Breakup locations: Intertwining effects of nuclear structure and reaction dynamics
NASA Astrophysics Data System (ADS)
Dasgupta, M.; Simpson, E. C.; Luong, D. H.; Kalkal, Sunil; Cook, K. J.; Carter, I. P.; Hinde, D. J.; Williams, E.
2016-05-01
Studies at the Australian National University aim to distinguish breakup of the projectile like-nucleus that occurs when approaching the target from that when receding from the target. Helped by breakup simulations, observables have been found that are sensitive to the breakup location, and thus to the mean-lives of unbound states; sensitivity to even sub-zeptosecond lifetime is found. These results provide insights to understand the reaction dynamics of weakly bound nuclei at near barrier energies.
Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
NASA Astrophysics Data System (ADS)
Steinhaus, Sebastian
2015-09-01
The universal coupling of matter and gravity is one of the most important features of general relativity. In quantum gravity, in particular spin foams, matter couplings have been defined in the past, yet the mutual dynamics, in particular if matter and gravity are strongly coupled, are hardly explored, which is related to the definition of both matter and gravitational degrees of freedom on the discretization. However, extracting these mutual dynamics is crucial in testing the viability of the spin foam approach and also establishing connections to other discrete approaches such as lattice gauge theories. Therefore, we introduce a simple two-dimensional toy model for Yang-Mills coupled to spin foams, namely an Ising model coupled to so-called intertwiner models defined for SU (2 )k. The two systems are coupled by choosing the Ising coupling constant to depend on spin labels of the background, as these are interpreted as the edge lengths of the discretization. We coarse grain this toy model via tensor network renormalization and uncover an interesting dynamics: the Ising phase transition temperature turns out to be sensitive to the background configurations and conversely, the Ising model can induce phase transitions in the background. Moreover, we observe a strong coupling of both systems if close to both phase transitions.
Friction and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
2016-07-01
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
Friction and nonlinear dynamics.
Manini, N; Braun, O M; Tosatti, E; Guerra, R; Vanossi, A
2016-07-27
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction. PMID:27249652
Nonlinear Dynamics in Cardiology
Krogh-Madsen, Trine; Christini, David J.
2013-01-01
The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counter-intuitively, result from a gradual change in a system parameter –this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work have suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity. PMID:22524390
Intramolecular and nonlinear dynamics
Davis, M.J.
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Chaos without nonlinear dynamics.
Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N
2006-07-14
A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system. PMID:16907450
Section 4: Requirements Intertwining
NASA Astrophysics Data System (ADS)
Loucopoulos, Pericles
Business analysts are being asked to develop increasingly complex and varied business systems that need to cater to the changing and dynamic market conditions of the new economy. This is particularly acute in today’s turbulent business environment where powerful forces such as deregulation, globalisation, mergers, advances in information and telecommunications technologies, and increasing education of people provide opportunities for organising work in ways that have never before been possible. Enterprises attempt to create wealth either by getting better at improving their products and services or by harnessing creativity and human-centred management to create innovative solutions. In these business settings, requirements become critical in bridging system solutions to organisational and societal problems. They intertwine organisational, social, cognitive, and implementation considerations and they can provide unique insights to change in systems and their business context. Such design situations often involve multiple stakeholders from different participating organisations, subcontractors, divisions, etc., who may have a diversity of expertise, come from different organisational cultures and often have competing goals. The success or failure of many projects depends, to a large extent, on understanding the contextual setting of requirements and their interaction amongst a diverse population of stakeholders.
Dynamics of Cochlear Nonlinearity.
Cooper, Nigel P; van der Heijden, Marcel
2016-01-01
Dynamic aspects of cochlear mechanical compression were studied by recording basilar membrane (BM) vibrations evoked by tone pairs ("beat stimuli") in the 11-19 kHz region of the gerbil cochlea. The frequencies of the stimulus components were varied to produce a range of "beat rates" at or near the characteristic frequency (CF) of the BM site under study, and the amplitudes of the components were balanced to produce near perfect periodic cancellations, visible as sharp notches in the envelope of the BM response. We found a compressive relation between instantaneous stimulus intensity and BM response magnitude that was strongest at low beat rates (e.g., 10-100 Hz). At higher beat rates, the amount of compression reduced progressively (i.e. the responses became linearized), and the rising and falling flanks of the response envelope showed increasing amounts of hysteresis; the rising flank becoming steeper than the falling flank. This hysteresis indicates that cochlear mechanical compression is not instantaneous, and is suggestive of a gain control mechanism having finite attack and release times. In gain control terms, the linearization that occurs at higher beat rates occurs because the instantaneous gain becomes smoothened, or low-pass filtered, with respect to the magnitude fluctuations in the stimulus. In terms of peripheral processing, the linearization corresponds to an enhanced coding, or decompression, of rapid amplitude modulations. These findings are relevant both to those who wish to understand the underlying mechanisms and those who need a realistic model of nonlinear processing by the auditory periphery. PMID:27080667
Nonlinear problems in flight dynamics
NASA Technical Reports Server (NTRS)
Chapman, G. T.; Tobak, M.
1984-01-01
A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.
Solution of second order supersymmetrical intertwining relations in Minkowski plane
NASA Astrophysics Data System (ADS)
Ioffe, M. V.; Kolevatova, E. V.; Nishnianidze, D. N.
2016-08-01
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Nonlinear dynamics and cryptosystem
Liu, Y.
1996-06-01
In this paper, a new cryptosystem using dynamical systems is introduced which features storing information in stable configurations of dynamical systems but representing the information in arbitrary configurations of dynamical systems. The message {ital p} in a plaintext can be considered as a stable configuration of a dynamical system. The encrypted string of {ital p} in a ciphertext is an arbitrary configuration which will lead the dynamical system to the attractor defined by the original string {ital p}. The encryption procedure, {ital C}={ital E}({ital p}), treats a string in a plaintext as an attractor of a finite dynamical system, and will generate a configuration {ital C} randomly, as long as the configuration leads to a correct attractor. The decryption procedure regenerates attractors of a dynamical system, {ital p}={ital D}({ital C})={ital D}({ital E}({ital p})), from the configurations contained in the ciphertext. Three families of cryptosystems (simple, compound, and stochastic cryptosystems) are presented. {copyright} {ital 1996 American Institute of Physics.}
Nonlinear analysis of pupillary dynamics.
Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo
2016-02-01
Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (p<0.001). Our results suggest that (a) pupil size at constant light condition is characterized by nonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. PMID:26351899
Nonlinear dynamical systems analyzer
NASA Astrophysics Data System (ADS)
Coffey, Adrian S.; Johnson, Martin; Jones, Robin
1994-10-01
Computationally intensive algorithms are an ever more common requirement of modern signal processing. Following the work of Gentleman and Kung, McWhirter, Shepherd and Proudler suggested that certain matrix-orientated algorithms can be mapped onto systolic array architectures for adaptive linear signal processing. This has been extended by Broomhead et al. to the calculation of nonlinear predictive models and applied by Jones et al. to target identification and recognition. We shall show that predictive models are extremely sharp discriminators. Our chosen problem, if implemented as a systolic array, would require 3403 processors which would result in high through-put rate at excessive cost. We are developing an efficient sub-optimally implemented systolic array; one processor servicing more than one systolic node. We describe a prototype Heuristic Processor which computes a multi- dimensional, nonlinear, predictive model. It consists of a Radial Basis Function Network and a least squares optimizer using QR decomposition. The optimized solution of a set of simultaneous equations in 81 unknowns is calculated in 150 (mu) S. The QR section emulates a triangular systolic array by the novel use of an array of 40 mature silicon DSP chips costing under DOL100 each. The DSP chips operate in synchronism at a 50 MHz clock rate passing data to each other through multi-port memories on a dead-letter box principle; there are no memory access conflicts and only two-port and three-port memories are required. The processor provides 1-GFlop of computing power per cubic-foot of electronics for a component cost of approximately DOL15,000.
Nonlinear dynamics and plasma transport
Antonsen, T.M. Jr.; Drake, J.F.; Finn, J.M.; Guzdar, P.N.; Hassam, A.B.; Sagdeev, R.Z.
1992-01-01
In this paper we summarize the progress made over the last year in three different areas of research: (a) shear flow generation and reduced transport in fluids and plasma, (b) nonlinear dynamics and visualization of 3D flows, and (c) application of wavelet analysis to the study of fractal dimensions in experimental and numerical data.
Edge detection by nonlinear dynamics
Wong, Yiu-fai
1994-07-01
We demonstrate how the formulation of a nonlinear scale-space filter can be used for edge detection and junction analysis. By casting edge-preserving filtering in terms of maximizing information content subject to an average cost function, the computed cost at each pixel location becomes a local measure of edgeness. This computation depends on a single scale parameter and the given image data. Unlike previous approaches which require careful tuning of the filter kernels for various types of edges, our scheme is general enough to be able to handle different edges, such as lines, step-edges, corners and junctions. Anisotropy in the data is handled automatically by the nonlinear dynamics.
Nonlinear dynamics and plasma transport
Antonsen, T.M. Jr.; Drake, J.F.; Finn, J.M.; Guzdar, P.N.; Hassam, A.B.; Sageev, R.Z.
1993-01-01
This progress report details work done on a program in nonlinear dynamical aspects of plasma turbulence and transport funded by DOE since 1989. This program has been in cooperation with laboratories in theUSSR [now Russia and the Confederation of Independent States (CIS)]. The purpose of this program has been: To promote the utilization of recent pathbreaking developments in nonlinear science in plasma turbulence and transport. To promote cooperative scientific investigations between the US and CIS in the related areas of nonlinear science and plasma turbulence and transport. In the work reported in our progress report, we have studied simple models which are motivated by observation on actual fusion devices. The models focus on the important physical processes without incorporating the complexity of the geometry of real devices. This allows for a deeper analysis and understanding of the system both analytically and numerically.
Noise in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2009-08-01
List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.
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.
Nonlinear Dynamics in Viscoelastic Jets
NASA Astrophysics Data System (ADS)
Majmudar, Trushant; Varagnat, Matthieu; McKinley, Gareth
2009-03-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain poorly understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in considerable detail, both theoretically and experimentally. Instability in viscous jets leads to regular periodic coiling of the jet, which exhibits a non-trivial frequency dependence with the height of the fall. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities. We observe complex nonlinear spatio-temporal dynamics of the jet, and uncover a transition from periodic to quasi-periodic to a multi-frequency, broad-spectrum dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo'' or the Kaye effect. We examine different dynamical regimes in terms of scaling variables, which depend on the geometry (dimensionless height), kinematics (dimensionless flow rate), and the fluid properties (elasto-gravity number) and present a regime map of the dynamics of the jet in terms of these dimensionless variables.
Nonlinear Dynamics in Viscoelastic Jets
NASA Astrophysics Data System (ADS)
Majmudar, Trushant; Varagnat, Matthieu; McKinley, Gareth
2008-11-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain poorly understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in considerable detail, both theoretically and experimentally. Instability in viscous jets leads to regular periodic coiling of the jet, which exhibits a non-trivial frequency dependence with the height of the fall. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities. We observe complex nonlinear spatio-temporal dynamics of the jet, and uncover a transition from periodic to quasi-periodic to a multi-frequency, broad-spectrum dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo'' or the Kaye effect. We examine different dynamical regimes in terms of scaling variables, which depend on the geometry (dimensionless height), kinematics (dimensionless flow rate), and the fluid properties (elasto-gravity number) and present a regime map of the dynamics of the jet in terms of these dimensionless variables.
Nonlinear dynamics in expanding plasmas
NASA Astrophysics Data System (ADS)
Sack, Ch.; Schamel, H.
1985-07-01
The expansion of a plasma occupying initially a half-space is investigated numerically and, by means of a novel description of the ion fluid, also analytically. A simple wave structure is found in the collisionless approximation. Stabilized by dissipation, the associated ion bunching gives rise to a fast ion component, similar to the ion blow-off in laser fusion. Three nonstationary regimes of this strongest nonlinear and inhomogeneous dynamical system are distinguished and discussed. For large t the ion front propagates with a speed proportional to the square root of t-t(1), where t(1) is a reference time. A simple picture emerges, explaining the diverse experimental data.
Nonlinear Analysis Of Rotor Dynamics
NASA Technical Reports Server (NTRS)
Day, William B.; Zalik, Richard
1988-01-01
Study explores analytical consequences of nonlinear Jeffcott equations of rotor dynamics. Section 1: Summary of previous studies. Section 2: Jeffcott Equations. Section 3: Proves two theorems that provide inequalities on coefficients of differential equations and magnitude of forcing function in absence of side force. Section 4: Numerical investigation of multiple-forcing-function problem by introducing both side force and mass imbalance. Section 5: Examples of numberical solutions of complex generalized Jeffcott equation with two forcing functions of different frequencies f1 and f2. Section 6: Boundedness and stability of solutions.Section 7: Concludes report reviewing analytical results and significance.
Nonlinear dynamics of cardiovascular ageing
Shiogai, Y.; Stefanovska, A.; McClintock, P.V.E.
2010-01-01
The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time–frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in
Nonlinear dynamics and plasma transport
Liu, C.S.; Sagdeev, R.; Antonsen, T.; Drake, J.; Hassma, A.; Guzdar, P.N.
1995-12-01
This progress report reports work done on a program in nonlinear dynamical aspects of plasma turbulence and transport funded by DOE from 1992-1995. The purpose of this program has been to promote the utilization of recent pathbreaking developments in nonlinear science in plasma turbulence and transport and to fully utilize the scientific expertise of Russian fusion and plasma community in collaboration with our group to address outstanding fusion theory problems. In the work reported in our progress report, we have studied simple models which are motivated by observation on actual fusion devices. The models focus on the important physical processes without incorporating the complexity of the geometry of real devices. We have also studied linear stability problems which incorporated important physics issues related to geometry involving closed field lines and open field lines. This allows for a deeper analysis and understanding of the system both analytically and numerically. The strong collaboration between the Russian visitors and the US participants has led to a fruitful and strong research program that taps the complementary analytic and numerical capabilities of the two groups. Over the years several distinguished Russian visitors have interacted with various members of the group and set up collaborative work which forms a significant part of proposed research. Dr. Galeev, Director of the Space Research Institute of Moscow and Dr. Novakovskii from the Kurchatov Institute are two such ongoing collaborations. 21 refs.
Nonlinear Opinion Dynamics on Networks
NASA Astrophysics Data System (ADS)
Gabbay, Michael; Das, Arindam
2013-03-01
A model which treats group decision making as nonlinear opinion dynamics occurring over a network is presented. The model makes predictions regarding the interaction of network structure and initial disagreement level upon decision outcomes and consensus formation. The model displays bifurcations at high disagreement levels which lead to behaviors that are qualitatively distinct from those at low disagreement. For example, at high disagreement, the model exhibits asymmetric, majority rule outcomes that arise even when the system is symmetric with respect to the distribution of initial opinions and network structure. Analytical approximations for the bifurcation boundaries agree well with numerically-determined boundaries. An ongoing experimental effort involving the use of online discussion groups to test the model predictions is briefly described. We acknowledge the support of the Defense Threat Reduction Agency and the Office of Naval Research under grant HDTRA1-10-1-0075
Nonlinear Collective Dynamics in Atomic Nuclei
NASA Astrophysics Data System (ADS)
Paar, N.; Vretenar, D.; Ring, P.; Lalazissis, G. A.
2001-11-01
Nonlinear dynamics of giant monopole resonances is investigated in the time-dependent relativistic mean-field model. The time-series analysis of dynamical variables that characterize nucleon distributions indicate regular motion for the isoscalar mode, and more complex dynamics for the isovector oscillations. Information entropy functionals disclose the underlying nonlinear collective dynamics in quantum systems that have spatial as well as temporal structure.
Nonlinear Dynamical Analysis of Fibrillation
NASA Astrophysics Data System (ADS)
Kerin, John A.; Sporrer, Justin M.; Egolf, David A.
2013-03-01
The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.
On Lambda and Time Operators: the Inverse Intertwining Problem Revisited
NASA Astrophysics Data System (ADS)
Gómez-Cubillo, F.; Suchanecki, Z.; Villullas, S.
2011-07-01
An exact theory of irreversibility was proposed by Misra, Prigogine and Courbage, based on non-unitary similarity transformations Λ that intertwine reversible dynamics and irreversible ones. This would advocate the idea that irreversible behavior would originate at the microscopic level. Reversible evolution with an internal time operator have the intertwining property. Recently the inverse intertwining problem has been answered in the negative, that is, not every unitary evolution allowing such Λ-transformation has an internal time. This work contributes new results in this direction.
Nonlinear Chemical Dynamics and Synchronization
NASA Astrophysics Data System (ADS)
Li, Ning
Alan Turing's work on morphogenesis, more than half a century ago, continues to motivate and inspire theoretical and experimental biologists even today. That said, there are very few experimental systems for which Turing's theory is applicable. In this thesis we present an experimental reaction-diffusion system ideally suited for testing Turing's ideas in synthetic "cells" consisting of microfluidically produced surfactant-stabilized emulsions in which droplets containing the Belousov-Zhabotinsky (BZ) oscillatory chemical reactants are dispersed in oil. The BZ reaction has become the prototype of nonlinear dynamics in chemistry and a preferred system for exploring the behavior of coupled nonlinear oscillators. Our system consists of a surfactant stabilized monodisperse emulsion of drops of aqueous BZ solution dispersed in a continuous phase of oil. In contrast to biology, here the chemistry is understood, rate constants are measured and interdrop coupling is purely diffusive. We explore a large set of parameters through control of rate constants, drop size, spacing, and spatial arrangement of the drops in lines and rings in one-dimension (1D) and hexagonal arrays in two-dimensions (2D). The Turing model is regarded as a metaphor for morphogenesis in biology but not for prediction. Here, we develop a quantitative and falsifiable reaction-diffusion model that we experimentally test with synthetic cells. We quantitatively establish the extent to which the Turing model in 1D describes both stationary pattern formation and temporal synchronization of chemical oscillators via reaction-diffusion and in 2D demonstrate that chemical morphogenesis drives physical differentiation in synthetic cells.
Nonlinear dynamics and numerical uncertainties in CFD
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.
1996-01-01
The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.
Nonlinear dynamics of false bottoms
NASA Astrophysics Data System (ADS)
Nizovtseva, Irina; Alexandrov, Dmitri; Ryashko, Lev
2014-05-01
Nansen from his observations in the Beaufort Sea published in 1897 noted that heat transfer from the fresh water to the arctic salt water is the only source of ice accretion during the polar summer. This transfer mechanism, unusual at first sight, is responsible for the initiation and evolution of a false bottom ice, changing ice properties to a great extent and affecting various processes while interacting with the ocean and the atmosphere. A false bottom represents a thin layer of ice which forms in summer underneath the floe where fresh water lies between the salt water and the ice. Details of how this process occurs in nature are now emerging from different laboratory and field experiments. The false bottoms appearing at the interface between the fresh and salt water as a result of double-diffusive convection normally lie below surface and under-ice melt ponds. Such false bottoms represent the only significant source of ice growth in the Arctic during the spring-summer period. Their evolution influences the mass balance of the Arctic sea-ice cover recognized as an indicator of climate change. However, the quantity, aerial extent and other properties of false bottoms are difficult to measure because coring under the surface melt ponds leads to direct mixing of surface and under-ice water. This explains why their aerial extent and overall volume is still not known despite the fact that the upper limit of the ice coverage by the false bottom is approximately half of the ice surface. The growth of false bottoms also leads to other important consequences for different physical, chemical and biological processes associated with their dynamics. This study addressed to a broad community of readers is concerned with non-linear behavior of false bottoms including their stochastic dynamics due to possible fluctuations of the main process parameters in the ocean and the atmosphere.
Dynamics of large constrained nonlinear systems -- A taxonomy theory
Venkatasubramanian, V.; Schaettler, H.; Zaborszky, J.
1995-11-01
This paper provides an overview of the taxonomy theory which has been proposed as a fundamental platform for solving practical stability related problems in large constrained nonlinear systems such as the electric power system. The theory reveals a two-level intertwined cellular nature of the constrained system dynamics which serves as a unifying structure, a taxonomy, for analyzing nonlinear phenomena in large system models. These broadly divide into the state space aspects (related to dynamic stability issues among others) and the parameter space aspects (connected with bifurcation phenomena among others). In the state-space formulation, the boundary of the region of attraction for the operating point is shown (under certain Morse-Smale like assumptions) to be composed of stable manifolds of certain anchors and portions of the singularity surface. Such boundary characterization provides the foundation for rigorous Lyapunov theoretic transient stability methods. In the parameter space analysis, the feasibility region which is bounded by the feasibility boundary provides a safe operating region for guaranteeing local stability at the equilibrium under slow parametric variations. The feasibility boundary where the operating point undergoes loss of local stability is characterized in the form of three principal bifurcations including a new bifurcation called the singularity induced bifurcation. An overview of the recent results which prove that the two-level structure exists even in nonsmooth models that incorporate the effects of system hard limits is also included. Specifically hard limits induce a number of new bifurcations. This natural taxonomy of the system dynamics stands as the backbone for developing practical and rigorous computational techniques in detecting diverse instability mechanisms.
