here we study the optical nonlinear properties of a nanometre scale gold quantum well by using the z-scan method and nonlinear spectrum broadening technique. The quantum size effect results in a giant optical Kerr susceptibility, which is four orders of magnitude higher than the intrinsic value of bulk gold and several orders larger than traditional nonlinear media. Such high nonlinearity enables efficient nonlinear interaction within a microscopic footprint, making quantum metallic films a promising candidate for integrated nonlinear optical applications.

Recent extensions to topological and nonlinear aspects of wave digital filter theory

The Wave Digital Filter approach can be used to create computational models of lumped reference systems, including rectilinear mechanical, rotational mechanical, acoustical, and electronic systems. When they are applicable, Wave Digital Filters enjoy properties including modularity, accuracy, and guaranteed incremental passivity that make them attractive in the context of musical instrument and audio effect simulation. However, the class of reference systems that can be modeled with Wave Digital Filters has historically been restricted to systems with simple topologies (which can be decomposed entirely into series and parallel connections) and which contain only a single “nonadaptable” element (e.g., a diode, ideal source, or switch). This talk details recent Wave Digital Filter advances from Stanford University's Center for Computer Research in Music and Acoustics (CCRMA), which broaden the applicability of Wave Digital Filters to reference systems with any topology and an arbitrary number of nonlinearit...

A decomposition approach to determining fleet size and structure with network flow effects and demand uncertainty

SummaryThis paper presents a new methodology to determine fleet size and structure for those airlines operating on hub‐and‐spoke networks. The methodology highlights the impact of stochastic traffic network flow effects on fleet planning process and is employed to construct an enhanced revenue model by incorporating the expected revenue optimization model into fleet planning process. The objective of the model is to find a feasible allocation of aircraft fleet types to route legs using minimum fleet purchasing cost, thus ensuring that the expected fleet profit is maximized subject to several critical resource constraints. By using a linear approximation to the total network revenue function, the fleet planning model with enhanced revenue modeling is decomposed into the nonlinear aspects of expected revenue optimization and the linear aspects of determining fleet size and structure by optimal allocation of aircraft fleet types to route legs. To illustrate this methodology and its economic benefits, an example consisting of 6 chosen aircraft fleet types, 12 route legs, and 57 path‐specific origin‐destination markets is presented and compared with the results found using revenue prorated fleet planning formulation. The results show that the fleet size and structure of the methodology proposed in this paper gain 211.4% improvement in fleet profit over the use of the revenue prorated fleet planning approach. In addition, comparison with the deterministic model reveals that the fleet size and structure of this proposed methodology are more adaptable to the fluctuations of passenger demands. Copyright © 2016 John Wiley &amp; Sons, Ltd.

A physics based approach to the pulse wave velocity prediction in compliant arterial segments

Pulse wave velocity (PWV) quantification commonly serves as a highly robust prognostic parameter being used in a preventative cardiovascular therapy. Being dependent on arterial elastance, it can serve as a marker of cardiovascular risk. Since it is influenced by a blood pressure (BP), the pertaining theory can lay the foundation in developing a technique for noninvasive blood pressure measurement. Previous studies have reported application of PWV, measured noninvasively, for both the estimation of arterial compliance and blood pressure, based on simplified physical or statistical models. A new theoretical model for pulse wave propagation in a compliant arterial segment is presented within the framework of pseudo-elastic deformation of biological tissue undergoing finite deformation. An essential ingredient is the dependence of results on nonlinear aspects of the model: convective fluid phenomena, hyperelastic constitutive relation, large deformation and a longitudinal pre-stress load. An exact analytical solution for PWV is presented as a function of pressure, flow and pseudo-elastic orthotropic parameters. Results from our model are compared with published in-vivo PWV measurements under diverse physiological conditions. Contributions of each of the nonlinearities are analyzed. It was found that the totally nonlinear model achieves the best match with the experimental data. To retrieve individual vascular information of a patient, the inverse problem of hemodynamics is presented, calculating local orthotropic hyperelastic properties of the arterial wall. The proposed technique can be used for non-invasive assessment of arterial elastance, and blood pressure using direct measurement of PWV, with account of hyperelastic orthotropic properties.