Earth solids and dynamic nonlinear elasticity
Johnson, P.A. |; Abeele, K.E.A. Van Den
1997-05-01
The authors` intention is to describe several manifestations of nonlinear behavior in rock. Nonlinear response may manifest itself in a variety of manners, including a nonlinear stress-strain relation, nonlinear attenuation, harmonic generation, resonant peak shift and slow dynamics, all of which are related. The authors have ample evidence that the responsible mechanism for nonlinear response [to first order] is the presence of compliant features and the influence of fluid. They define compliant features as those features that are the weakest in the rock, e.g., grain-to-grain contacts, low aspect ratio cracks, joints, etc. In addition, there may be other mechanisms responsible as yet unidentified. In the following, the authors emphasize the robust nature of observations by illustrating several experimental examples. They do not review the related theoretical framework. Finally, they do not present nonlinear parameters derived from these experiments as the purpose in this paper is to illustrate rather than quantify nonlinear response.
Dissipative nonlinear dynamics in holography
NASA Astrophysics Data System (ADS)
Basu, Pallab; Ghosh, Archisman
2014-02-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of O, the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems.
Nonlinear dynamical system approaches towards neural prosthesis
Torikai, Hiroyuki; Hashimoto, Sho
2011-04-19
An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.
Nonlinear dynamics of additive pulse modelocked lasers
Sucha, G.; Bolton, S.R.; Chemla, D.S.
1995-04-01
Nonlinear dynamics have been studied in a number of modelocked laser systems, primarily in actively modelocked systems. However, less attention has been paid to the dynamics of passively modelocked laser systems. With the recent revolutionary advances in femtosecond modelocked laser technology, the understanding of instabilities and dynamics in passively modelocked lasers is an important issue. Here, the authors present experimental and numerical studies of the dynamics of an additive-pulse modelocked (APM) color-center laser.
Singularity perturbed zero dynamics of nonlinear systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.
1992-01-01
Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.
Nonlinear dynamics of axially moving plates
NASA Astrophysics Data System (ADS)
Ghayesh, Mergen H.; Amabili, Marco; Païdoussis, Michael P.
2013-01-01
The nonlinear dynamics for forced motions of an axially moving plate is numerically investigated using Von Kármán plate theory and retaining in-plane displacements and inertia. The equations of motion are obtained via an energy method based on Lagrange equations. This yields a set of second-order nonlinear ordinary differential equations with coupled terms. The equations are transformed into a set of first-order nonlinear ordinary differential equations and are solved via the pseudo-arclength continuation technique. The near-resonance nonlinear dynamics is examined via plotting the frequency-response curves of the system. Results are shown through frequency-response curves, time histories, and phase-plane diagrams. The effect of system parameters, such as the axial speed and the pretension, on the resonant responses is also highlighted.
Modeling the dynamics of nonlinear inductor circuits
NASA Astrophysics Data System (ADS)
Deane, Jonathan H. B.
1994-09-01
The Jiles-Atherton (J-A) model is applied to the problem of describing the dynamics of a nonlinear circuit driven by a square wave voltage source and comprising a linear resistor and capacitor in series with a nonlinear inductor, whose core displays saturation and hysteresis. The presence of hysteresis is shown to increase the order of the circuit by one. Period-multiplication and chaos are observed and excellent agreement is obtained between experiment and simulation.
Galerkin Method for Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
Noack, Bernd R.; Schlegel, Michael; Morzynski, Marek; Tadmor, Gilead
A Galerkin method is presented for control-oriented reduced-order models (ROM). This method generalizes linear approaches elaborated by M. Morzyński et al. for the nonlinear Navier-Stokes equation. These ROM are used as plants for control design in the chapters by G. Tadmor et al., S. Siegel, and R. King in this volume. Focus is placed on empirical ROM which compress flow data in the proper orthogonal decomposition (POD). The chapter shall provide a complete description for construction of straight-forward ROM as well as the physical understanding and teste
Nonlinear dynamics of cell orientation
NASA Astrophysics Data System (ADS)
Safran, S. A.; de, Rumi
2009-12-01
The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, τc , for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, τc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.
Impulsive synchronization of networked nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Jiang, Haibo; Bi, Qinsheng
2010-06-01
In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.
Nonlinear Dynamic Models in Advanced Life Support
NASA Technical Reports Server (NTRS)
Jones, Harry
2002-01-01
To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.
Battery electrochemical nonlinear/dynamic SPICE model
Glass, M.C.
1996-12-31
An Integrated Battery Model has been produced which accurately represents DC nonlinear battery behavior together with transient dynamics. The NiH{sub 2} battery model begins with a given continuous-function electrochemical math model. The math model for the battery consists of the sum of two electrochemical process DC currents, which are a function of the battery terminal voltage. This paper describes procedures for realizing a voltage-source SPICE model which implements the electrochemical equations using behavioral sources. The model merges the essentially DC non-linear behavior of the electrochemical model, together with the empirical AC dynamic terminal impedance from measured data. Thus the model integrates the short-term linear impedance behavior, with the long-term nonlinear DC resistance behavior. The long-duration non-Faradaic capacitive behavior of the battery is represented by a time constant. Outputs of the model include battery voltage/current, state-of-charge, and charge-current efficiency.
Nonlinear Dynamics and the Growth of Literature.
ERIC Educational Resources Information Center
Tabah, Albert N.
1992-01-01
Discussion of nonlinear dynamic mechanisms focuses on whether information production and dissemination can be described by similar mechanisms. The exponential versus linear growth of literature is discussed, the time factor is considered, an example using literature from the field of superconductivity is given, and implications for information…
Estimating the uncertainty in underresolved nonlinear dynamics
Chorin, Alelxandre; Hald, Ole
2013-06-12
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise term that describes the uncertainty turns out to be neither Markovian nor Gaussian. It is argued that this is the general situation.
Nonlinear astrophysical fluid dynamics: the video.
NASA Astrophysics Data System (ADS)
Norman, M. L.
A videotape has been assembled containing animations shown by speakers at the Nonlinear Astrophysical Fluid Dynamics Conference. This videotape forms a useful supplement to the conference proceedings. The videotape is available from the National Center for Supercomputing Applications for the cost of materials (6 for 1/2″tapes; 12.50 for 3/4″tapes) and shipping.
Nonlinear dynamics of Aeolian sand ripples.
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. PMID:11969814
Principal nonlinear dynamical modes of climate variability
NASA Astrophysics Data System (ADS)
Mukhin, Dmitry; Gavrilov, Andrey; Feigin, Alexander; Loskutov, Evgeny; Kurths, Juergen
2015-10-01
We suggest a new nonlinear expansion of space-distributed observational time series. The expansion allows constructing principal nonlinear manifolds holding essential part of observed variability. It yields low-dimensional hidden time series interpreted as internal modes driving observed multivariate dynamics as well as their mapping to a geographic grid. Bayesian optimality is used for selecting relevant structure of nonlinear transformation, including both the number of principal modes and degree of nonlinearity. Furthermore, the optimal characteristic time scale of the reconstructed modes is also found. The technique is applied to monthly sea surface temperature (SST) time series having a duration of 33 years and covering the globe. Three dominant nonlinear modes were extracted from the time series: the first efficiently separates the annual cycle, the second is responsible for ENSO variability, and combinations of the second and the third modes explain substantial parts of Pacific and Atlantic dynamics. A relation of the obtained modes to decadal natural climate variability including current hiatus in global warming is exhibited and discussed.
Nonlinear Dynamics on Interconnected Networks
NASA Astrophysics Data System (ADS)
Arenas, Alex; De Domenico, Manlio
2016-06-01
Networks of dynamical interacting units can represent many complex systems, from the human brain to transportation systems and societies. The study of these complex networks, when accounting for different types of interactions has become a subject of interest in the last few years, especially because its representational power in the description of users' interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.) [1], or in representing different transportation modes in urban networks [2,3]. The general name coined for these networks is multilayer networks, where each layer accounts for a type of interaction (see Fig. 1).
Nonlinear adhesion dynamics of confined lipid membranes
NASA Astrophysics Data System (ADS)
To, Tung; Le Goff, Thomas; Pierre-Louis, Olivier
Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems. Supported by the grand ANR Biolub.
Algorithms and software for nonlinear structural dynamics
NASA Technical Reports Server (NTRS)
Belytschko, Ted; Gilbertsen, Noreen D.; Neal, Mark O.
1989-01-01
The objective of this research is to develop efficient methods for explicit time integration in nonlinear structural dynamics for computers which utilize both concurrency and vectorization. As a framework for these studies, the program WHAMS, which is described in Explicit Algorithms for the Nonlinear Dynamics of Shells (T. Belytschko, J. I. Lin, and C.-S. Tsay, Computer Methods in Applied Mechanics and Engineering, Vol. 42, 1984, pp 225 to 251), is used. There are two factors which make the development of efficient concurrent explicit time integration programs a challenge in a structural dynamics program: (1) the need for a variety of element types, which complicates the scheduling-allocation problem; and (2) the need for different time steps in different parts of the mesh, which is here called mixed delta t integration, so that a few stiff elements do not reduce the time steps throughout the mesh.
Nonlinear dynamics of a double bilipid membrane.
Sample, C; Golovin, A A
2007-09-01
The nonlinear dynamics of a biological double membrane that consists of two coupled lipid bilayers, typical of some intracellular organelles such as mitochondria or nuclei, is studied. A phenomenological free-energy functional is formulated in which the curvatures of the two parts of the double membrane and the distance between them are coupled to the lipid chemical composition. The derived nonlinear evolution equations for the double-membrane dynamics are studied analytically and numerically. A linear stability analysis is performed, and the domains of parameters are found in which the double membrane is stable. For the parameter values corresponding to an unstable membrane, numerical simulations are performed that reveal various types of complex dynamics, including the formation of stationary, spatially periodic patterns. PMID:17930289
Nonlinear dynamics of a double bilipid membrane
NASA Astrophysics Data System (ADS)
Sample, C.; Golovin, A. A.
2007-09-01
The nonlinear dynamics of a biological double membrane that consists of two coupled lipid bilayers, typical of some intracellular organelles such as mitochondria or nuclei, is studied. A phenomenological free-energy functional is formulated in which the curvatures of the two parts of the double membrane and the distance between them are coupled to the lipid chemical composition. The derived nonlinear evolution equations for the double-membrane dynamics are studied analytically and numerically. A linear stability analysis is performed, and the domains of parameters are found in which the double membrane is stable. For the parameter values corresponding to an unstable membrane, numerical simulations are performed that reveal various types of complex dynamics, including the formation of stationary, spatially periodic patterns.
Nonlinear dynamic analysis for elastic robotic arms
NASA Astrophysics Data System (ADS)
Korayem, M. H.; Rahimi, H. N.
2011-06-01
The aim of the paper is to analyze the nonlinear dynamics of robotic arms with elastic links and joints. The main contribution of the paper is the comparative assessment of assumed modes and finite element methods as more convenient approaches for computing the nonlinear dynamic of robotic systems. Numerical simulations comprising both methods are carried out and results are discussed. Hence, advantages and disadvantages of each method are illustrated. Then, adding the joint flexibility to the system is dealt with and the obtained model is demonstrated. Finally, a brief description of the optimal motion generation is presented and the simulation is carried out to investigate the role of robot dynamic modeling in the control of robots.
Dynamic functional tuning of nonlinear cortical networks
NASA Astrophysics Data System (ADS)
Stetter, Martin
2006-03-01
The mammalian neocortex is a highly complex and nonlinear dynamic system. One of its most prominent features is an omnipresent spontaneous neuronal activity. Here the possible functional role of this global background for cognitive flexibility is studied in a prototypic mean-field model area. It is demonstrated that the level of global background current efficiently controls the stimulus-response threshold and the stability and properties of short-term memory states. Moreover, it can dynamically gate arbitrary cortical subnetworks, when applied to parts of the area as a weak bias signal. These results suggest a central functional role of the level of background activation: the dynamic functional tuning of neocortical circuits.
Characterizing Nonlinear Heartbeat Dynamics within a Point Process Framework
Chen, Z; Brown, EN; Barbieri, R
2009-01-01
Heartbeat intervals are known to have nonlinear and non-stationary dynamics. In this paper, we propose a nonlinear Volterra-Wiener expansion modeling of human heartbeat dynamics within a point process framework. Inclusion of second-order nonlinearity allows us to estimate dynamic bispectrum. The proposed probabilistic model was examined with two recorded heartbeat interval data sets. Preliminary results show that our model is beneficial to characterize the inherent nonlinearity of the heartbeat dynamics. PMID:19163282
Nonlinear dynamics in tunable graphene nanoelectromechanical systems
NASA Astrophysics Data System (ADS)
Guan, Fen; Kumaravadivel, Piranavan; Averin, Dmitri; Du, Xu
2015-03-01
We report the fabrication and characterization of graphene nanoelectromechanical resonators (GNEMR) on flexible substrates. The intrinsic stain in graphene is tuned by bending the substrate, during which a transition from hardening to softening resonance behavior and a minimum resonance frequency are observed. To explain these observations, a resonator model taking into account the intrinsic strain and electrostatic force is developed. Including higher-order nonlinear terms, a minimum frequency is obtained analytically from the model and matches with experimental data. Results from numerical simulation demonstrate also the transition in the nonlinear behavior. Additionally, the model-based fittings determine the intrinsic strain and mass of graphene samples accurately. Our devices allow thorough exploration of the nonlinear dynamics in GNEMR and may help further study of the intrinsic electrical properties of the materials under strain.
Bubble nonlinear dynamics and stimulated scattering process
NASA Astrophysics Data System (ADS)
Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu
2016-02-01
A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).
Application of dynamical systems theory to nonlinear aircraft dynamics
NASA Technical Reports Server (NTRS)
Culick, Fred E. C.; Jahnke, Craig C.
1988-01-01
Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.
Ultrahigh energy neutrinos and nonlinear QCD dynamics
Machado, Magno V.T.
2004-09-01
The ultrahigh energy neutrino-nucleon cross sections are computed taking into account different phenomenological implementations of the nonlinear QCD dynamics. Based on the color dipole framework, the results for the saturation model supplemented by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution as well as for the Balitskii-Fadin-Kuraev-Lipatov (BFKL) formalism in the geometric scaling regime are presented. They are contrasted with recent calculations using next-to-leading order DGLAP and unified BFKL-DGLAP formalisms.
Nonlinear dynamics, chaos and complex cardiac arrhythmias
NASA Technical Reports Server (NTRS)
Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.
1987-01-01
Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.
Predictable nonlinear dynamics: Advances and limitations
Anosov, L.A.; Butkovskii, O.Y.; Kravtsov, Y.A.; Surovyatkina, E.D.
1996-06-01
Methods for reconstruction chaotic dynamical system structure directly from experimental time series are described. Effectiveness of general methods is illustrated with the results of numerical simulation. It is of common interest that from the single time series it is possible to reconstruct a set of interconnected variables. Predictive power of dynamical models, provided by the nonlinear dynamics inverse problem solution, is limited firstly by the noise level in the system under study and is characterized by the horizon of predictability. New physical results are presented, concerning nonstationary and bifurcation nonlinear systems: (1) algorithms for revealing of nonstationarity in random-like chaotic time-series are suggested based on discriminant analysis with nonlinear discriminant function; (2) an opportunity is established to predict the final state in bifurcation system with quickly varying control parameters; (3) hysteresis is founded out in bifurcation system with quickly varying parameters; (4) delayed correlation {l_angle}noise-prediction error{r_angle} in chaotic systems is revealed. {copyright} {ital 1996 American Institute of Physics.}
Linear pattern dynamics in nonlinear threshold systems
Rundle, John B.; Klein, W.; Tiampo, Kristy; Gross, Susanna
2000-03-01
Complex nonlinear threshold systems frequently show space-time behavior that is difficult to interpret. We describe a technique based upon a Karhunen-Loeve expansion that allows dynamical patterns to be understood as eigenstates of suitably constructed correlation operators. The evolution of space-time patterns can then be viewed in terms of a ''pattern dynamics'' that can be obtained directly from observable data. As an example, we apply our methods to a particular threshold system to forecast the evolution of patterns of observed activity. Finally, we perform statistical tests to measure the quality of the forecasts. (c) 2000 The American Physical Society.
Polarization dynamics in nonlinear anisotropic fibers
Komarov, Andrey; Komarov, Konstantin; Meshcheriakov, Dmitry; Amrani, Foued; Sanchez, Francois
2010-07-15
We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincare sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincare sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi's functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered.
Nonlinear and Stochastic Dynamics in the Heart
Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.
2014-01-01
In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872
Exploring the nonlinear dynamics of a physiologically viable model neuron
Lindner, J.F.; Ditto, W.L.
1996-06-01
We describe efforts underway to explore the nonlinear dynamics of the Pinsky-Rinzel model neuron. Via computer simulations, we seek to discover nonlinear phenomena in this physiologically accurate model, thereby complementing ongoing and future experiments. Here we describe the model in detail and analyze it using tools of nonlinear dynamics to demonstrate nontrivial behaviors. {copyright} {ital 1996 American Institute of Physics.}
Nonlinear dynamics of neural delayed feedback
Longtin, A.
1990-01-01
Neural delayed feedback is a property shared by many circuits in the central and peripheral nervous systems. The evolution of the neural activity in these circuits depends on their present state as well as on their past states, due to finite propagation time of neural activity along the feedback loop. These systems are often seen to undergo a change from a quiescent state characterized by low level fluctuations to an oscillatory state. We discuss the problem of analyzing this transition using techniques from nonlinear dynamics and stochastic processes. Our main goal is to characterize the nonlinearities which enable autonomous oscillations to occur and to uncover the properties of the noise sources these circuits interact with. The concepts are illustrated on the human pupil light reflex (PLR) which has been studied both theoretically and experimentally using this approach. 5 refs., 3 figs.
The Nonlinear Dynamics of Pacemaker Dependency
NASA Astrophysics Data System (ADS)
Buechley, Leah
2003-08-01
A person is considered pacemaker dependent when most of his or her heartbeats are supplied by a pacemaker. The purpose of this study was to determine whether there are significant differences between the heart dynamics of pacemaker-dependent patients and those of normal patients. Nonlinear dynamics techniques and statistical methods were used to analyze the ECGs of normal patients and pacemaker-dependent patients. Standard embedding of the ECG data yielded inconclusive results, but embedding the beat intervals proved to be much more useful. Lyapunov exponent calculations, recurrence plot analyses, and standard statistical analyses of these data showed significant differences in heart behavior between the two groups of patients. In particular, the beat intervals appear to exhibit chaotic behavior for the normal patients and fixed-point dynamics for pacemaker-dependent patients.
Nonlinear dynamical triggering of slow slip
Johnson, Paul A; Knuth, Matthew W; Kaproth, Bryan M; Carpenter, Brett; Guyer, Robert A; Le Bas, Pierre - Yves; Daub, Eric G; Marone, Chris
2010-12-10
Among the most fascinating, recent discoveries in seismology have been the phenomena of triggered slip, including triggered earthquakes and triggered-tremor, as well as triggered slow, silent-slip during which no seismic energy is radiated. Because fault nucleation depths cannot be probed directly, the physical regimes in which these phenomena occur are poorly understood. Thus determining physical properties that control diverse types of triggered fault sliding and what frictional constitutive laws govern triggered faulting variability is challenging. We are characterizing the physical controls of triggered faulting with the goal of developing constitutive relations by conducting laboratory and numerical modeling experiments in sheared granular media at varying load conditions. In order to simulate granular fault zone gouge in the laboratory, glass beads are sheared in a double-direct configuration under constant normal stress, while subject to transient perturbation by acoustic waves. We find that triggered, slow, silent-slip occurs at very small confining loads ({approx}1-3 MPa) that are smaller than those where dynamic earthquake triggering takes place (4-7 MPa), and that triggered slow-slip is associated with bursts of LFE-like acoustic emission. Experimental evidence suggests that the nonlinear dynamical response of the gouge material induced by dynamic waves may be responsible for the triggered slip behavior: the slip-duration, stress-drop and along-strike slip displacement are proportional to the triggering wave amplitude. Further, we observe a shear-modulus decrease corresponding to dynamic-wave triggering relative to the shear modulus of stick-slips. Modulus decrease in response to dynamical wave amplitudes of roughly a microstrain and above is a hallmark of elastic nonlinear behavior. We believe that the dynamical waves increase the material non-affine elastic deformation during shearing, simultaneously leading to instability and slow-slip. The inferred
Hierarchical nonlinear dynamics of human attention.
Rabinovich, Mikhail I; Tristan, Irma; Varona, Pablo
2015-08-01
Attention is the process of focusing mental resources on a specific cognitive/behavioral task. Such brain dynamics involves different partially overlapping brain functional networks whose interconnections change in time according to the performance stage, and can be stimulus-driven or induced by an intrinsically generated goal. The corresponding activity can be described by different families of spatiotemporal discrete patterns or sequential dynamic modes. Since mental resources are finite, attention modalities compete with each other at all levels of the hierarchy, from perception to decision making and behavior. Cognitive activity is a dynamical process and attention possesses some universal dynamical characteristics. Thus, it is time to apply nonlinear dynamical theory for the description and prediction of hierarchical attentional tasks. Such theory has to include the analyses of attentional control stability, the time cost of attention switching, the finite capacity of informational resources in the brain, and the normal and pathological bifurcations of attention sequential dynamics. In this paper we have integrated today's knowledge, models and results in these directions. PMID:25869439
Beam stability & nonlinear dynamics. Formal report
Parsa, Z.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
Non-Linear Dynamics of Saturn's Rings
NASA Astrophysics Data System (ADS)
Esposito, L. W.
2015-10-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Results of driven N-body systems by Stuart Robbins: Even unforced rings show large variations; Forcing triggers aggregation; Some limit cycles and phase lags seen, but not always as predicted by predator-prey model. Summary of Halo Results: A predatorprey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw'. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon
Non-Linear Dynamics of Saturn's Rings
NASA Astrophysics Data System (ADS)
Esposito, Larry W.
2015-04-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible Results of driven N-body systems by Stuart Robbins: Even unforced rings show large variations; Forcing triggers aggregation; Some limit cycles and phase lags seen, but not always as predicted by predator-prey model. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw'. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon
Nonlinear dynamic macromodeling techniques for audio systems
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Quadratic boundedness of uncertain nonlinear dynamic systems
NASA Astrophysics Data System (ADS)
Brockman, Mark Lawrence
Physical systems are often perturbed by unknown external disturbances or contain important system parameters which are difficult to model exactly. However, engineers are expected to design systems which perform well even in the presence of uncertainties. For example, an airplane designer can never know the precise direction or magnitude of wind gusts, or the exact mass distribution inside the aircraft, but passengers expect to arrive on time after a smooth ride. This thesis will first present the concept of quadratic boundedness of an uncertain nonlinear dynamic system, and then develop analysis techniques and control design methods for systems containing unknown disturbances and parameters. For a class of nonlinear systems, conditions for quadratic boundedness are given, and the relationship between quadratic boundedness and quadratic stability is explored. An important consequence of quadratic boundedness is the ability to calculate an upper bound on the system gain of an uncertain nonlinear system. For nominally linear systems, necessary and sufficient conditions for quadratic boundedness are given. The innovative use of linear matrix inequalities in an iterative algorithm provides a means to analyze the quadratic boundedness properties of systems containing parameter uncertainties. The analysis results establish a framework for the development of design methods which integrate performance specifications into the control design process for all the types of systems considered. Numerous examples illustrate the major results of the thesis.
Indirect learning control for nonlinear dynamical systems
NASA Technical Reports Server (NTRS)
Ryu, Yeong Soon; Longman, Richard W.
1993-01-01
In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.
Nonlinear Dynamical Friction in a Gaseous Medium
NASA Astrophysics Data System (ADS)
Kim, Hyosun; Kim, Woong-Tae
2009-10-01
Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber Mp moving at velocity Vp through a uniform gaseous medium of adiabatic sound speed a ∞. We model the perturber as a Plummer potential with softening radius rs , and run various models with differing A=GM_p/(a_∞ ^2r_s) and M=V_p/a_∞ by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibrium. We find that the detached shock distance δ and the nonlinear drag force F depend solely on η = A/M^2-1) such that δ/rs = η and F/F_lin=(η/2)^{-0.45} for 100 > η>2, where F lin is the linear drag force of Ostriker. The reduction of F compared with F lin is caused by front-back symmetry in the nonlinear density wakes. In subsonic cases, the flows without involving a shock do not readily reach a steady state. Nevertheless, the subsonic density wake near a perturber is close to being hydrostatic, resulting in the drag force similar to the linear case. Our results suggest that dynamical friction of a very massive object as in a merger of black holes near a galaxy center will take considerably longer than the linear prediction.
Bubble and Drop Nonlinear Dynamics experiment
NASA Technical Reports Server (NTRS)
2003-01-01
The Bubble and Drop Nonlinear Dynamics (BDND) experiment was designed to improve understanding of how the shape and behavior of bubbles respond to ultrasound pressure. By understanding this behavior, it may be possible to counteract complications bubbles cause during materials processing on the ground. This 12-second sequence came from video downlinked from STS-94, July 5 1997, MET:3/19:15 (approximate). The BDND guest investigator was Gary Leal of the University of California, Santa Barbara. The experiment was part of the space research investigations conducted during the Microgravity Science Laboratory-1R mission (STS-94, July 1-17 1997). Advanced fluid dynamics experiments will be a part of investigations plarned for the International Space Station. (189KB JPEG, 1293 x 1460 pixels; downlinked video, higher quality not available) The MPG from which this composite was made is available at http://mix.msfc.nasa.gov/ABSTRACTS/MSFC-0300163.html.
Overview of magnetic nonlinear beam dynamics in the RHIC
Luo,Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, f.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, g.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.
2009-05-04
In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed.
Bubble and Drop Nonlinear Dynamics (BDND)
NASA Technical Reports Server (NTRS)
Trinh, E. H.; Leal, L. Gary; Thomas, D. A.; Crouch, R. K.
1998-01-01
Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.
Neuromechanical tuning of nonlinear postural control dynamics
NASA Astrophysics Data System (ADS)
Ting, Lena H.; van Antwerp, Keith W.; Scrivens, Jevin E.; McKay, J. Lucas; Welch, Torrence D. J.; Bingham, Jeffrey T.; DeWeerth, Stephen P.
2009-06-01
Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.
Non-Linear Dynamics of Saturn's Rings
NASA Astrophysics Data System (ADS)
Esposito, L. W.
2015-12-01
Non-linear processes can explain why Saturn's rings are so active and dynamic. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like 'straw' that can explain the halo structure and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; Surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km); We propose 'straw', as observed ny Cassini cameras. Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing. Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn's rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. This confirms the triple architecture of ring particles: a broad size distribution of particles; these aggregate into temporary rubble piles; coated by a regolith of dust. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from
Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings
Kadtke, J.B.; Bulsara, A.
1997-12-01
These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)
Nonlinear Dynamics of Atom-Molecule Conversion
NASA Astrophysics Data System (ADS)
Fu, Li-Bin; Liu, Jie
2014-03-01
The creation of ultracold molecules has opened up new possibilities for studies on molecular matter waves, strongly interacting superfluids, high-precision molecular spectroscopy and coherent molecular optics. In an atomic Bose-Einstein condensate (BEC) and a degenerate Fermi-Fermi or Fermi-Bose mixture, magnetic Feshbach resonance or optical photoassociation (PA) technique has been used to create not only diatomic molecules but also more complex molecules. In this chapter, we focus on many issues of nonlinear dynamics of atom-molecule systems. In Sec. 1, on the basis of the two-channelmean-field approach, we study the manybody effects on the Landau-Zener(LZ) picture of two-body molecular production through dramatically distorting the energy levels near the Feshbach resonance. In Sec. 2, we investigate the Feshbach resonance with modulation of an oscillating magnetic field. In Sec. 3, we include the nonlinear interparticle collisions and focus on the linear instability induced by the collisions and the adiabatic fidelity of the atom-trimer dark state in a stimulated Raman adiabatic passage (STIRAP). In Sec. 4, we theoretically investigate conversion problem from atom to N-body polyatomic molecule in an ultracold bosonic system by implementing the generalized STIRAP. In the last section, we discuss role of two-body interactions in the Feshbach conversion of fermionic atoms to bosonic molecules.
Nonlinear dynamics of a rotating double pendulum
NASA Astrophysics Data System (ADS)
Maiti, Soumyabrata; Roy, Jyotirmoy; Mallik, Asok K.; Bhattacharjee, Jayanta K.
2016-01-01
Nonlinear dynamics of a double pendulum rotating at a constant speed about a vertical axis passing through the top hinge is investigated. Transitions of oscillations from chaotic to quasiperiodic and back to chaotic again are observed with increasing speed of rotation. With increasing speed, a pair of new stable equilibrium states, different from the normal vertical one, appear and the quasiperiodic oscillations occur. These oscillations are first centered around the origin, but with increasing rotation speed they cover the origin and the new fixed points. At a still higher speed, more than one pair of fixed points appear and the oscillation again turns chaotic. The onset of chaos is explained in terms of internal resonance. Analytical and numerical results confirm the critical values of the speed parameter at various transitions.
Nonlinear dynamic analysis of flexible multibody systems
NASA Technical Reports Server (NTRS)
Bauchau, Olivier A.; Kang, Nam Kook
1991-01-01
Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.
Spin-current emission governed by nonlinear spin dynamics
Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya
2015-01-01
Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators. PMID:26472712
Spin-current emission governed by nonlinear spin dynamics.
Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya
2015-01-01
Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators. PMID:26472712
NONLINEAR DYNAMICAL FRICTION IN A GASEOUS MEDIUM
Kim, Hyosun; Kim, Woong-Tae E-mail: wkim@astro.snu.ac.k
2009-10-01
Using high-resolution, two-dimensional hydrodynamic simulations, we investigate nonlinear gravitational responses of gas to, and the resulting drag force on, a very massive perturber M{sub p} moving at velocity V{sub p} through a uniform gaseous medium of adiabatic sound speed a{sub i}nfinity. We model the perturber as a Plummer potential with softening radius r{sub s} , and run various models with differing A=GM{sub p}/(a{sub i}nfinity{sup 2}r{sub s}) and M=V{sub p}/a{sub i}nfinity by imposing cylindrical symmetry with respect to the line of perturber motion. For supersonic cases, a massive perturber quickly develops nonlinear flows that produce a detached bow shock and a vortex ring, which is unlike in the linear cases where Mach cones are bounded by low-amplitude Mach waves. The flows behind the shock are initially non-steady, displaying quasi-periodic, overstable oscillations of the vortex ring and the shock. The vortex ring is eventually shed downstream and the flows evolve toward a quasi-steady state where the density wake near the perturber is in near hydrostatic equilibrium. We find that the detached shock distance delta and the nonlinear drag force F depend solely on eta=A/(M{sup 2}-1) such that delta/r{sub s} = eta and F/F{sub lin}=(eta/2){sup -0.45} for 100 >eta>2, where F {sub lin} is the linear drag force of Ostriker. The reduction of F compared with F{sub lin} is caused by front-back symmetry in the nonlinear density wakes. In subsonic cases, the flows without involving a shock do not readily reach a steady state. Nevertheless, the subsonic density wake near a perturber is close to being hydrostatic, resulting in the drag force similar to the linear case. Our results suggest that dynamical friction of a very massive object as in a merger of black holes near a galaxy center will take considerably longer than the linear prediction.
Surfactant and nonlinear drop dynamics in microgravity
NASA Astrophysics Data System (ADS)
Jankovsky, Joseph Charles
2000-11-01
Large amplitude drop dynamics in microgravity were conducted during the second United States Microgravity Laboratory mission carried onboard the Space Shuttle Columbia (20 October-5 November 1995). Centimeter- sized drops were statically deformed by acoustic radiation pressure and released to oscillate freely about a spherical equilibrium. Initial aspect ratios of up to 2.0 were achieved. Experiments using pure water and varying aqueous concentrations of Triton-X 100 and bovine serum albumin (BSA) were performed. The axisymmetric drop shape oscillations were fit using the degenerate spherical shape modes. The frequency and decay values of the fundamental quadrupole and fourth order shape mode were analyzed. Several large amplitude nonlinear oscillation dynamics were observed. Shape entrainment of the higher modes by the fundamental quadrupole mode occurred. Amplitude- dependent effects were observed. The nonlinear frequency shift, where the oscillation frequency is found to decrease with larger amplitudes, was largely unaffected by the presence of surfactants. The percentage of time spent in the prolate shape over one oscillation cycle was found to increase with oscillation amplitude. This prolate shape bias was also unaffected by the addition of surfactants. These amplitude-dependent effects indicate that the nonlinearities are a function of the bulk properties and not the surface properties. BSA was found to greatly enhance the surface viscoelastic properties by increasing the total damping of the oscillation, while Triton had only a small influence on damping. The surface concentration of BSA was found to be diffusion-controlled over the time of the experiments, while the Triton diffusion rate was very rapid. Using the experimental frequency and decay values, the suface viscoelastic properties of surface dilatational viscosity ( ks ) and surface shear viscosity ( ms ) were found for varying surfactant concentrations using the transcendental equation of Lu
Direct adaptive control for nonlinear uncertain dynamical systems
NASA Astrophysics Data System (ADS)
Hayakawa, Tomohisa
In light of the complex and highly uncertain nature of dynamical systems requiring controls, it is not surprising that reliable system models for many high performance engineering and life science applications are unavailable. In the face of such high levels of system uncertainty, robust controllers may unnecessarily sacrifice system performance whereas adaptive controllers are clearly appropriate since they can tolerate far greater system uncertainty levels to improve system performance. In this dissertation, we develop a Lyapunov-based direct adaptive and neural adaptive control framework that addresses parametric uncertainty, unstructured uncertainty, disturbance rejection, amplitude and rate saturation constraints, and digital implementation issues. Specifically, we consider the following research topics; direct adaptive control for nonlinear uncertain systems with exogenous disturbances; robust adaptive control for nonlinear uncertain systems; adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints; adaptive reduced-order dynamic compensation for nonlinear uncertain systems; direct adaptive control for nonlinear matrix second-order dynamical systems with state-dependent uncertainty; adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia; direct adaptive control of nonnegative and compartmental dynamical systems with time delay; adaptive control for nonlinear nonnegative and compartmental dynamical systems with applications to clinical pharmacology; neural network adaptive control for nonlinear nonnegative dynamical systems; passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems; neural network adaptive dynamic output feedback control for nonlinear nonnegative systems using tapped delay memory units; Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances
Overview of nonlinear dynamical systems and complexity theory
Herbert, D.E.
1996-06-01
A brief overview is presented of the principal elements of {open_quote}{open_quote}nonlinear dynamics{close_quote}{close_quote}: catastrophes, fractals, chaos, solitary waves, and coherent and dissipative structures. The text is followed by a set of 10 portraits of the strange and violent world of nonlinear dynamics. {copyright} {ital 1996 American Institute of Physics.}
Nonlinear Dynamics, Artificial Cognition and Galactic Export
NASA Astrophysics Data System (ADS)
Rössler, Otto E.
2004-08-01
The field of nonlinear dynamics focuses on function rather than structure. Evolution and brain function are examples. An equation for a brain, described in 1973, is explained. Then, a principle of interactional function change between two coupled equations of this type is described. However, all of this is not done in an abstract manner but in close contact with the meaning of these equations in a biological context. Ethological motivation theory and Batesonian interaction theory are reencountered. So is a fairly unknown finding by van Hooff on the indistinguishability of smile and laughter in a single primate species. Personhood and evil, two human characteristics, are described abstractly. Therapies and the question of whether it is ethically allowed to export benevolence are discussed. The whole dynamic approach is couched in terms of the Cartesian narrative, invented in the 17th century and later called Enlightenment. Whether or not it is true that a "second Enlightenment" is around the corner is the main question raised in the present paper.
Laser-driven nonlinear cluster dynamics
Fennel, Th.; Meiwes-Broer, K.-H.; Tiggesbaeumker, J.; Reinhard, P.-G.; Dinh, P. M.; Suraud, E.
2010-04-15
Laser excitation of nanometer-sized atomic and molecular clusters offers various opportunities to explore and control ultrafast many-particle dynamics. Whereas weak laser fields allow the analysis of photoionization, excited-state relaxation, and structural modifications on these finite quantum systems, large-amplitude collective electron motion and Coulomb explosion can be induced with intense laser pulses. This review provides an overview of key phenomena arising from laser-cluster interactions with focus on nonlinear optical excitations and discusses the underlying processes according to the current understanding. A general survey covers basic cluster properties and excitation mechanisms relevant for laser-driven cluster dynamics. Then, after an excursion in theoretical and experimental methods, results for single-photon and multiphoton excitations are reviewed with emphasis on signatures from time- and angular-resolved photoemission. A key issue of this review is the broad spectrum of phenomena arising from clusters exposed to strong fields, where the interaction with the laser pulse creates short-lived and dense nanoplasmas. The implications for technical developments such as the controlled generation of ion, electron, and radiation pulses will be addressed along with corresponding examples. Finally, future prospects of laser-cluster research as well as experimental and theoretical challenges are discussed.
Nonlinear Dynamics and Control in Microfluidic Networks
NASA Astrophysics Data System (ADS)
Case, Daniel; Angilella, Jean-Regis; Motter, Adilson
2015-03-01
Researchers currently use abundant external devices (e.g., pumps and computers) to achieve precise flow dynamics in microfluidic systems. Here, I show our use of network concepts and computational methods to design microfluidic systems that do not depend on external devices yet still exhibit a diverse range of flow dynamics. I present an example of a microfluidic channel described by a nonlinear pressure-flow relation and show that complex flow behavior can emerge in systems designed around this channel. By controlling the pressure at only a single terminal in such a system, I demonstrate the ability to switch the direction of fluid flow through intermediate channels not directly connected to the controlled terminal. I also show that adding (or removing) flow channels to a system can result in unexpected changes in the total mass flow rate, depending on the network structure of the system. We expect this work to both expand the applicability of microfluidics and promote scaling up of current experiments. This research was funded by the National Science Foundation.
Passive dynamic controllers for nonlinear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1991-01-01
A methodology for model-independant controller design for controlling large angular motion of multi-body dynamic systems is outlined. The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system and at the same time suppress the vibration due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameter, even if the controlled system is nonlinear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach to a flexible six-degree-of-freedom manipulator.
Nonlinear ship waves and computational fluid dynamics
MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei
2014-01-01
Research works undertaken in the first author’s laboratory at the University of Tokyo over the past 30 years are highlighted. Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design. Based on these findings, a multitude of the Computational Fluid Dynamic (CFD) techniques have been developed over this period, and are highlighted in this paper. The TUMMAC code has been developed for wave problems, based on a rectangular grid system, while the WISDAM code treats both wave and viscous flow problems in the framework of a boundary-fitted grid system. These two techniques are able to cope with almost all fluid dynamical problems relating to ships, including the resistance, ship’s motion and ride-comfort issues. Consequently, the two codes have contributed significantly to the progress in the technology of ship design, and now form an integral part of the ship-designing process. PMID:25311139
NASA Astrophysics Data System (ADS)
Pai, P. Frank
2011-10-01
Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.
Nonlinear dynamics, granular media and dynamic earthquake triggering.