Nonlinear thermal radiation aspects in stagnation point flow of tangent hyperbolic nanofluid with double diffusive convection

The objective of present study is to examine the nonlinear thermal radiation behavior in the mixed convection stagnation point flow of tangent hyperbolic nanofluid towards a stretching surface. Flow analysis is presented by considering the chemical reaction and heat generation/absorption effects. The convective type conditions are imposed to make the analysis of heat and mass transfer. Nanoparticles effects are encountered due to consideration of thermophoresis and Brownian motion. The governing nonlinear partial differential systems are transform into nonlinear ordinary differential systems by adequate similarity variables. Convergence of the series solutions are obtained for velocity, temperature and concentration. The behavior of significant physical quantities on the velocity, temperature and concentration distributions are analyzed through plots. Graphical results of the skin friction coefficient, local Nusselt and Sherwood numbers are also plotted and examined.

Intermittent plasticity associated with the spatio-temporal dynamics of deformation bands during creep tests in an AlMg polycrystal

Many structural Al-based alloys, and AlMg alloys, in particular, exhibit an intermittent plasticity on the macroscopic scale also known as the Portevin-Le Chatelier (PLC) effect which is associated with repetitive stress drops related with the formation of the bands of localized plastic deformation in tests with a constant imposed strain rate. In the current work we present a comprehensive investigation of a discontinuous creep in commercial AlMg6 alloy used in the aerospace industry. This phenomenon manifests itself as strain bursts during creep tensile tests, where the creep curves contain macroscopic strain jumps in the magnitudes of several percent. The experimental investigation employs the measurements of the load and strain sensors synchronized with a high-speed video camera to capture the deformation band formation and propagation. Unexpectedly, an individual strain burst is found to generate a complex jerky load response which consists of a number of stress drops (similar to the PLC effect) due to inertia of the specimen – creep machine mechanical system. Each stress drop is associated with a fast evolution stage of a single deformation band which takes the shape of a widening neck in a flat specimen. During the widening of the band its “center of gravity” remains stationary. We have established that the main mechanism responsible for the development of the strain burst is the multiplication of the deformation bands, when the boundary of each band generates a secondary band and so on. As a result of the relay-race transfer of the deformation from band to band, a macrolocalized plastic deformation propagates along the specimen. Complementary statistical, spectral, fractal and dynamical analyses are performed on the stress-time series recorded during a single strain burst evolution. It is shown that when the initial specimen length increases the intermittent load response exhibits a tendency to the state of self-organized criticality. Furthermore, transitions between distinct dynamical PLC-like regimes of type A and B during strain burst are explored. We found that the time-periodic stress oscillations in form of a limit cycle can be spontaneously generated in short-time range during dynamical regime of type A. Nonlinear aspects of crystal plasticity conformably to discontinuous creep are discussed.

Black holes and Abelian symmetry breaking

Black hole configurations offer insights on the nonlinear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector–tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector–tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarisation, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.

Sub-nm emittance lattice design for CANDLE storage ring

The most effective way to increase the brilliance of synchrotron light sources is the reduction of beam emittance. Following the recent developments in low emittance lattice design, a new sub-nm emittance lattice based on implementation of multi-band achromat concept and application of longitudinal gradient bending magnets was developed for CANDLE storage ring. The paper presents the main design considerations, linear and non-linear beam dynamics aspects of the new lattice proposed.

Control of Continuous Stirred Tank Reactor using Neural Networks

Background/Objectives: This paper presents the design of neuro controller NARMA-L2 for composition control in an isothermal Continuous Stirred Tank Reactor (CSTR) by manipulating the input feed composition. Methods/Statistical Analysis: The NARMA-L2 controller design is implemented in two stages in which the first stage is system identification to model the process and the second stage is designing the process controller. For controlling the product composition in the CSTR, the neuro controller NARMA-L2 is implemented in MATLAB Simulink environment. Findings: The simulation results show the superiority of the NARMA-L2 in accurately tracking the composition set-point changes in the CSTR and control the system better as compared to that of the conventional PID. The neuro controller NARMA-L2 can handle non-linear aspects of the CSTR by transforming its non-linear dynamic into an implicit algebraic model which can control the trajectory of the CSTR efficiently. Application/Improvements: The advantage of using the neuro controller NARMA-L2 is that it requires the minimal online computation compared to other neural network architecture for control such as model reference control and model predictive control.