Johnson, Paul A; Jia, Xiaoping
2005-10-01
The 1992 magnitude 7.3 Landers earthquake triggered an exceptional number of additional earthquakes within California and as far north as Yellowstone and Montana. Since this observation, other large earthquakes have been shown to induce dynamic triggering at remote distances--for example, after the 1999 magnitude 7.1 Hector Mine and the 2002 magnitude 7.9 Denali earthquakes--and in the near-field as aftershocks. The physical origin of dynamic triggering, however, remains one of the least understood aspects of earthquake nucleation. The dynamic strain amplitudes from a large earthquake are exceedingly small once the waves have propagated more than several fault radii. For example, a strain wave amplitude of 10(-6) and wavelength 1 m corresponds to a displacement amplitude of about 10(-7) m. Here we show that the dynamic, elastic-nonlinear behaviour of fault gouge perturbed by a seismic wave may trigger earthquakes, even with such small strains. We base our hypothesis on recent laboratory dynamic experiments conducted in granular media, a fault gouge surrogate. From these we infer that, if the fault is weak, seismic waves cause the fault core modulus to decrease abruptly and weaken further. If the fault is already near failure, this process could therefore induce fault slip. PMID:16208368
Chaotic behavior in nonlinear polarization dynamics
David, D.; Holm, D.D.; Tratnik, M.V. )
1989-01-01
We analyze the problem of two counterpropagating optical laser beams in a slightly nonlinear medium from the point of view of Hamiltonian systems; the one-beam subproblem is also investigated as a special case. We are interested in these systems as integrable dynamical systems which undergo chaotic behavior under various types of perturbations. The phase space for the two-beam problem is C{sup 2} {times} C{sup 2} when we restricted the the regime of travelling-wave solutions. We use the method of reduction for Hamiltonian systems invariant under one-parameter symmetry groups to demonstrate that the phase space reduces to the two-sphere S{sup 2} and is therefore completely integrable. The phase portraits of the system are classified and we also determine the bifurcations that modify these portraits; some new degenerate bifurcations are presented in this context. Finally, we introduce various physically relevant perturbations and use the Melnikov method to prove that horseshoe chaos and Arnold diffusion occur as consequences of these perturbations. 10 refs., 7 figs., 1 tab.
Nonlinear dynamics of attractive magnetic bearings
NASA Technical Reports Server (NTRS)
Hebbale, K. V.; Taylor, D. L.
1987-01-01
The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.
Transistor-based metamaterials with dynamically tunable nonlinear susceptibility
NASA Astrophysics Data System (ADS)
Barrett, John P.; Katko, Alexander R.; Cummer, Steven A.
2016-08-01
We present the design, analysis, and experimental demonstration of an electromagnetic metamaterial with a dynamically tunable effective nonlinear susceptibility. Split-ring resonators loaded with transistors are shown theoretically and experimentally to act as metamaterials with a second-order nonlinear susceptibility that can be adjusted through the use of a bias voltage. Measurements confirm that this allows for the design of a nonlinear metamaterial with adjustable mixing efficiency.
Nonlinear switching dynamics in a photonic-crystal nanocavity
Yu, Yi Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper
2014-08-18
We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.
The numerical dynamic for highly nonlinear partial differential equations
NASA Technical Reports Server (NTRS)
Lafon, A.; Yee, H. C.
1992-01-01
Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.
Nonlinear Dynamics of the Perceived Pitch of Complex Sounds
NASA Astrophysics Data System (ADS)
Cartwright, Julyan H. E.; González, Diego L.; Piro, Oreste
1999-06-01
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system. PMID:24808035
Characterizing Nonlinear Heartbeat Dynamics within a Point Process Framework
Brown, Emery N.; Barbieri, Riccardo
2010-01-01
Human heartbeat intervals are known to have nonlinear and nonstationary dynamics. In this paper, we propose a model of R–R interval dynamics based on a nonlinear Volterra–Wiener expansion within a point process framework. Inclusion of second-order nonlinearities into the heartbeat model allows us to estimate instantaneous heart rate (HR) and heart rate variability (HRV) indexes, as well as the dynamic bispectrum characterizing higher order statistics of the nonstationary non-Gaussian time series. The proposed point process probability heartbeat interval model was tested with synthetic simulations and two experimental heartbeat interval datasets. Results show that our model is useful in characterizing and tracking the inherent nonlinearity of heartbeat dynamics. As a feature, the fine temporal resolution allows us to compute instantaneous nonlinearity indexes, thus sidestepping the uneven spacing problem. In comparison to other nonlinear modeling approaches, the point process probability model is useful in revealing nonlinear heartbeat dynamics at a fine timescale and with only short duration recordings. PMID:20172783
Assessment of anxiety using heart rate nonlinear dynamics
NASA Astrophysics Data System (ADS)
Thayer, Julian F.; Friedman, Bruce H.
1993-11-01
Various anxiety states have been linked with disorders of the autonomic nervous system. These autonomic disorders may be revealed by analysis of physiological time series such as the heart rate interbeat interval series. The present paper reports a general model of biological system functioning and related assessment indices based on recent nonlinear dynamical systems approaches. In particular, two experimental studies are reported which suggest the utility of heart rate nonlinear dynamics in the assessment of anxiety.
The periodic structure of the natural record, and nonlinear dynamics.
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
Nonlinear Dynamics: Maps, Integrators and Solitons
Parsa, Z.
1998-10-01
For many physical systems of interest in various disciplines, the solution to nonlinear differential equations describing the physical systems can be generated using maps, symplectic integrators and solitons. We discuss these methods and apply them for various examples.
Chaotic dynamics of weakly nonlinear systems
Vavriv, D.M.
1996-06-01
A review is given on the recent results in studying chaotic phenomena in weakly nonlinear systems. We are concerned with the class of chaotic states that can arise in physical systems with any degree of nonlinearity however small. The conditions for, and the mechanisms of, the transitions to chaos are discussed. These findings are illustrated by the results of the stability analysis of practical microwave and optical devices. {copyright} {ital 1996 American Institute of Physics.}
Intertwined narratives of the human caring story.
Rosa, William; Coach, Caritas
2014-01-01
The story of human caring is universal; built on a foundation of caring-healing-loving and comprising intersubjective shared intimacy, authenticity, and presence. Each person's relationship with story is worthy of telling as it connects the individual to the collective, the personal to the global. The story of human caring is the result of intertwined narratives; the love, light, and prayer we hold for ourselves and each other in the world. PMID:25252379
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
NASA Astrophysics Data System (ADS)
Schöll, Eckehard
2005-08-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
NASA Astrophysics Data System (ADS)
Schöll, Eckehard
2001-02-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
An experimental study of nonlinear dynamic system identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D. Joseph
1990-01-01
A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.
Employment of CB models for non-linear dynamic analysis
NASA Technical Reports Server (NTRS)
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Nonlinear dynamics based digital logic and circuits
Kia, Behnam; Lindner, John. F.; Ditto, William L.
2015-01-01
We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two. PMID:26029096
Nonlinear dynamics based digital logic and circuits.
Kia, Behnam; Lindner, John F; Ditto, William L
2015-01-01
We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two. PMID:26029096
Nonlinear Dynamics in the Ultradian Rhythm of Desmodium motorium
NASA Astrophysics Data System (ADS)
Chen, Jyh-Phen; Engelmann, Wolfgang; Baier, Gerold
1995-12-01
The dynamics of the lateral leaflet movement of Desmodium motorium is studied. Simple periodic, quasiperiodic and aperiodic time series are observed. The long-scale dynamics may either be uniform or composed of several prototypic oscillations (one of them reminiscent of homoclinic chaos). Diffusively coupled nonlinear oscillators may account for the variety of ultradian rhythms.
Nonlinear dynamics and collective excitations in layered superconducting structures
NASA Astrophysics Data System (ADS)
Zel'Tser, A. S.; Kivshar', Iu. S.; Soboleva, T. K.
1991-06-01
Nonlinear excitations in layered superconducting structures representing a system of interacting extended Josephson junctions are investigated theoretically. The possibility of the propagation of dynamic supersolitons, localized vortex lattice density excitations, in such a system is demonstrated. Particular attention is given to soliton excitations of two types: kinks and envelope solitons. The relaxation of dynamic kinks is investigated numerically.
Global attractors for a third order in time nonlinear dynamics
NASA Astrophysics Data System (ADS)
Caixeta, Arthur H.; Lasiecka, Irena; Cavalcanti, Valéria N. D.
2016-07-01
Long time behavior of a third order (in time) nonlinear PDE equation is considered. This type of equations arises in the context of nonlinear acoustics [12,20,22,24] where modeling accounts for a finite speed of propagation paradox, the latter results in hyperbolic nature of the dynamics. It will be proved that the underlying PDE generates a well-posed dynamical system which admits a global and finite dimensional attractor. The main difficulty associated with the problem studied is the lack of Lyapunov function along with the lack of compactness of trajectories, which fact prevents applicability of standard tools in the area of dynamical systems.
Nonlinear system guidance in the presence of transmission zero dynamics
NASA Technical Reports Server (NTRS)
Meyer, G.; Hunt, L. R.; Su, R.
1995-01-01
An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.
Nonlinear dynamics of fluid-structure systems. Annual technical report
Moon, F.C.; Muntean, G.
1994-01-01
We are investigating the nonlinear dynamics of a row of cylindrical tubes excited by the cross flow of fluid. Both experimental and analytical/numerical studies have been conducted. The goal of this research is to look for low dimensional dynamic models in flow- induced vibrations using modern methods of dynamical systems and chaos theory. The experimental study uses a 25 cm {times} 25 cm wind tunnel with flow velocity in the range of 15 m/sec. The use of a wind tunnel to explore dynamic phenomenon compliments the work of Chen at Argonne National Laboratory who also is conducting experiments with a water tunnel. The principal nonlinearities studies are impact constraints due to gaps in the cylinder supports and nonlinear fluid forces.
Dynamic Time Expansion and Compression Using Nonlinear Waveguides
Findikoglu, Alp T.; Hahn, Sangkoo F.; Jia, Quanxi
2004-06-22
Dynamic time expansion or compression of a small amplitude input signal generated with an initial scale is performed using a nonlinear waveguide. A nonlinear waveguide having a variable refractive index is connected to a bias voltage source having a bias signal amplitude that is large relative to the input signal to vary the reflective index and concomitant speed of propagation of the nonlinear waveguide and an electrical circuit for applying the small amplitude signal and the large amplitude bias signal simultaneously to the nonlinear waveguide. The large amplitude bias signal with the input signal alters the speed of propagation of the small-amplitude signal with time in the nonlinear waveguide to expand or contract the initial time scale of the small-amplitude input signal.
Dynamic time expansion and compression using nonlinear waveguides
Findikoglu, Alp T.; Hahn, Sangkoo F.; Jia, Quanxi
2004-06-22
Dynamic time expansion or compression of a small-amplitude input signal generated with an initial scale is performed using a nonlinear waveguide. A nonlinear waveguide having a variable refractive index is connected to a bias voltage source having a bias signal amplitude that is large relative to the input signal to vary the reflective index and concomitant speed of propagation of the nonlinear waveguide and an electrical circuit for applying the small-amplitude signal and the large amplitude bias signal simultaneously to the nonlinear waveguide. The large amplitude bias signal with the input signal alters the speed of propagation of the small-amplitude signal with time in the nonlinear waveguide to expand or contract the initial time scale of the small-amplitude input signal.
Nonlinear dynamic phenomena in the space shuttle thermal protection system
NASA Technical Reports Server (NTRS)
Housner, J. M.; Edighoffer, H. H.; Park, K. C.
1981-01-01
The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.
Photonic nonlinear transient computing with multiple-delay wavelength dynamics.
Martinenghi, Romain; Rybalko, Sergei; Jacquot, Maxime; Chembo, Yanne K; Larger, Laurent
2012-06-15
We report on the experimental demonstration of a hybrid optoelectronic neuromorphic computer based on a complex nonlinear wavelength dynamics including multiple delayed feedbacks with randomly defined weights. This neuromorphic approach is based on a new paradigm of a brain-inspired computational unit, intrinsically differing from Turing machines. This recent paradigm consists in expanding the input information to be processed into a higher dimensional phase space, through the nonlinear transient response of a complex dynamics excited by the input information. The computed output is then extracted via a linear separation of the transient trajectory in the complex phase space. The hyperplane separation is derived from a learning phase consisting of the resolution of a regression problem. The processing capability originates from the nonlinear transient, resulting in nonlinear transient computing. The computational performance is successfully evaluated on a standard benchmark test, namely, a spoken digit recognition task. PMID:23004274
Photonic Nonlinear Transient Computing with Multiple-Delay Wavelength Dynamics
NASA Astrophysics Data System (ADS)
Martinenghi, Romain; Rybalko, Sergei; Jacquot, Maxime; Chembo, Yanne K.; Larger, Laurent
2012-06-01
We report on the experimental demonstration of a hybrid optoelectronic neuromorphic computer based on a complex nonlinear wavelength dynamics including multiple delayed feedbacks with randomly defined weights. This neuromorphic approach is based on a new paradigm of a brain-inspired computational unit, intrinsically differing from Turing machines. This recent paradigm consists in expanding the input information to be processed into a higher dimensional phase space, through the nonlinear transient response of a complex dynamics excited by the input information. The computed output is then extracted via a linear separation of the transient trajectory in the complex phase space. The hyperplane separation is derived from a learning phase consisting of the resolution of a regression problem. The processing capability originates from the nonlinear transient, resulting in nonlinear transient computing. The computational performance is successfully evaluated on a standard benchmark test, namely, a spoken digit recognition task.
Dynamics of elastic nonlinear rotating composite beams with embedded actuators
NASA Astrophysics Data System (ADS)
Ghorashi, Mehrdaad
2009-08-01
A comprehensive study of the nonlinear dynamics of composite beams is presented. The study consists of static and dynamic solutions with and without active elements. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Numerical solutions for the steady state and transient responses have been obtained. It is shown that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. The effect of perturbing the steady state solution has also been calculated and the results are shown to be compatible with those of the accelerating beam analysis. Next, the coupled flap-lag rigid body dynamics of a rotating articulated beam with hinge offset and subjected to aerodynamic forces is formulated. The solution to this rigid-body problem is then used, together with the finite difference method, in order to produce the nonlinear elasto-dynamic solution of an accelerating articulated beam. Next, the static and dynamic responses of nonlinear composite beams with embedded Anisotropic Piezo-composite Actuators (APA) are presented. The effect of activating actuators at various directions on the steady state force and moments generated in a rotating composite beam has been presented. With similar results for the transient response, this analysis can be used in controlling the response of adaptive rotating beams.
Effect of motor dynamics on nonlinear feedback robot arm control
NASA Technical Reports Server (NTRS)
Tarn, Tzyh-Jong; Li, Zuofeng; Bejczy, Antal K.; Yun, Xiaoping
1991-01-01
A nonlinear feedback robot controller that incorporates the robot manipulator dynamics and the robot joint motor dynamics is proposed. The manipulator dynamics and the motor dynamics are coupled to obtain a third-order-dynamic model, and differential geometric control theory is applied to produce a linearized and decoupled robot controller. The derived robot controller operates in the robot task space, thus eliminating the need for decomposition of motion commands into robot joint space commands. Computer simulations are performed to verify the feasibility of the proposed robot controller. The controller is further experimentally evaluated on the PUMA 560 robot arm. The experiments show that the proposed controller produces good trajectory tracking performances and is robust in the presence of model inaccuracies. Compared with a nonlinear feedback robot controller based on the manipulator dynamics only, the proposed robot controller yields conspicuously improved performance.
Electron dynamics with radiation and nonlinear wigglers
Jowett, J.M.
1986-06-01
The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches.
Nonlinear Network Dynamics on Earthquake Fault Systems
Rundle, Paul B.; Rundle, John B.; Tiampo, Kristy F.; Sa Martins, Jorge S.; McGinnis, Seth; Klein, W.
2001-10-01
Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.
Nonlinear dynamics of inhomogeneous mismatched charged particle beams
Nunes, R. P.; Rizzato, F. B.
2012-08-13
This work analyzes the transversal dynamics of an inhomogeneous and mismatched charged particle beam. The beam is azimuthally symmetric, initially cold, and evolves in a linear channel permeated by an external constant magnetic field. Based on a Lagrangian approach, a low-dimensional model for the description of the beam dynamics has been obtained. The small set of nonlinear dynamical equations provided results that are in reasonable agreement with that ones observed in full self-consistent N-particle beam numerical simulations.
An experimental study of nonlinear dynamic system identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D, Joseph
1991-01-01
A technique based on the Minimum Model Error optimal estimation approach is employed for robust identification of a nonlinear dynamic system. A simple harmonic oscillator with quadratic position feedback was simulated on an analog computer. With the aid of analog measurements and an assumed linear model, the Minimum Model Error Algorithm accurately identifies the quadratic nonlinearity. The tests demonstrate that the method is robust with respect to prior ignorance of the nonlinear system model and with respect to measurement record length, regardless of initial conditions.
Nonlinear dynamics and control of a vibrating rectangular plate
NASA Technical Reports Server (NTRS)
Shebalin, J. V.
1983-01-01
The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.
Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.
Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C
2014-01-01
Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations. PMID:24580333
Theoretical and software considerations for nonlinear dynamic analysis
NASA Technical Reports Server (NTRS)
Schmidt, R. J.; Dodds, R. H., Jr.
1983-01-01
In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.
Nonlinear Dynamic Characteristics of Oil-in-Water Emulsions
NASA Astrophysics Data System (ADS)
Yin, Zhaoqi; Han, Yunfeng; Ren, Yingyu; Yang, Qiuyi; Jin, Ningde
2016-08-01
In this article, the nonlinear dynamic characteristics of oil-in-water emulsions under the addition of surfactant were experimentally investigated. Firstly, based on the vertical upward oil-water two-phase flow experiment in 20 mm inner diameter (ID) testing pipe, dynamic response signals of oil-in-water emulsions were recorded using vertical multiple electrode array (VMEA) sensor. Afterwards, the recurrence plot (RP) algorithm and multi-scale weighted complexity entropy causality plane (MS-WCECP) were employed to analyse the nonlinear characteristics of the signals. The results show that the certainty is decreasing and the randomness is increasing with the increment of surfactant concentration. This article provides a novel method for revealing the nonlinear dynamic characteristics, complexity, and randomness of oil-in-water emulsions with experimental measurement signals.
A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics
Jay R. Johnson; Simon Wing
2004-01-28
Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach.
Adaptive control of nonlinear systems using multistage dynamic neural networks
NASA Astrophysics Data System (ADS)
Gupta, Madan M.; Rao, Dandina H.
1992-11-01
In this paper we present a new architecture of neuron, called the dynamic neural unit (DNU). The topology of the proposed neuronal model embodies delay elements, feedforward and feedback signals weighted by the synaptic weights and a time-varying nonlinear activation function, and is thus different from the conventionally and assumed architecture of neurons. The learning algorithm for the proposed neuronal structure and the corresponding implementation scheme are presented. A multi-stage dynamic neural network is developed using the DNU as the basic processing element. The performance evaluation of the dynamic neural network is presented for nonlinear dynamic systems under various situations. The capabilities of the proposed neural network model not only account for the learning and control actions emulating some of the biological control functions, but also provide a promising parallel-distributed intelligent control scheme for large-scale complex dynamic systems.
Nonlinearly coupled dynamics of irregularities in the equatorial electrojet
NASA Astrophysics Data System (ADS)
Atul, J. K.; Sarkar, S.; Singh, S. K.
2016-04-01
Kinetic wave description is used to study the nonlinear influence of background Farley Buneman (FB) modes on the Gradient Drift (GD) modes in the equatorial electrojet ionosphere. The dominant nonlinearity is mediated through the electron flux term in the governing fluid equation which further invokes a turbulent current into the system. Electron dynamics reveals the modification in electron collision frequency and inhomogeneity scale length. It is seen that the propagation and growth rate of GD modes get modified by the background FB modes. Also, a new quasimode gets excited through the quadratic dispersion relation. Physical significance of coupled dynamics between the participating modes is also discussed.
Nonlinear dynamics of a flexible mechanism with impact
NASA Astrophysics Data System (ADS)
Dupac, Mihai; Marghitu, Dan B.
2006-02-01
The nonlinear dynamics of a slider-crank mechanism with a flexible rod is considered in this study. The flexible rod is modeled with lumped masses and periodically impacted by an external flexible sphere. The impact is modeled using a kinematic coefficient of restitution. Nonlinear dynamics tools are applied to analyze the simulated data captured from the connecting rod of the mechanism. The chaotic behavior of the system is analyzed. The stability of the motion is studied using the Lyapunov exponents. The dependence between the Lyapunov exponents and the corresponding angular velocity of the driver link of the mechanism is investigated.
Dynamics of two nonlinear oligopoly models
NASA Astrophysics Data System (ADS)
Ibrahim, Adyda
2014-06-01
This paper considers an n firms oligopoly model with isoelastic demand function and linear cost function. This model is introduced in two different dynamical systems. In the first system, firms are assumed have naive expectation, while in the second system, firms are assumed to have bounded rationality. We study the dynamics of both dynamical systems in the special case of firms behaving identically. The main result shows that as the number of firm increases, the equilibrium in the first system becomes unstable when the number of firms is greater than four, while in the second system, there is a change in the region of stability for the equilibrium.
Nonlinear dynamical modes of climate variability: from curves to manifolds
NASA Astrophysics Data System (ADS)
Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander
2016-04-01
The necessity of efficient dimensionality reduction methods capturing dynamical properties of the system from observed data is evident. Recent study shows that nonlinear dynamical mode (NDM) expansion is able to solve this problem and provide adequate phase variables in climate data analysis [1]. A single NDM is logical extension of linear spatio-temporal structure (like empirical orthogonal function pattern): it is constructed as nonlinear transformation of hidden scalar time series to the space of observed variables, i. e. projection of observed dataset onto a nonlinear curve. Both the hidden time series and the parameters of the curve are learned simultaneously using Bayesian approach. The only prior information about the hidden signal is the assumption of its smoothness. The optimal nonlinearity degree and smoothness are found using Bayesian evidence technique. In this work we do further extension and look for vector hidden signals instead of scalar with the same smoothness restriction. As a result we resolve multidimensional manifolds instead of sum of curves. The dimension of the hidden manifold is optimized using also Bayesian evidence. The efficiency of the extension is demonstrated on model examples. Results of application to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510
Fully nonlinear dynamics of parallel wakes
NASA Astrophysics Data System (ADS)
Chomaz, Jean-Marc
2003-11-01
The fully nonlinear theory of global modes in open flows, proposed in recent analyses of amplitude equations, is extended to the case of Navier Stokes equations using direct numerical simulations. The basic flow under consideration is a parallel wake in a finite domain generated by imposing the wake profile at the inlet boundary and by adding a body force to compensate the basic flow diffusion. The link between the global bifurcation, the absolute or convective nature of the local linear instability, and the theory of speed selection for the front separating an unperturbed domain of the flow from a fully saturated solution is elucidated. In particular, thanks to the parallelism of the flow, the bifurcation scenario and the associated scaling laws for the frequency, the healing length, and the slope at the origin predicted by a previous analysis of amplitude equations are recovered with great precision.
Phase portrait visualization of nonlinear dynamics
Stewart, H.B. )
1989-01-01
Poncare's advice to construct the curves defined by differential quations takes on new meaning with the widespread availability of computer graphics devices. Computer graphics now provide a much easier way of visualizing curves constructed by solving initial value problems for differential equations, making both the geometric theory and its application to practical problems accessible to a wider audience of scientists and engineers. Recent studies in a wide range of disciplines, including mechanical vibrations, fluid dynamics, electrical engineering, and meteorology, have shown that chaotic attractors are common and typical behavior in real dynamical systems. Complete understanding of a dissipative dynamical system begins with constructing the phase portrait, i.e., a geometric phase space picture of any and all attractors, their basins of attraction, and the phase foliation of basins. As an example of the concepts and techniques of phase space visualization, a computer-generated 16-mm movie has been produced dealing with a simple model of thermally driven fluid convection.
Nonlinear Dynamics, Chaotic and Complex Systems
NASA Astrophysics Data System (ADS)
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Numerical investigation of bubble nonlinear dynamics characteristics
Shi, Jie Yang, Desen; Shi, Shengguo; Hu, Bo; Zhang, Haoyang; Jiang, Wei
2015-10-28
The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.
Numerical investigation of bubble nonlinear dynamics characteristics
NASA Astrophysics Data System (ADS)
Shi, Jie; Yang, Desen; Zhang, Haoyang; Shi, Shengguo; Jiang, Wei; Hu, Bo
2015-10-01
The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.
Role of temperature on nonlinear cardiac dynamics
NASA Astrophysics Data System (ADS)
Fenton, Flavio H.; Gizzi, Alessio; Cherubini, Christian; Pomella, Nicola; Filippi, Simonetta
2013-04-01
Thermal effects affecting spatiotemporal behavior of cardiac tissue are discussed by relating temperature variations to proarrhythmic dynamics in the heart. By introducing a thermoelectric coupling in a minimal model of cardiac tissue, we are able to reproduce experimentally measured dynamics obtained simultaneously from epicardial and endocardial canine right ventricles at different temperatures. A quantitative description of emergent proarrhythmic properties of restitution, conduction velocity, and alternans regimes as a function of temperature is presented. Complex discordant alternans patterns that enhance tissue dispersion consisting of one wave front and three wave backs are described in both simulations and experiments. Possible implications for model generalization are finally discussed.
Nonlinear dynamics of the human lumbar intervertebral disc.
Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J
2015-02-01
Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. PMID:25573099
Slow dynamics in the nonlinear elastic response of Berea sandstone
NASA Astrophysics Data System (ADS)
Ten Cate, James A.; Shankland, Thomas J.
A typical resonance curve—measured acceleration versus drive frequency—made on a thin bar of rock shows peak bending with a softening (nonlinear) modulus as drive levels are increased. The shapes of these nonlinear resonance curves were found in earlier work to depend somewhat on sweep rate; these “slow dynamics” are now examined and quantified. We have measured slow dynamics in a 0.3 m long, 50 mm diameter bar of Berea sandstone under ambient conditions. Peak strain levels during the experiments ranged from 10-11 to 10-5 at driving frequencies near 4 kHz, the fundamental longitudinal resonance frequency of the bar. Slow dynamics begin to manifest themselves at strain amplitudes above 10-6 at ambient conditions and at the onset of nonlinear peak bending. Strains above this value condition the rock, altering its response for minutes to hours after the drive has been turned off.
Nonlinear tuning of microresonators for dynamic range enhancement
Saghafi, M.; Dankowicz, H.; Lacarbonara, W.
2015-01-01
This paper investigates the development of a novel framework and its implementation for the nonlinear tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes into account rotary inertia effects. The partial differential equations of motion are discretized, according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift as well as a hardening effect are observed in the frequency response of the beam. These results are confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse problem is then proposed for the continuation of the critical amplitude at which the transition to nonlinear response characteristics occurs. Path-following techniques are employed to explore the dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude of the dynamic range in nano/microresonators. PMID:26345078
Intertwined Multiple Spiral Fracture in Perforated Sheets
NASA Astrophysics Data System (ADS)
Fuentealba, Juan-Francisco; Hamm, Eugenio; Roman, Benoît
2016-04-01
We study multiple tearing of a thin, elastic, brittle sheet indented with a rigid cone. The n cracks initially prepared symmetrically propagate radially for n ≥4 . However, if n <4 the radial symmetry is broken and fractures spontaneously intertwine along logarithmic spiral paths, respecting order n rotational symmetry. In the limit of very thin sheets, we find that fracture mechanics is reduced to a geometrical model that correctly predicts the maximum number of spirals to be strictly 4, together with their growth rate and the perforation force. Similar spirals are also observed in a different tearing experiment (this time up to n =4 , in agreement with the model), in which bending energy of the sheet is dominant.
Intertwined Multiple Spiral Fracture in Perforated Sheets.
Fuentealba, Juan-Francisco; Hamm, Eugenio; Roman, Benoît
2016-04-22
We study multiple tearing of a thin, elastic, brittle sheet indented with a rigid cone. The n cracks initially prepared symmetrically propagate radially for n≥4. However, if n<4 the radial symmetry is broken and fractures spontaneously intertwine along logarithmic spiral paths, respecting order n rotational symmetry. In the limit of very thin sheets, we find that fracture mechanics is reduced to a geometrical model that correctly predicts the maximum number of spirals to be strictly 4, together with their growth rate and the perforation force. Similar spirals are also observed in a different tearing experiment (this time up to n=4, in agreement with the model), in which bending energy of the sheet is dominant. PMID:27152809
Nonlinear dynamics and predictability in the atmospheric sciences
Ghil, M.; Kimoto, M.; Neelin, J.D. )
1991-01-01
Systematic applications of nonlinear dynamics to studies of the atmosphere and climate are reviewed for the period 1987-1990. Problems discussed include paleoclimatic applications, low-frequency atmospheric variability, and interannual variability of the ocean-atmosphere system. Emphasis is placed on applications of the successive bifurcation approach and the ergodic theory of dynamical systems to understanding and prediction of intraseasonal, interannual, and Quaternary climate changes.
Nonlinear dynamic analysis of hydrodynamically-coupled stainless steel structures
Zhao, Y.
1996-12-01
Spent nuclear fuel is usually stored temporarily on the site of nuclear power plants. The spent fuel storage racks are nuclear-safety-related stainless steel structures required to be analyzed for seismic loads. When the storage pool is subjected to three-dimensional (3-D) floor seismic excitations, rack modules, stored fuel bundles, adjacent racks and pool walls, and surrounding water are hydrodynamically coupled. Hydrodynamic coupling (HC) significantly affects the dynamic responses of the racks that are free-standing and submerged in water within the pool. A nonlinear time-history dynamic analysis is usually needed to describe the motion behavior of the racks that are both geometrically nonlinear and material nonlinear in nature. The nonlinearities include the friction resistance between the rack supporting legs and the pool floor, and various potential impacts of fuel-rack, rack-rack, and rack-pool wall. The HC induced should be included in the nonlinear dynamic analysis using the added-hydrodynamic-mass concept based on potential theory per the US Nuclear Regulatory Commission (USNRC) acceptance criteria. To this end, a finite element analysis constitutes a feasible and effective tool. However, most people perform somewhat simplified 1-D, or 2-D, or 3-D single rack and 2-D multiple rack analyses. These analyses are incomplete because a 3-D single rack model behaves quite differently from a 2-D mode. Furthermore, a 3-D whole pool multi-rack model behaves differently than a 3-D single rack model, especially when the strong HC effects are unsymmetrical. In this paper 3-D nonlinear dynamic time-history analyses were performed in a more quantitative manner using sophisticated finite element models developed for a single rack as well as all twelve racks in the whole-pool. Typical response results due to different HC effects are determined and discussed.
Exploring intertwined orders in cuprate superconductors
Tranquada, John M.
2014-11-22
In this study, the concept of intertwined orders has been introduced to describe the cooperative relationship between antiferromagnetic spin correlations and electron (or hole) pair correlations that develop in copper-oxide superconductors. This contrasts with systems in which, for example, charge-density-wave (CDW) order competes for Fermi surface area with superconductivity. La2-xBaxCuO4 with x = 0.125 provides an example in which the ordering of spin stripes coincides with the onset of two-dimensional superconducting correlations. The apparent frustration of the interlayer Josephson coupling has motivated the concept of the pair-density-wave superconductor, a state that theoretical calculations show to be energetically competitive with themore » uniform d-wave superconductor. Even at x = 0.095, where there is robust superconductivity below 32 K in zero field, the coexistence of strong, low-energy, incommensurate spin excitations implies a spatially modulated and intertwined pair wave function. Recent observations of CDW order in YBa2Cu3O6+x and other cuprate families have raised interesting questions regarding the general role of charge modulations and the relation to superconductivity. While there are differences in the doping dependence of the modulation wave vectors in YBa2Cu3O6+x and La2-xBaxCuO4, the maximum ordering strength is peaked at the hole concentration of 1/8 in both cases. There are also possible connections with the quantum oscillations that have been detected about the same hole concentration but at high magnetic fields. Resolving these relationships remains a research challenge.« less
Exploring intertwined orders in cuprate superconductors
Tranquada, John M.
2014-11-22
In this study, the concept of intertwined orders has been introduced to describe the cooperative relationship between antiferromagnetic spin correlations and electron (or hole) pair correlations that develop in copper-oxide superconductors. This contrasts with systems in which, for example, charge-density-wave (CDW) order competes for Fermi surface area with superconductivity. La_{2-x}Ba_{x}CuO_{4} with x = 0.125 provides an example in which the ordering of spin stripes coincides with the onset of two-dimensional superconducting correlations. The apparent frustration of the interlayer Josephson coupling has motivated the concept of the pair-density-wave superconductor, a state that theoretical calculations show to be energetically competitive with the uniform d-wave superconductor. Even at x = 0.095, where there is robust superconductivity below 32 K in zero field, the coexistence of strong, low-energy, incommensurate spin excitations implies a spatially modulated and intertwined pair wave function. Recent observations of CDW order in YBa_{2}Cu_{3}O_{6+x} and other cuprate families have raised interesting questions regarding the general role of charge modulations and the relation to superconductivity. While there are differences in the doping dependence of the modulation wave vectors in YBa_{2}Cu_{3}O_{6+x} and La_{2-x}Ba_{x}CuO_{4}, the maximum ordering strength is peaked at the hole concentration of 1/8 in both cases. There are also possible connections with the quantum oscillations that have been detected about the same hole concentration but at high magnetic fields. Resolving these relationships remains a research challenge.
Chaos Theory: Implications for Nonlinear Dynamics in Counseling.
ERIC Educational Resources Information Center
Stickel, Sue A.
The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…
Coherence, chaos and communication: Exploring and applying nonlinear laser dynamics
NASA Astrophysics Data System (ADS)
Roy, Rajarshi
2000-12-01
Surprising conceptual connections between quite different physical systems are traced. Nonlinear dynamics is the common formalism that provides the basis for understanding many puzzling observations, including laser instabilities. Experiments in our laboratory to investigate coupled laser systems and communication with chaotic waveforms are described.
Passive dynamic controllers for non-linear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1992-01-01
The objective is to develop active model-independent controllers for slewing and vibration control of nonlinear multibody flexible systems, including flexible robots. The topics are presented in viewgraph form and include: passive stabilization; work-energy rate principle; Liapunov theory; displacement feedback; dynamic controller; displacement and acceleration feedback; velocity feedback; displacement feedback; physical interaction; a 6-DOF robot; and simulation results.
Non-linear dynamic analysis of geared systems, part 2
NASA Technical Reports Server (NTRS)
Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet
1990-01-01
A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.
Population mixture model for nonlinear telomere dynamics
NASA Astrophysics Data System (ADS)
Itzkovitz, Shalev; Shlush, Liran I.; Gluck, Dan; Skorecki, Karl
2008-12-01
Telomeres are DNA repeats protecting chromosomal ends which shorten with each cell division, eventually leading to cessation of cell growth. We present a population mixture model that predicts an exponential decrease in telomere length with time. We analytically solve the dynamics of the telomere length distribution. The model provides an excellent fit to available telomere data and accounts for the previously unexplained observation of telomere elongation following stress and bone marrow transplantation, thereby providing insight into the nature of the telomere clock.
Process and meaning: nonlinear dynamics and psychology in visual art.
Zausner, Tobi
2007-01-01
Creating and viewing visual art are both nonlinear experiences. Creating a work of art is an irreversible process involving increasing levels of complexity and unpredictable events. Viewing art is also creative with collective responses forming autopoietic structures that shape cultural history. Artists work largely from the chaos of the unconscious and visual art contains elements of chaos. Works of art by the author are discussed in reference to nonlinear dynamics. "Travelogues" demonstrates continued emerging interpretations and a deterministic chaos. "Advice to the Imperfect" signifies the resolution of paradox in the nonlinear tension of opposites. "Quanah" shows the nonlinear tension of opposites as an ongoing personal evolution. "The Mother of All Things" depicts seemingly separate phenomena arising from undifferentiated chaos. "Memories" refers to emotional fixations as limit cycles. "Compassionate Heart," "Wind on the Lake," and "Le Mal du Pays" are a series of works in fractal format focusing on the archetype of the mother and child. "Sameness, Depth of Mystery" addresses the illusion of hierarchy and the dynamics of symbols. In "Chasadim" the origin of worlds and the regeneration of individuals emerge through chaos. References to chaos in visual art mirror the nonlinear complexity of life. PMID:17173732
Self-Organized Biological Dynamics and Nonlinear Control
NASA Astrophysics Data System (ADS)
Walleczek, Jan
2006-04-01
The frontiers and challenges of biodynamics research Jan Walleczek; Part I. Nonlinear Dynamics in Biology and Response to Stimuli: 1. External signals and internal oscillation dynamics - principal aspects and response of stimulated rhythmic processes Friedemann Kaiser; 2. Nonlinear dynamics in biochemical and biophysical systems: from enzyme kinetics to epilepsy Raima Larter, Robert Worth and Brent Speelman; 3. Fractal mechanisms in neural control: human heartbeat and gait dynamics in health and disease Chung-Kang Peng, Jeffrey M. Hausdorff and Ary L. Goldberger; 4. Self-organising dynamics in human coordination and perception Mingzhou Ding, Yanqing Chen, J. A. Scott Kelso and Betty Tuller; 5. Signal processing in biochemical reaction networks Adam P. Arkin; Part II. Nonlinear Sensitivity of Biological Systems to Electromagnetic Stimuli: 6. Electrical signal detection and noise in systems with long-range coherence Paul C. Gailey; 7. Oscillatory signals in migrating neutrophils: effects of time-varying chemical and electrical fields Howard R. Petty; 8. Enzyme kinetics and nonlinear biochemical amplification in response to static and oscillating magnetic fields Jan Walleczek and Clemens F. Eichwald; 9. Magnetic field sensitivity in the hippocampus Stefan Engström, Suzanne Bawin and W. Ross Adey; Part III. Stochastic Noise-Induced Dynamics and Transport in Biological Systems: 10. Stochastic resonance: looking forward Frank Moss; 11. Stochastic resonance and small-amplitude signal transduction in voltage-gated ion channels Sergey M. Bezrukov and Igor Vodyanoy; 12. Ratchets, rectifiers and demons: the constructive role of noise in free energy and signal transduction R. Dean Astumian; 13. Cellular transduction of periodic and stochastic energy signals by electroconformational coupling Tian Y. Tsong; Part IV. Nonlinear Control of Biological and Other Excitable Systems: 14. Controlling chaos in dynamical systems Kenneth Showalter; 15. Electromagnetic fields and biological
Dynamic analysis of nonlinear rotor-housing systems
NASA Technical Reports Server (NTRS)
Noah, Sherif T.
1988-01-01
Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.
Nonlinearity in the dynamics of photoinduced nucleation process.
Ishida, Kunio; Nasu, Keiichiro
2008-03-21
Coherent nonlinear dynamics of photoinduced cooperative phenomena at 0 K is studied by numerical calculations on a model of molecular crystals. We found that the photoinduced nucleation process is triggered only when a certain amount of excitation energy is supplied in a narrow part of the system; i.e., there exists the smallest size of the cluster of excited molecules which makes the nucleation possible. As a result, the portion of the cooperatively converted molecules is nonlinearly dependent on the photoexcitation strength, which has been observed in various materials. PMID:18517805
Dynamic magnetic hysteresis and nonlinear susceptibility of antiferromagnetic nanoparticles
NASA Astrophysics Data System (ADS)
Kalmykov, Yuri P.; Ouari, Bachir; Titov, Serguey V.
2016-08-01
The nonlinear ac stationary response of antiferromagnetic nanoparticles subjected to both external ac and dc fields of arbitrary strength and orientation is investigated using Brown's continuous diffusion model. The nonlinear complex susceptibility and dynamic magnetic hysteresis (DMH) loops of an individual antiferromagnetic nanoparticle are evaluated and compared with the linear regime for extensive ranges of the anisotropy, the ac and dc magnetic fields, damping, and the specific antiferromagnetic parameter. It is shown that the shape and area of the DMH loops of antiferromagnetic particles are substantially altered by applying a dc field that permits tuning of the specific magnetic power loss in the nanoparticles.
An Energy Decaying Scheme for Nonlinear Dynamics of Shells
NASA Technical Reports Server (NTRS)
Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)
2000-01-01
A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.
Arithmetic coding as a non-linear dynamical system
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin; Vaidya, Prabhakar G.; Bhat, Kishor G.
2009-04-01
In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.
Online optimization of storage ring nonlinear beam dynamics
NASA Astrophysics Data System (ADS)
Huang, Xiaobiao; Safranek, James
2015-08-01
We propose to optimize the nonlinear beam dynamics of existing and future storage rings with direct online optimization techniques. This approach may have crucial importance for the implementation of diffraction limited storage rings. In this paper considerations and algorithms for the online optimization approach are discussed. We have applied this approach to experimentally improve the dynamic aperture of the SPEAR3 storage ring with the robust conjugate direction search method and the particle swarm optimization method. The dynamic aperture was improved by more than 5 mm within a short period of time. Experimental setup and results are presented.
On the nonlinear dynamics and control of large space structures
Modi, V.J.
1994-12-31
The paper reviews, using the Lagrangian approach, dynamics of flexible multibody systems, of contemporary interest, and their control. To begin with, a relatively general formulation for studying the dynamics and control of an arbitrary spacecraft with interconnected flexible bodies is developed accounting for thermal deflection, transient system properties, shift in the center of mass, shear deformations, rotary inertias and geometric nonlinearities. A rather self-contained, comprehensive, numerical algorithm using system as well as component modes follows which is applicable to a large class of spacecraft configurations. In particular, versatility of the approach is demonstrated through the dynamics and control studies aimed at the proposed Space Station and the associated mobile manipulator system.
Nonlinear analysis and dynamic structure in the energy market
NASA Astrophysics Data System (ADS)
Aghababa, Hajar
This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non
Parallel processors and nonlinear structural dynamics algorithms and software
NASA Technical Reports Server (NTRS)
Belytschko, Ted
1989-01-01
A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.
Nonlinearity of local dynamics promotes multi-chimeras
NASA Astrophysics Data System (ADS)
Omelchenko, Iryna; Zakharova, Anna; Hövel, Philipp; Siebert, Julien; Schöll, Eckehard
2015-08-01
Chimera states are complex spatio-temporal patterns in which domains of synchronous and asynchronous dynamics coexist in coupled systems of oscillators. We examine how the character of the individual elements influences chimera states by studying networks of nonlocally coupled Van der Pol oscillators. Varying the bifurcation parameter of the Van der Pol system, we can interpolate between regular sinusoidal and strongly nonlinear relaxation oscillations and demonstrate that more pronounced nonlinearity induces multi-chimera states with multiple incoherent domains. We show that the stability regimes for multi-chimera states and the mean phase velocity profiles of the oscillators change significantly as the nonlinearity becomes stronger. Furthermore, we reveal the influence of time delay on chimera patterns.
An experimental nonlinear low dynamic stiffness device for shock isolation
NASA Astrophysics Data System (ADS)
Francisco Ledezma-Ramirez, Diego; Ferguson, Neil S.; Brennan, Michael J.; Tang, Bin
2015-07-01
The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements.
The landscape of nonlinear structural dynamics: an introduction
Butlin, T.; Woodhouse, J.; Champneys, A. R.
2015-01-01
Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner’s guide to what hitherto might seem like a vast and complex research landscape. PMID:26303925
Photonic single nonlinear-delay dynamical node for information processing
NASA Astrophysics Data System (ADS)
Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel
2012-06-01
An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.
The landscape of nonlinear structural dynamics: an introduction.
Butlin, T; Woodhouse, J; Champneys, A R
2015-09-28
Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner's guide to what hitherto might seem like a vast and complex research landscape. PMID:26303925
Treatment of material creep and nonlinearities in flexible mulitbody dynamics
NASA Astrophysics Data System (ADS)
Xie, M.; Amirouche, F. M. L.
1994-01-01
This paper addresses the modeling of the generalized active forces resulting from deformable bodies when subjected to high temperature conditions, elastic-plastic deformations, creep effects, and material nonlinearities. The effects of elastic-plastic deformations are studied making use of the nonlinear stress-strain relationship and the geometrical stiffness concepts. Creep conditions resulting from high temperature are studied through several proposed models. Materials nonlinearities for isotropic and composites are accounted for by their tangential elasticity matrix. A general procedure used in the study of multibody systems dynamics with elastic-plastic bodies depicting the characteristics mentioned is developed. This includes an explicit formulation of the equations of motion using Kane's equations, finite element method, continuum mechanics, and modal coordinate reduction techniques. A numerical simulation of a flexible robotic arm with a prescribed angular velocity subject to high temperature conditions is analyzed. The effects of creep are discussed.
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. PMID:26707373
A nonlinear dynamic model of relaxation oscillations in tokamaks
NASA Astrophysics Data System (ADS)
Thyagaraja, A.; Haas, F. A.; Harvey, D. J.
1999-06-01
Tokamaks exhibit several types of relaxation oscillations such as sawteeth, fishbones and Edge Localized Modes (ELMs) under appropriate conditions. Several authors have introduced model nonlinear dynamic systems with a small number of degrees of freedom which can illustrate the generic characteristics of such oscillations. In these models, one focuses on physically "relevant" degrees of freedom, without attempting to simulate all the myriad details of the fundamentally nonlinear tokamak phenomena. Such degrees of freedom often involve the plasma macroscopic quantities such as pressure or density and also some measure of the plasma turbulence, which is thought to control transport. In addition, "coherent" modes may be involved in the dynamics of relaxation, as well as radial electric fields, sheared flows, etc. In the present work, an extension of an earlier sawtooth model (which involved only two degrees of freedom) due to the authors is presented. The dynamical consequences of a pressure-driven "coherent" mode, which interacts with the turbulence in a specific manner, are investigated. Varying only the two parameters related to the coherent mode, the bifurcation properties of the system have been studied. These turn out to be remarkably rich and varied and qualitatively similar to the behavior found experimentally in actual tokamaks. The dynamic model presented involves only continuous nonlinearities and is the simplest known to the authors that can yield features such as sawteeth, "compound sawteeth" with partial crashes, "monster" sawteeth, metastability, intermittency, chaos, periodic and "grassy" ELMing in appropriate regions of parameter space. The results suggest that linear stability analysis of systems, while useful in elucidating instability drives, can be misleading in understanding the dynamics of nonlinear systems over time scales much longer than linear growth times and states far from stable equilibria.
Nonlinear Network Dynamics on Earthquake Fault Systems
NASA Astrophysics Data System (ADS)
Rundle, P. B.; Rundle, J. B.; Tiampo, K. F.
2001-12-01
Understanding the physics of earthquakes is essential if large events are ever to be forecast. Real faults occur in topologically complex networks that exhibit cooperative, emergent space-time behavior that includes precursory quiescence or activation, and clustering of events. The purpose of this work is to investigate the sensitivity of emergent behavior of fault networks to changes in the physics on the scale of single faults or smaller. In order to investigate the effect of changes at small scales on the behavior of the network, we need to construct models of earthquake fault systems that contain the essential physics. A network topology is therefore defined in an elastic medium, the stress Green's functions (i.e. the stress transfer coefficients) are computed, frictional properties are defined and the system is driven via the slip deficit as defined below. The long-range elastic interactions produce mean-field dynamics in the simulations. We focus in this work on the major strike-slip faults in Southern California that produce the most frequent and largest magnitude events. To determine the topology and properties of the network, we used the tabulation of fault properties published in the literature. We have found that the statistical distribution of large earthquakes on a model of a topologically complex, strongly correlated real fault network is highly sensitive to the precise nature of the stress dissipation properties of the friction laws associated with individual faults. These emergent, self-organizing space-time modes of behavior are properties of the network as a whole, rather than of the individual fault segments of which the network is comprised (ref: PBR et al., Physical Review Letters, in press, 2001).
Nonlinear Alfvén wave dynamics in plasmas
NASA Astrophysics Data System (ADS)
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
The coupled nonlinear dynamics of a lift system
NASA Astrophysics Data System (ADS)
Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan
2014-12-01
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Nonlinear Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil
2015-07-15
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Dissipative effects in nonlinear Klein-Gordon dynamics
NASA Astrophysics Data System (ADS)
Plastino, A. R.; Tsallis, C.
2016-03-01
We consider dissipation in a recently proposed nonlinear Klein-Gordon dynamics that admits exact time-dependent solutions of the power-law form e_qi(kx-wt) , involving the q-exponential function naturally arising within the nonextensive thermostatistics (e_qz \\equiv [1+(1-q)z]1/(1-q) , with e_1^z=ez ). These basic solutions behave like free particles, complying, for all values of q, with the de Broglie-Einstein relations p=\\hbar k , E=\\hbar ω and satisfying a dispersion law corresponding to the relativistic energy-momentum relation E2 = c^2p2 + m^2c4 . The dissipative effects explored here are described by an evolution equation that can be regarded as a nonlinear generalization of the celebrated telegraph equation, unifying within one single theoretical framework the nonlinear Klein-Gordon equation, a nonlinear Schrödinger equation, and the power-law diffusion (porous-media) equation. The associated dynamics exhibits physically appealing traveling solutions of the q-plane wave form with a complex frequency ω and a q-Gaussian square modulus profile.
Nonlinear dynamics in eccentric Taylor-Couette-Poiseuille flow
NASA Astrophysics Data System (ADS)
Pier, Benoît; Caulfield, C. P.
2015-11-01
The flow in the gap between two parallel but eccentric cylinders and driven by an axial pressure gradient and inner cylinder rotation is characterized by two geometrical parameters (radius ratio and eccentricity) and two dynamic parameters (axial and azimuthal Reynolds numbers). Such a theoretical configuration is a model for the flow between drill string and wellbore in the hydrocarbon drilling industry. The linear convective and absolute instability properties have been systematically derived in a recent study [Leclercq, Pier & Scott, J. Fluid Mech. 2013 and 2014]. Here we address the nonlinear dynamics resulting after saturation of exponentially growing small-amplitude perturbations. By using direct numerical simulations, a range of finite-amplitude states are found and characterized: nonlinear traveling waves (an eccentric counterpart of Taylor vortices, associated with constant hydrodynamic loading on the inner cylinder), modulated nonlinear waves (with time-periodic torque and flow rate) and more irregular states. In the nonlinear regime, the hydrodynamic forces are found to depart significantly from those prevailing for the base flow, even in situations of weak linear instability.
The coupled nonlinear dynamics of a lift system
Crespo, Rafael Sánchez E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Picton, Phil E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk
2014-12-10
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Dynamics of nonlinear excitations of helically confined charges
NASA Astrophysics Data System (ADS)
Zampetaki, A. V.; Stockhofe, J.; Schmelcher, P.
2015-10-01
We explore the long-time dynamics of a system of identical charged particles trapped on a closed helix. This system has recently been found to exhibit an unconventional deformation of the linear spectrum when tuning the helix radius. Here we show that the same geometrical parameter can affect significantly also the dynamical behavior of an initially broad excitation for long times. In particular, for small values of the radius, the excitation disperses into the whole crystal whereas within a specific narrow regime of larger radii the excitation self-focuses, assuming finally a localized form. Beyond this regime, the excitation defocuses and the dispersion gradually increases again. We analyze this geometrically controlled nonlinear behavior using an effective discrete nonlinear Schrödinger model, which allows us among others to identify a number of breatherlike excitations.
Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas
Hnat, B.
2011-09-22
Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.
Quantum simulations of nonlinear resonance and torsional dynamics
NASA Astrophysics Data System (ADS)
Collins, Michael A.; Schranz, Harold W.
1994-02-01
A simple model of the vibrational dynamics of ABBA type sequentially bonded tetra-atomic molecules is investigated by quantum mechanical methods. The model Hamiltonian excludes bond stretching and asymmetric bending but includes the kinematic coupling between the torsional motion and symmetric bond bending which results in nonlinear resonances. The effect of this coupling on energy levels and the timescale of intramolecular energy transfer is evaluated and discussed in terms of both resonant and nonresonant effects.
Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas
NASA Astrophysics Data System (ADS)
Hnat, B.
2011-09-01
Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.
Nonlinear dynamic behavior of microscopic bubbles near a rigid wall
NASA Astrophysics Data System (ADS)
Suslov, Sergey A.; Ooi, Andrew; Manasseh, Richard
2012-06-01
The nonlinear dynamic behavior of microscopic bubbles near a rigid wall is investigated. Oscillations are driven by the ultrasonic pressure field that arises in various biomedical applications such as ultrasound imaging or targeted drug delivery. It is known that, when bubbles approach a blood-vessel wall, their linear dynamic response is modified. This modification may be very useful for real-time detection of bubbles that have found targets; in future therapeutic technologies, it may be useful for controlled release of medical agents encapsulating microbubbles. In this paper, the nonlinear response of microbubbles near a wall is studied. The Keller-Miksis-Parlitz equation is adopted, but modified to account for the presence of a rigid wall. This base model describes the time evolution of the bubble surface, which is assumed to remain spherical, and accounts for the effect of acoustic radiation losses owing to liquid compressibility in the momentum conservation. Two situations are considered: the base case of an isolated bubble in an unbounded medium, and a bubble near a rigid wall. In the latter case, the wall influence is modeled by including a symmetrically oscillating image bubble. The bubble dynamics is traced using a numerical solution of the model equation. Subsequently, Floquet theory is used to accurately detect the bifurcation point where bubble oscillations stop following the driving ultrasound frequency and undergo period-changing bifurcations. Of particular interest is the detection of the subcritical period-tripling and -quadrupling transition. The parametric bifurcation maps are obtained as functions of nondimensional parameters representing the bubble radius, the frequency and pressure amplitude of the driving ultrasound field, and the distance from the wall. It is shown that the presence of the wall generally stabilises the bubble dynamics, so that much larger values of the pressure amplitude are needed to generate nonlinear responses. Thus, a
Application of bifurcation methods to nonlinear flight dynamics problems
NASA Astrophysics Data System (ADS)
Goman, M. G.; Zagainov, G. I.; Khramtsovsky, A. V.
Applications of global stability and bifurcational analysis methods are presented for different nonlinear flight dynamics problems, such as roll-coupling, stall, spin, etc. Based on the results for different real aircraft, F-4, F-14, F-15, High Incidence Research Model, (HIRM), the general methods developed by many authors are presented. The outline of basic concepts and methods from dynamcal system theory are also introduced.
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
Nonlinear Delayed Differential Dynamics for Encryption Using Chaos
NASA Astrophysics Data System (ADS)
Larger, Laurent; Goedgebuer, Jean-Pierre; Lee, Min Won
2003-08-01
Nonlinear time-delayed differential dynamics are knowing an increasing interest, especially in the area of encryption using chaos. Such dynamics are also met in many other fields, such as mechanics, biology, medicine and optics. In the frame of high dimensional chaotic encryption systems, we have explored several nonlinear oscillators in optics and electronics ruled by nonlinear delayed (or difference) differential equations. After a presentation of the general architecture of such systems, we describe four different experimental set-ups, which are operating respectively with the wavelength of a tunable laser diode, the optical intensity at the output of an integrated electro-optic Mach-Zehnder, the optical path-difference in a coherence modulation scheme, and the electronic frequency at the output of a voltage-controlled oscillator. Numerical bifurcation diagrams are compared with experimental ones, and various dynamical properties are discussed, such as entropy, Lyapunov dimension, time behavior statistics, and spectral properties. Recent developments are also discussed in the view of improving the performances of chaos generators in encryption systems.
Selecting Earthquake Records for Nonlinear Dynamic Analysis of Structures
Rodriguez, Mario E.
2008-07-08
An area in earthquake risk reduction that needs an urgent examination is the selection of earthquake records for nonlinear dynamic analysis of structures. An often-mentioned shortcoming from results of nonlinear dynamic analyses of structures is that these results are limited to the type of records that these analyses use as input data. This paper proposes a procedure for selecting earthquake records for nonlinear dynamic analysis of structures. This procedure uses a seismic damage index evaluated using the hysteretic energy dissipated by a Single Degree of Freedom System (SDOF) representing a multi-degree-of freedom structure responding to an earthquake record, and the plastic work capacity of the system at collapse. The type of structural system is considered using simple parameters. The proposed method is based on the evaluation of the damage index for a suite of earthquake records and a selected type of structural system. A set of 10 strong ground motion records is analyzed to show an application of the proposed procedure for selecting earthquake records for structural design.
Classical black holes: the nonlinear dynamics of curved spacetime.
Thorne, Kip S
2012-08-01
Numerical simulations have revealed two types of physical structures, made from curved spacetime, that are attached to black holes: tendexes, which stretch or squeeze anything they encounter, and vortexes, which twist adjacent inertial frames relative to each other. When black holes collide, their tendexes and vortexes interact and oscillate (a form of nonlinear dynamics of curved spacetime). These oscillations generate gravitational waves, which can give kicks up to 4000 kilometers per second to the merged black hole. The gravitational waves encode details of the spacetime dynamics and will soon be observed and studied by the Laser Interferometer Gravitational Wave Observatory and its international partners. PMID:22859479
Nonlinear slew maneuver dynamics of large flexible spacecrafts
NASA Technical Reports Server (NTRS)
Kakad, Y. P.
1990-01-01
In this paper, the dynamics of three-dimensional, large-angle arbitrary slew maneuvers of a large flexible spacecraft are developed. The dynamical equations obtained allow maneuver specifications about any axis and are highly nonlinear. They also include coupling between the rigid orbiter and the flexible appendage and correction for motion stiffness. A decentralized control scheme is utilized for performing the maneuver of the rigidized body and for vibration suppression of the flexible appendage. The method developed in this paper is further applied to NASA Spacecraft Control Laboratory Experiment (SCOLE) test facility.
Predicting catastrophes in nonlinear dynamical systems by compressive sensing
Wang, Wen-Xu; Yang, Rui; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso
2013-01-01
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea and potential challenges are discussed. PMID:21568562
Nonlinear dynamics, fractals, cardiac physiology and sudden death
NASA Technical Reports Server (NTRS)
Goldberger, Ary L.
1987-01-01
The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.
Nonlinear dynamics induced anomalous Hall effect in topological insulators
Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng
2016-01-01
We uncover an alternative mechanism for anomalous Hall effect. In particular, we investigate the magnetisation dynamics of an insulating ferromagnet (FM) deposited on the surface of a three-dimensional topological insulator (TI), subject to an external voltage. The spin-polarised current on the TI surface induces a spin-transfer torque on the magnetisation of the top FM while its dynamics can change the transmission probability of the surface electrons through the exchange coupling and hence the current. We find a host of nonlinear dynamical behaviors including multistability, chaos, and phase synchronisation. Strikingly, a dynamics mediated Hall-like current can arise, which exhibits a nontrivial dependence on the channel conductance. We develop a physical understanding of the mechanism that leads to the anomalous Hall effect. The nonlinear dynamical origin of the effect stipulates that a rich variety of final states exist, implying that the associated Hall current can be controlled to yield desirable behaviors. The phenomenon can find applications in Dirac-material based spintronics. PMID:26819223
Nonlinear dynamics induced anomalous Hall effect in topological insulators
NASA Astrophysics Data System (ADS)
Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng
2016-01-01
We uncover an alternative mechanism for anomalous Hall effect. In particular, we investigate the magnetisation dynamics of an insulating ferromagnet (FM) deposited on the surface of a three-dimensional topological insulator (TI), subject to an external voltage. The spin-polarised current on the TI surface induces a spin-transfer torque on the magnetisation of the top FM while its dynamics can change the transmission probability of the surface electrons through the exchange coupling and hence the current. We find a host of nonlinear dynamical behaviors including multistability, chaos, and phase synchronisation. Strikingly, a dynamics mediated Hall-like current can arise, which exhibits a nontrivial dependence on the channel conductance. We develop a physical understanding of the mechanism that leads to the anomalous Hall effect. The nonlinear dynamical origin of the effect stipulates that a rich variety of final states exist, implying that the associated Hall current can be controlled to yield desirable behaviors. The phenomenon can find applications in Dirac-material based spintronics.
Nonlinear dynamics induced anomalous Hall effect in topological insulators.
Wang, Guanglei; Xu, Hongya; Lai, Ying-Cheng
2016-01-01
We uncover an alternative mechanism for anomalous Hall effect. In particular, we investigate the magnetisation dynamics of an insulating ferromagnet (FM) deposited on the surface of a three-dimensional topological insulator (TI), subject to an external voltage. The spin-polarised current on the TI surface induces a spin-transfer torque on the magnetisation of the top FM while its dynamics can change the transmission probability of the surface electrons through the exchange coupling and hence the current. We find a host of nonlinear dynamical behaviors including multistability, chaos, and phase synchronisation. Strikingly, a dynamics mediated Hall-like current can arise, which exhibits a nontrivial dependence on the channel conductance. We develop a physical understanding of the mechanism that leads to the anomalous Hall effect. The nonlinear dynamical origin of the effect stipulates that a rich variety of final states exist, implying that the associated Hall current can be controlled to yield desirable behaviors. The phenomenon can find applications in Dirac-material based spintronics. PMID:26819223
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Nonlinear dynamics of dipoles in microtubules: Pseudospin model
NASA Astrophysics Data System (ADS)
Nesterov, Alexander I.; Ramírez, Mónica F.; Berman, Gennady P.; Mavromatos, Nick E.
2016-06-01
We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frame of the classical pseudospin model. We derive the system of nonlinear dynamical partial differential equations of motion for interacting dipoles and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to achieve a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.
Intertwining Risk Insights and Design Decisions
NASA Technical Reports Server (NTRS)
Cornford, Steven L.; Feather, Martin S.; Jenkins, J. Steven
2006-01-01
The state of systems engineering is such that a form of early and continued use of risk assessments is conducted (as evidenced by NASA's adoption and use of the 'Continuous Risk Management' paradigm developed by SEI). ... However, these practices fall short of theideal: (1) Integration between risk assessment techniques and other systems engineering tools is weak. (2) Risk assessment techniques and the insights they yield are only informally coupled to design decisions. (3) Individual riskassessment techniques lack the mix of breadth, fidelity and agility required to span the gamut of the design space. In this paper we present an approach that addresses these shortcomings. The hallmark of our approach is a simple representation comprising objectives (what the system is to do), risks (whose occurrence would detract from attainment of objectives) and activities (a.k.a. 'mitigations') that, if performed, will decrease those risks. These are linked to indicate by how much a risk would detract from attainment of an objective, and by how much an activity would reduce a risk. The simplicity of our representational framework gives it the breadth to encompass the gamut of the design space concerns, the agility to be utilized in even the earliest phases of designs, and the capability to connect to system engineering models and higher-fidelity risk tools. It is through this integration that we address the shortcomings listed above, and so achieve the intertwining between risk insights and design decisions needed to guide systems engineering towards superior final designs while avoiding costly rework to achieve them. The paper will use an example, constructed to be representative of space mission design, to illustrate our approach.
Nonlinear strain-displacement relations and flexible multibody dynamics
NASA Technical Reports Server (NTRS)
Padilla, Carlos E.; Vonflotow, Andreas H.
1989-01-01
Dynamics of chains of flexible bodies undergoing large rigid body motions, but small elastic deflections are considered. The role of nonlinear strain-displacement relations in the development of the motion equations correct to first order in elastic deflections is investigated. The general form of these equations linearized only in the small elastic deflections is presented, and the relative significance of various nonlinear terms is studied both analytically and through the use of the numerical simulations. Numerical simulations are performed for a two link chain constrained to move in the plane, subject to hinge torques. Each link is modeled as a thin beam. Slew maneuver simulation results are compared for models with and without properly modeled kinematics of deformation. The goal of this case study is to quantify the importance of the terms in the equations of motion which arise from the inclusion of nonlinear strain-displacement relations. It is concluded that unless the consistently linearized equations in elastic deflections and speeds are available and necessary, the inconsistently (prematurely) linearized equations should be replaced in all cases by ruthlessly linearized equations: equations in which all nonlinear terms involving the elastic deflections and speeds are ignored.
Dynamical Nonlinear Interactions of Solids with Strong Terahertz Pulses
NASA Astrophysics Data System (ADS)
Hirori, Hideki; Tanaka, Koichiro
2016-08-01
Table-top high-power terahertz (THz) pulse sources based on the femtosecond lasers are able to reveal fascinating nonlinear transport phenomena in materials and coherently drive low-energy transitions into the nonperturbative nonlinear regime. This article summarizes recent studies on THz nonlinear interactions with solid materials as follows. The tilted-pump-intensity-front scheme uses a LiNbO3 crystal to generate high-field single-cycle THz pulses with a 1 MV/cm amplitude. Such a high amplitude pulse can cause impact ionization in GaAs that excites electrons from the valence band to the conduction band, leading to exciton luminescence. A narrow-bandwidth THz pulse can be generated by using a chirped-pulse-beating method; this scheme has been used to show that resonant intraexcitonic excitation in GaAs induces a large Autler-Townes splitting. Moreover, nonlinear dynamics of magnetism can be studied by using a metallic split ring resonator to enhance the THz magnetic field.
Effect of dynamical friction on nonlinear energetic particle modes
Lilley, M. K.; Breizman, B. N.; Sharapov, S. E.
2010-09-15
A fully nonlinear model is developed for the bump-on-tail instability including the effects of dynamical friction (drag) and velocity space diffusion on the energetic particles driving the wave. The results show that drag provides a destabilizing effect on the nonlinear evolution of waves. Specifically, in the early nonlinear phase of the instability, the drag facilitates the explosive scenario of the wave evolution, leading to the creation of phase space holes and clumps that move away from the original eigenfrequency. Later in time, the electric field associated with a hole is found to be enhanced by the drag, whereas for a clump it is reduced. This leads to an asymmetry of the frequency evolution between holes and clumps. The combined effect of drag and diffusion produces a diverse range of nonlinear behaviors including hooked frequency chirping, undulating, and steady state regimes. An analytical model is presented, which explains the aforementioned diversity. A continuous production of hole-clump pairs in the absence of collisions is also observed.
Optimal spatiotemporal reduced order modeling for nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
LaBryer, Allen
Proposed in this dissertation is a novel reduced order modeling (ROM) framework called optimal spatiotemporal reduced order modeling (OPSTROM) for nonlinear dynamical systems. The OPSTROM approach is a data-driven methodology for the synthesis of multiscale reduced order models (ROMs) which can be used to enhance the efficiency and reliability of under-resolved simulations for nonlinear dynamical systems. In the context of nonlinear continuum dynamics, the OPSTROM approach relies on the concept of embedding subgrid-scale models into the governing equations in order to account for the effects due to unresolved spatial and temporal scales. Traditional ROMs neglect these effects, whereas most other multiscale ROMs account for these effects in ways that are inconsistent with the underlying spatiotemporal statistical structure of the nonlinear dynamical system. The OPSTROM framework presented in this dissertation begins with a general system of partial differential equations, which are modified for an under-resolved simulation in space and time with an arbitrary discretization scheme. Basic filtering concepts are used to demonstrate the manner in which residual terms, representing subgrid-scale dynamics, arise with a coarse computational grid. Models for these residual terms are then developed by accounting for the underlying spatiotemporal statistical structure in a consistent manner. These subgrid-scale models are designed to provide closure by accounting for the dynamic interactions between spatiotemporal macroscales and microscales which are otherwise neglected in a ROM. For a given resolution, the predictions obtained with the modified system of equations are optimal (in a mean-square sense) as the subgrid-scale models are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. Methods are suggested for efficient model construction, appraisal, error measure, and implementation with a couple of well-known time
Alfven soliton and multisoliton dynamics perturbed by nonlinear Landau damping
Sanchez-Arriaga, G.
2010-08-15
The evolution of weakly dispersive nonlinear Alfven waves propagating either parallel or oblique to the ambient magnetic field is investigated through the derivative nonlinear Schroedinger equation (DNLS) perturbed by nonlinear Landau damping. The dynamics is analyzed with the aid of a numeric algorithm based on the inverse scattering transform (IST) and an adiabatic model that takes advantages of the perturbed DNLS invariants. Both techniques are applied to five types of DNLS soliton and multisoliton solutions: (i) the parallel Alfven soliton, (ii) the bright and dark one-parameter oblique, (iii) the breather two-parameter oblique, (iv) two parallel Alfven solitons, and (v) the combination of a dark and a bright oblique solitons. For the parallel solitons, the adiabatic model describes correctly the dynamics and it also recovers the well-known result given by the perturbed IST. Due to the radiation emission and the formation of dark solitons, the behavior of oblique solitons is more complicated and multisoliton solutions are required in the adiabatic model. The analysis shows that parallel solitons develop into the normal regime, whereas the oblique waves leads to the formation of dark solitons and breathers with a wavepacket form.
Success Stories in Control: Nonlinear Dynamic Inversion Control
NASA Technical Reports Server (NTRS)
Bosworth, John T.
2010-01-01
NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.
Nonlinear dynamic behaviors of a floating structure in focused waves
NASA Astrophysics Data System (ADS)
Cao, Fei-feng; Zhao, Xi-zeng
2015-12-01
Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.
Telescopic systems with dynamic nonlinear optical correction for distortions
Vasil'ev, Michail V; Venediktov, Vladimir Yu; Leshchev, Alexey A
2001-01-31
The review of basic achievements in the field of non-linear adaptive optics is presented. In particular, schematics and properties of adaptive optical telescopes considered in which the image distortions introduced by defects of the primary mirror and other optical elements are compensated by nonlinear optical methods. The conventional methods of laser optics, such as phase conjugation and dynamic holography, make it possible both to solve the problems of classical (imaging) optics related to the building of telescopes for imaging remote objects with high resolution, which are based on large, light-weight or sectional mirrors, and create the systems that produce laser beams with the high-quality wave front. The basic designs of such telescopes are considered and the possibilities of corrections for distortions in them are analysed and confirmed by experiments. (review)
Emergent geometries and nonlinear-wave dynamics in photon fluids
Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.
2016-01-01
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level. PMID:27001128
Nonlinear dynamics of absorption and photobleaching of dyes
NASA Astrophysics Data System (ADS)
Serra, Francesca; Terentjev, Eugene M.
2008-06-01
The celebrated Lambert-Beer law of light absorption in photochromic media is only valid at low intensities of incident light and low concentration of chromophore. Here we address the generic problem of photoabsorption dynamics, experimentally studying the case of azobenzene isomerization. We show that the nonlinear regime is very common and easy to achieve in many practical situations, especially in thick samples where the light depletes the chromophore in the first layers and can propagate through the medium with a subexponential law. This result holds not only for azobenzene isomerization but for all photochromic processes. Importantly, the crossover into the nonlinear absorption regime only weakly depends on the dye concentration and solution viscosity. We experimentally quantify the characteristics of this peculiar optical response and determine the key transition rate constants.
Nonlinear dynamics of optical absorption of intense beams
NASA Astrophysics Data System (ADS)
Corbett, D.; van Oosten, C. L.; Warner, M.
2008-07-01
On traversing materials with absorbing dyes, weak optical beams decay exponentially (a Beer profile), while intense beams develop in time a profile that is spatially linear until at great depth it becomes spatially exponential. This anomalous, deep penetration, due to photobleaching of surface layers, is important for heavy dye loading and intense beams, for instance in photo-actuation. We address the problem of the evolution in time from initial Beer’s Law to a finally deeply-penetrating optical profile in dyes. Our largely analytic solution of the coupled, nonlinear, partial differential equations governing the spatiotemporal decay of the Poynting flux and the nonlinear population dynamics of the photo-active molecules under intense irradiation has application to optomechanical devices.
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-01-01
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level. PMID:27001128
Dynamics of the antiplane strain of a nonlinear elastic body
NASA Astrophysics Data System (ADS)
Bondar', B. D.
2015-07-01
The dynamic antiplane strain of an incompressible cylindrical body is studied in a nonlinear formulation in actual variables. A representation of the velocity and acceleration through the displacement is obtained. The problem of the body deformation with account for geometrical and physical nonlinearities is reduced to an initial boundary-value problem for the displacement. The displacement found is used to determine the pressure and stresses. For a body with a quadratic elastic potential, plane waves and self-similar motion are studied. The linear potential is used to investigate the deformation of a hollow elliptical cylinder for which analytical expressions for displacement and stresses are found and the external load is determined. It is shown that, due to the degeneration of the inner cavity of the body to a plane section, the load on the section remains limited.
On-line control of the nonlinear dynamics for synchrotrons
NASA Astrophysics Data System (ADS)
Bengtsson, J.; Martin, I. P. S.; Rowland, J. H.; Bartolini, R.
2015-07-01
We propose a simple approach to the on-line control of the nonlinear dynamics in storage rings, based on compensation of the nonlinear resonance driving terms using beam losses as the main indicator of the strength of a resonance. The correction scheme is built on the analysis of the resonance driving terms in first perturbative order and on the possibility of using independent power supplies in the sextupole magnets, which is nowadays present in many synchrotron light sources. Such freedom allows the definition of "smart sextupole knobs" attacking each resonance separately. The compensation scheme has been tested at the Diamond light source and proved to be effective in opening up the betatron tune space, resonance free, available to the electron beam and to improve the beam lifetime.
Swarming behaviors in multi-agent systems with nonlinear dynamics
Yu, Wenwu; Chen, Guanrong; Cao, Ming; Lü, Jinhu; Zhang, Hai-Tao
2013-12-15
The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.
Emergent geometries and nonlinear-wave dynamics in photon fluids
NASA Astrophysics Data System (ADS)
Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.
2016-03-01
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.
Nonlinear dynamic phase contrast microscopy for microfluidic and microbiological applications
NASA Astrophysics Data System (ADS)
Denz, C.; Holtmann, F.; Woerdemann, M.; Oevermann, M.
2008-08-01
In live sciences, the observation and analysis of moving living cells, molecular motors or motion of micro- and nano-objects is a current field of research. At the same time, microfluidic innovations are needed for biological and medical applications on a micro- and nano-scale. Conventional microscopy techniques are reaching considerable limits with respect to these issues. A promising approach for this challenge is nonlinear dynamic phase contrast microscopy. It is an alternative full field approach that allows to detect motion as well as phase changes of living unstained micro-objects in real-time, thereby being marker free, without contact and non destructive, i.e. fully biocompatible. The generality of this system allows it to be combined with several other microscope techniques such as conventional bright field or fluorescence microscopy. In this article we will present the dynamic phase contrast technique and its applications in analysis of micro organismic dynamics, micro flow velocimetry and micro-mixing analysis.
Nonlinear dynamics of a ball rolling on a surface
NASA Astrophysics Data System (ADS)
Virgin, L. N.; Lyman, T. C.; Davis, R. B.
2010-03-01
An underlying potential energy function can provide visual and intuitive insight into a system's stability and overall behavior. In particular, the motion of a ball moving along a curve or surface in a gravitational field provides a macroscale demonstration of interesting dynamics. We investigate the motion of a small ball rolling along a smooth two-dimensional potential surface. A direct experimental realization of this situation is suitable for demonstrating some classic features of nonlinear dynamics. The results of numerical simulations are directly compared with experimental data. To better characterize the dynamical behavior of the ball, especially when it is undergoing chaotic motion, several descriptive measures are discussed, including time-lag embedding, initial condition maps, power spectra, Lyapunov exponents, and fractal dimensions.
Dynamical Approach Study of Spurious Numerics in Nonlinear Computations
NASA Technical Reports Server (NTRS)
Yee, H. C.; Mansour, Nagi (Technical Monitor)
2002-01-01
The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.
SLOW DYNAMICS EXPERIMENTS IN SOLIDS WITH NONLINEAR MESOSCOPIC ELASTICITY
J. TEN CATE; ET AL
1999-09-01
As revealed by longitudinal bar resonance experiments, materials such as rocks and concrete show a rich diversity of nonlinear elastic behavior. As a function of increasing drive level, resonance frequencies shift downward by several percent, the resonant line shape changes, and harmonics and slow dynamics appear. Slow dynamics [1] refers to the time-dependent recovery of an elastic modulus to its initial value after being softened by large strain. In order to explore the mechanisms of nonlinear response including slow dynamics, we performed experiments on concrete and several different earth materials. The softening (conditioning) and recovery processes appear to be asymmetric. Conditioning takes place quickly; full recovery of the elastic modulus (as measured by drift of the resonance peak) takes minutes to hours, depending on the length of time the conditioning strain was applied. We find that for a wide variety of rocks and concretes, the recovery of the resonant frequency goes as log(time). Logarithmic time-dependence is a phenomenon associated with static friction and restoration of surface contacts, which in rocks probably takes place at touching crack surfaces.
Nonlinear Dynamic Theory of Acute Cell Injuries and Brain Ischemia
NASA Astrophysics Data System (ADS)
Taha, Doaa; Anggraini, Fika; Degracia, Donald; Huang, Zhi-Feng
2015-03-01
Cerebral ischemia in the form of stroke and cardiac arrest brain damage affect over 1 million people per year in the USA alone. In spite of close to 200 clinical trials and decades of research, there are no treatments to stop post-ischemic neuron death. We have argued that a major weakness of current brain ischemia research is lack of a deductive theoretical framework of acute cell injury to guide empirical studies. A previously published autonomous model based on the concept of nonlinear dynamic network was shown to capture important facets of cell injury, linking the concept of therapeutic to bistable dynamics. Here we present an improved, non-autonomous formulation of the nonlinear dynamic model of cell injury that allows multiple acute injuries over time, thereby allowing simulations of both therapeutic treatment and preconditioning. Our results are connected to the experimental data of gene expression and proteomics of neuron cells. Importantly, this new model may be construed as a novel approach to pharmacodynamics of acute cell injury. The model makes explicit that any pro-survival therapy is always a form of sub-lethal injury. This insight is expected to widely influence treatment of acute injury conditions that have defied successful treatment to date. This work is supported by NIH NINDS (NS081347) and Wayne State University President's Research Enhancement Award.
Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics
NASA Technical Reports Server (NTRS)
Zhu, Yanqui; Cohn, Stephen E.; Todling, Ricardo
1999-01-01
The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
Nonlinear dynamics of drift structures in a magnetized dissipative plasma
Aburjania, G. D.; Rogava, D. L.; Kharshiladze, O. A.
2011-06-15
A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense
Nonlinear dynamic theory for photorefractive phase hologram formation
NASA Technical Reports Server (NTRS)
Kim, D. M.; Shah, R. R.; Rabson, T. A.; Tittle, F. K.
1976-01-01
A nonlinear dynamic theory is developed for the formation of photorefractive volume phase holograms. A feedback mechanism existing between the photogenerated field and free-electron density, treated explicitly, yields the growth and saturation of the space-charge field in a time scale characterized by the coupling strength between them. The expression for the field reduces in the short-time limit to previous theories and approaches in the long-time limit the internal or photovoltaic field. Additionally, the phase of the space charge field is shown to be time-dependent.
Coupled nonlinear aeroelasticity and flight dynamics of fully flexible aircraft
NASA Astrophysics Data System (ADS)
Su, Weihua
This dissertation introduces an approach to effectively model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircraft. A reduced-order, nonlinear, strain-based finite element framework is used, which is capable of assessing the fundamental impact of structural nonlinear effects in preliminary vehicle design and control synthesis. The cross-sectional stiffness and inertia properties of the wings are calculated along the wing span, and then incorporated into the one-dimensional nonlinear beam formulation. Finite-state unsteady subsonic aerodynamics is used to compute airloads along lifting surfaces. Flight dynamic equations are then introduced to complete the aeroelastic/flight dynamic system equations of motion. Instead of merely considering the flexibility of the wings, the current work allows all members of the vehicle to be flexible. Due to their characteristics of being slender structures, the wings, tail, and fuselage of highly flexible aircraft can be modeled as beams undergoing three dimensional displacements and rotations. New kinematic relationships are developed to handle the split beam systems, such that fully flexible vehicles can be effectively modeled within the existing framework. Different aircraft configurations are modeled and studied, including Single-Wing, Joined-Wing, Blended-Wing-Body, and Flying-Wing configurations. The Lagrange Multiplier Method is applied to model the nodal displacement constraints at the joint locations. Based on the proposed models, roll response and stability studies are conducted on fully flexible and rigidized models. The impacts of the flexibility of different vehicle members on flutter with rigid body motion constraints, flutter in free flight condition, and roll maneuver performance are presented. Also, the static stability of the compressive member of the Joined-Wing configuration is studied. A spatially-distributed discrete gust model is incorporated into the time simulation
Predicting dynamic performance limits for servosystems with saturating nonlinearities
NASA Technical Reports Server (NTRS)
Webb, J. A., Jr.; Blech, R. A.
1979-01-01
A generalized treatment for a system with a single saturating nonlinearity is presented and compared with frequency response plots obtained from an analog model of the system. Once the amplitude dynamics are predicted with the limit lines, an iterative technique is employed to determine the system phase response. The saturation limit line technique is used in conjunction with velocity and acceleration limits to predict the performance of an electro-hydraulic servosystem containing a single-stage servovalve. Good agreement was obtained between predicted performance and experimental data.
Nonlinear dynamics of global atmospheric and earth system processes
NASA Technical Reports Server (NTRS)
Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu
1995-01-01
During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.
Barothropic relaxing media under pressure perturbations: Nonlinear dynamics
NASA Astrophysics Data System (ADS)
Kuetche, Victor K.
2015-12-01
In this paper, we delve into the dynamics of a barothropic relaxing medium under pressure perturbations originating from blast wave explosions in the milieu. Analyzing the problem within the viewpoint of the Lyakhov formalism of geodynamic systems, we derive a complex-valued nonlinear evolution equation which models the wave propagation of the pressure perturbations within the barothropic medium. As a result, we find that the previous system can be circularly polarized and hence support traveling rotating pressure excitations which profiles strongly depend upon their angular momenta. In the wake of these results, we address some physical implications of the findings alongside their potential applications.
Nonlinear complex dynamics and Keynesian rigidity: A short introduction
NASA Astrophysics Data System (ADS)
Jovero, Edgardo
2005-09-01
The topic of this paper is to show that the greater acceptance and intense use of complex nonlinear dynamics in macroeconomics makes sense only within the neoKeynesian tradition. An example is presented regarding the behavior of an open-economy two-sector growth model endowed with Keynesian rigidity. The Keynesian view that structural instability globally exists in the aggregate economy is put forward, and therefore the need arises for policy to alleviate this instability in the form of dampened fluctuations is presented as an alternative view for macroeconomic theorizing.
Nonlinear dynamic analysis of quasi-symmetric anisotropic structures
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1987-01-01
An efficient computational method for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures is proposed. The application of mixed models simplifies the analytical development and improves the accuracy of the response predictions, and operator splitting allows the reduction of the analysis model of the quasi-symmetric structure to that of the corresponding symmetric structure. The preconditoned conjugate gradient provides a stable and effective technique for generating the unsymmetric response of the structure as the sum of a symmetrized response plus correction modes. The effectiveness of the strategy is demonstrated with the example of a laminated anisotropic shallow shell of quadrilateral planform subjected to uniform normal loading.
Nonlinear dynamics of a stack/cable system
Cai, Y.; Chen, S.S.
1995-07-01
In this study, we developed a coupled model of wind-induced vibration of a stack, based on an unsteady-flow theory and nonlinear dynamics of the stack`s heavy elastic suspended cables. Numerical analysis was performed to identify excitation mechanisms. The stack was found to be excited by vortex shedding. Once lock-in resonance occurred, the cables were excited by the transverse motion of the stack. Large-amplitude oscillations of the cables were due to parametric resonance. Appropriate techniques have been proposed to alleviate the vibration problem.
Non-Linear Dynamics of Saturn’s Rings
NASA Astrophysics Data System (ADS)
Esposito, Larry W.
2015-11-01
Non-linear processes can explain why Saturn’s rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. We find that stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, pushing the system across thresholds that lead to persistent states.Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity, and allows aggregates to grow. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit.Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like ‘straw’ that can explain the halo structure and spectroscopy: This requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping at perturbed regions in Saturn’s rings creates both high velocity dispersion and large aggregates at these distances, explaining both small and large particles observed there. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating the Markov chain as an asymmetric random walk with reflecting boundaries allows us to determine the power law index from results of numerical simulations in the tidal environment surrounding Saturn. Aggregates can explain many dynamic aspects
Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems
NASA Astrophysics Data System (ADS)
Mikhlin, Yu V.; Perepelkin, N. V.; Klimenko, A. A.; Harutyunyan, E.
2012-08-01
Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.
Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials
NASA Astrophysics Data System (ADS)
Tankeyev, A. P.; Smagin, V. V.; Borich, M. A.; Zhuravlev, A. S.
2009-03-01
Within the framework of the extended nonlinear Schrödinger equation (ENSE), two types of nonlinear states of magnetization in a ferromagnet-dielectric-metal metamagnetic structure have been obtained and investigated. These states have an internal structure; e.g., a periodic sequence of compound solitons is formed by kink-antikink pairs (shock waves), and coherent periodic breather structures are formed by “bright” quasi-solitons. Conditions have been found under which the envelope of these states is described by a modified Korteweg-de Vries (mKdV) equation. It is shown that the compound solitons are described by an mKdV equation with repulsion, and the breather structures, by an mKdV equation with attraction. It is shown also that the characteristic properties of the solutions are determined by the sign of the group-velocity dispersion rather than by the sign of the group velocity itself. The results obtained can be used for searching new nonlinear dynamic coherent structures, e.g., compound solitons and breathers in high-dispersion magnetic metamaterials.
A nonlinear dynamic finite element approach for simulating muscular hydrostats.
Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A
2014-01-01
An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching. PMID:23025686
Phase and amplitude dynamics of nonlinearly coupled oscillators
NASA Astrophysics Data System (ADS)
Cudmore, P.; Holmes, C. A.
2015-02-01
This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type of nonlinear coupling. We show that this system exhibits synchronisation, where all oscillators are rotating at the same rate, and that in the synchronised state the system has a regular structure related to the distribution of the frequencies of the individual oscillators. Using a geometric description, we show how changes in the non-linear coupling function can cause pitchfork and saddle-node bifurcations which create or destroy stable and unstable synchronised solutions. We apply these results to show how in-phase and anti-phase solutions are created in a system with a bi-modal distribution of frequencies.
Nonlinear EEG dynamics during imagined self-paced movements.
Popivanov, D; Dushanova, J; Sauleva, Z
2001-01-01
The majority of studies devoted to reveal electrophysiological correlates of words and sentences comprehension, imageability and remembering are based on the event-related potentials and frequency synchronization in different narrow frequency bands. These linear methods reveal some patterns of EEG activity in time and frequency domain. Having in mind that the activation of many cortical structures is a result of mass of nonlinearly interconnected neurons, the linear methods seem to be insufficient to discover the complexity of the information transfer. We revealed recently nonlinear dynamic transients in EEG, long before real performance of goal-directed voluntary movements with different temporal and spatial distributions over frontal, sensorimotor and parietal cortical areas (Popivanov and Dushanova, 1999). The aim of this study was to establish whether similar behavior of the nonlinear characteristics exists when the subject imagines movements of a given type. The Kolmogorov entropy computed over time after the sentence end proved to be an useful characteristic that complement the linear methods. PMID:11693391
Reduced bases for nonlinear structural dynamic systems: A comparative study
NASA Astrophysics Data System (ADS)
Lülf, Fritz Adrian; Tran, Duc-Minh; Ohayon, Roger
2013-07-01
The presented work provides an overview of some commonly used approaches for generating reduced bases for discrete nonlinear dynamic systems. It investigates the performance and the robustness of these bases if they are applied in a reduction-by-projection procedure on different test cases. The bases are created from the Linear Normal Modes, the Ritz-vectors, the Proper and the Smooth Orthogonal Decomposition method, the A Priori Reduction, the Centroidal Voronoi Tessellation and the Local Equivalent Linear Stiffness Method. Second-Order Terms and an Enhanced Proper Orthogonal Decomposition formulation are included as variants. The test cases are small dimensional, locally or entirely nonlinear system subjected to a harmonic or an impulse force excitation. The double objective of this numerical study is, first, to determine which bases are most adequate for a given combination of nonlinearity and excitation and, second, to which extend the bases exhibit an inherent robustness if the parameterisation of the excitation is changed. A specific multicriteria decision analysis score is developed to assess the bases' performance. As a major result, a strong dependence of the performance of the bases on the type of excitation is established and thus some bases become more adequate for a certain situation than others. Also a lack of robustness for all considered bases can be observed. This situation improves in most cases if the basis is generated with the most critical values of the parameter.
Nonlinear model order reduction of jointed structures for dynamic analysis
NASA Astrophysics Data System (ADS)
Festjens, H.; Chevallier, G.; Dion, J. L.
2014-03-01
Assembled structures generally show weak nonlinearity, thus it is rather commonplace to assume that their modes are both linear and uncoupled. At small to modest amplitude, the linearity assumption remains correct in terms of stiffness but, on the contrary, the dissipation in joints is strongly amplitude-dependent. Besides, the modes of any large structure may be LOCALLY collinear in the localized region of a joint. As a result the projection of the structure on normal modes is not appropriate since the corresponding generalized coordinates may be strongly coupled. Instead of using this global basis, the present paper deals with the use of a local basis to reduce the size of the problem without losing the nonlinear physics. Under an appropriate set of assumptions, the method keeps the dynamic properties of joints, even for large amplitude, which include coupling effects, nonlinear damping and softening effects. The formulation enables us to take into account FE models of any realistic geometry. It also gives a straightforward process for experimental identification. The formulation is detailed and investigated on a jointed structure.
Semiconductor Nonlinear Dynamics Study by Broadband Terahertz Spectroscopy
NASA Astrophysics Data System (ADS)
Ho, I.-Chen
Semiconductor nonlinearity in the terahertz (THz) frequency range has been attracting considerable attention due to the recent development of high-power semiconductor-based nanodevices. However, the underlying physics concerning carrier dynamics in the presence of high-field THz transients is still obscure. This thesis introduces an ultrafast, time-resolved THz pump/THz probe approach to the study of semiconductor properties in the nonlinear regime. The carrier dynamics regarding two mechanisms, intervalley scattering and impact ionization, is observed for doped InAs on a sub-picosecond time scale. In addition, polaron modulation driven by intense THz pulses is experimentally and theoretically investigated. The observed polaron dynamics verifies the interaction between energetic electrons and a phonon field. In contrast to previous work which reports optical phonon responses, acoustic phonon modulations are addressed in this study. A further understanding of the intense field interacting with solid materials will accelerate the development of semiconductor devices. This thesis starts with the design and performance of a table-top THz spectrometer which has the advantages of ultra-broad bandwidth (one order higher bandwidth compared to a conventional ZnTe sensor) and high electric field strength (>100 kV/cm). Unlike the conventional THz time-domain spectroscopy, the spectrometer integrates a novel THz air-biased-coherent-detection (THz-ABCD) technique and utilizes selected gases as THz emitters and sensors. In comparison with commonly used electro-optic (EO) crystals or photoconductive (PC) dipole antennas, the gases have the benefits of no phonon absorption as existing in EO crystals and no carrier life time limitation as observed in PC dipole antennas. The newly development THz-ABCD spectrometer with a strong THz field strength capability provides a platform for various research topics especially on the nonlinear carrier dynamics of semiconductors. Two mechanisms
Nonlinear dynamics of global atmospheric and Earth-system processes
NASA Technical Reports Server (NTRS)
Saltzman, Barry; Ebisuzaki, Wesley; Maasch, Kirk A.; Oglesby, Robert; Pandolfo, Lionel
1990-01-01
Researchers are continuing their studies of the nonlinear dynamics of global weather systems. Sensitivity analyses of large-scale dynamical models of the atmosphere (i.e., general circulation models i.e., GCM's) were performed to establish the role of satellite-signatures of soil moisture, sea surface temperature, snow cover, and sea ice as crucial boundary conditions determining global weather variability. To complete their study of the bimodality of the planetary wave states, they are using the dynamical systems approach to construct a low-order theoretical explanation of this phenomenon. This work should have important implications for extended range forecasting of low-frequency oscillations, elucidating the mechanisms for the transitions between the two wave modes. Researchers are using the methods of jump analysis and attractor dimension analysis to examine the long-term satellite records of significant variables (e.g., long wave radiation, and cloud amount), to explore the nature of mode transitions in the atmosphere, and to determine the minimum number of equations needed to describe the main weather variations with a low-order dynamical system. Where feasible they will continue to explore the applicability of the methods of complex dynamical systems analysis to the study of the global earth-system from an integrative viewpoint involving the roles of geochemical cycling and the interactive behavior of the atmosphere, hydrosphere, and biosphere.
Nonlinear Dynamics of Biofilm Growth on Sediment Surfaces
NASA Astrophysics Data System (ADS)
Molz, F. J.; Murdoch, L. C.; Faybishenko, B.
2013-12-01
Bioclogging often begins with the establishment of small colonies (microcolonies), which then form biofilms on the surfaces of a porous medium. These biofilm-porous media surfaces are not simple coatings of single microbes, but complex assemblages of cooperative and competing microbes, interacting with their chemical environment. This leads one to ask: what are the underlying dynamics involved with biofilm growth? To begin answering this question, we have extended the work of Kot et al. (1992, Bull. Mathematical Bio.) from a fully mixed chemostat to an idealized, one-dimensional, biofilm environment, taking into account a simple predator-prey microbial competition, with the prey feeding on a specified food source. With a variable (periodic) food source, Kot et al. (1992) were able to demonstrate chaotic dynamics in the coupled substrate-prey-predator system. Initially, deterministic chaos was thought by many to be mainly a mathematical phenomenon. However, several recent publications (e.g., Becks et al, 2005, Nature Letters; Graham et al. 2007, Int. Soc Microb. Eco. J.; Beninca et al., 2008, Nature Letters; Saleh, 2011, IJBAS) have brought together, using experimental studies and relevant mathematics, a breakthrough discovery that deterministic chaos is present in relatively simple biochemical systems. Two of us (Faybishenko and Molz, 2013, Procedia Environ. Sci)) have numerically analyzed a mathematical model of rhizosphere dynamics (Kravchenko et al., 2004, Microbiology) and detected patterns of nonlinear dynamical interactions supporting evidence of synchronized synergetic oscillations of microbial populations, carbon and oxygen concentrations driven by root exudation into a fully mixed system. In this study, we have extended the application of the Kot et al. model to investigate a spatially-dependent biofilm system. We will present the results of numerical simulations obtained using COMSOL Multi-Physics software, which we used to determine the nature of the
Nonlinear dynamics of musical reed and brass wind instruments
NASA Astrophysics Data System (ADS)
Campbell, D. M.
1999-06-01
A musical wind instrument transforms a constant pressure input from the player's mouth into a fluctuating pressure output in the form of a radiating sound wave. In reed woodwind and brass instruments, this transformation is achieved through a nonlinear coupling between two vibrating systems: the flow control valve formed by the mechanical reed or the lips of the player, and the air column contained by the pipe. Although the basic physics of reed wind instruments was developed by Helmholtz in the nineteenth century, the application of ideas from the modern theory of nonlinear dynamics has led to recent advances in our understanding of some musically important features of wind instrument behaviour. As a first step, the nonlinear aspects of the musical oscillator can be considered to be concentrated in the flow control valve; the air column can be treated as a linear vibrating system, with a set of natural modes of vibration corresponding to the standing waves in the pipe. Recent models based on these assumptions have had reasonable success in predicting the threshold blowing pressure and sounding frequency of a clarinet, as well as explaining at least qualitatively the way in which the timbre of the sound varies with blowing pressure. The situation is more complicated for brass instruments, in which the player's lips provide the flow valve. Experiments using artificial lips have been important in permitting systematic studies of the coupling between lips and air column; the detailed nature of this coupling is still not fully understood. In addition, the assumption of linearity in the air column vibratory system sometimes breaks down for brass instruments. Nonlinear effects in the propagation of high amplitude sound waves can lead to the development of shock waves in trumpets and trombones, with important musical consequences.
Nonlinear dynamics and primordial curvature perturbations from preheating
NASA Astrophysics Data System (ADS)
Frolov, Andrei V.
2010-06-01
In this paper I review the theory and numerical simulations of nonlinear dynamics of preheating, a stage of dynamical instability at the end of inflation during which the homogeneous inflaton explosively decays and deposits its energy into excitation of other matter fields. I focus on preheating in chaotic inflation models, which proceeds via broad parametric resonance. I describe a simple method to evaluate Floquet exponents, calculating stability diagrams of Mathieu and Lame equations describing development of instability in m2phi2 and λphi4 preheating models. I discuss basic numerical methods and issues, and present simulation results highlighting non-equilibrium transitions, topological defect formation, late-time universality, turbulent scaling and approach to thermalization. I explain how preheating can generate large-scale primordial (non-Gaussian) curvature fluctuations manifest in cosmic microwave background anisotropy and large-scale structure, and discuss potentially observable signatures of preheating.
Interaction dynamics in small networks of nonlinear elements
NASA Astrophysics Data System (ADS)
Stich, Michael; Velarde, Manuel G.
2015-03-01
We study a small circuit of coupled nonlinear elements to investigate general features of signal transmission through networks. The small circuit itself is perceived as building block for larger networks. Individual dynamics and coupling are motivated by neuronal systems: We consider two types of dynamical modes for an individual element, regular spiking and chattering and each individual element can receive excitatory and/or inhibitory inputs and is subjected to different feedback types (excitatory and inhibitory; forward and recurrent). Both, deterministic and stochastic simulations are carried out to study the input-output relationships of these networks. Major results for regular spiking elements include frequency locking, spike rate amplification for strong synaptic coupling, and inhibition-induced spike rate control which can be interpreted as a output frequency rectification. For chattering elements, spike rate amplification for low frequencies and silencing for large frequencies is characteristic.
Nonlinear dynamics of cosmic strings with nonscaling loops
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2010-09-01
At early stages the dynamics of cosmic string networks is expected to be influenced by an excessive production of small loops at the scales of initial conditions lmin. To understand the late time behavior we propose a very simple analytical model of strings with a nonscaling population of loops. The complicated nonlinear dynamics is described by only a single parameter Ñ2/(1-C(lmin)) where C(l) is a correlation function of the string tangent vectors. The model predicts an appearance of two new length scales: the coherence length ξ˜t/N2 and the cross-correlation length χ˜t/N. At the onset of evolution Ñ10 and at late times N is expected to grow logarithmically due to cosmological stretching and emission of small loops. The very late time evolution might be modified further when the gravitational back-reaction scale grows larger than lmin.
Inverse problem of nonlinear dynamical systems: a constructive approach
Gonzalez-Gascon, F.; Moreno-Insertis, F.; Rodriguez-Camino, E.
1980-08-01
A quite simple and practical method is developed for the construction of two dimensional nonlinear dynamical systems (plane vector fields) possessing an arbitrary number of given limit cycles. The method is applied to the construction of n-dimensional dynamical systems (R/sup n/ vector fields) possessing at least one limit cycle and, under certain circumstances, more than one, or even a numerable infinity. Interesting open problems arise when n is greater than two, or where more than one limit cycle appears. Our constructive algorithm for this type of inverse problem is also applied to the construction of second order differential equations (Newtonian differential equations) possessing a finite or infinite number of invariant speeds. This last problem is relevant for certain aspects of the special theory of relativity.
Analysis of the human electroencephalogram with methods from nonlinear dynamics
Mayer-Kress, G.; Holzfuss, J.
1986-09-08
We apply several different methods from nonlinear dynamical systems to the analysis of the degree of temporal disorder in data from human EEG. Among these are methods of geometrical reconstruction, dimensional complexity, mutual information content, and two different approaches for estimating Lyapunov characteristic exponents. We show how the naive interpretation of numerical results can lead to a considerable underestimation of the dimensional complexity. This is true even when the errors from least squares fits are small. We present more realistic error estimates and show that they seem to contain additional, important information. By applying independent methods of analysis to the same data sets for a given lead, we find that the degree of temporal disorder is minimal in a ''resting awake'' state and increases in sleep as well as in fluroxene induced general anesthesia. At the same time the statistical errors appear to decrease, which can be interpretated as a transition to a more uniform dynamical state. 29 refs., 10 figs.
Nonlinear flight dynamics and stability of hovering model insects
Liang, Bin; Sun, Mao
2013-01-01
Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier–Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect. PMID:23697714
Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials
NASA Astrophysics Data System (ADS)
Herbold, Eric B.
New aspects of strongly nonlinear wave and structural phenomena in granular media are developed numerically, theoretically and experimentally. One-dimensional chains of particles and compressed powder composites are the two main types of materials considered here. Typical granular assemblies consist of linearly elastic spheres or layers of masses and effective nonlinear springs in one-dimensional columns for dynamic testing. These materials are highly sensitive to initial and boundary conditions, making them useful for acoustic and shock-mitigating applications. One-dimensional assemblies of spherical particles are examples of strongly nonlinear systems with unique properties. For example, if initially uncompressed, these materials have a sound speed equal to zero (sonic vacuum), supporting strongly nonlinear compression solitary waves with a finite width. Different types of assembled metamaterials will be presented with a discussion of the material's response to static compression. The acoustic diode effect will be presented, which may be useful in shock mitigation applications. Systems with controlled dissipation will also be discussed from an experimental and theoretical standpoint emphasizing the critical viscosity that defines the transition from an oscillatory to monotonous shock profile. The dynamic compression of compressed powder composites may lead to self-organizing mesoscale structures in two and three dimensions. A reactive granular material composed of a compressed mixture of polytetrafluoroethylene (PTFE), tungsten (W) and aluminum (Al) fine-grain powders exhibit this behavior. Quasistatic, Hopkinson bar, and drop-weight experiments show that composite materials with a high porosity and fine metallic particles exhibit a higher strength than less porous mixtures with larger particles, given the same mass fraction of constituents. A two-dimensional Eulerian hydrocode is implemented to investigate the mechanical deformation and failure of the compressed
Reconstruction of principal dynamical modes from climatic variability: nonlinear approach
NASA Astrophysics Data System (ADS)
Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Feigin, Alexander; Kurths, Juergen
2015-04-01
Analysis of multivariate time-series produced by complex systems requires efficient tools for reduction of data dimension. We consider this problem in relation to empirical modeling of climate, which implies an analysis of spatial-distributed time-series. The main goal is to establish the number of principal modes which have key contribution to data and actually governs the observed variability. Currently, the number of widely used linear methods based on PCA and factor analysis exists, which yield different data decompositions taking into consideration simultanious/time-lag correlations between spatial grid points. However, the question about possibility of improving the decomposition by taking into account nonlinear couplings between variables often remains untouched. In the report the method for constructing principal dynamic modes on the basis of low-dimensional nonlinear parametric representation of observed multivariate time-series is suggested. It is aimed to extracting the set of latent modes that both explains an essential part of variability, and obeys the simplest evolution law. Thus, this approach can be used for optimal reconstruction of the phase space for empirical prognostic modeling of observed dynamics. The evidence of nonlinear couplings in SST space-distributed data covering the Globe is investigated by the proposed approach. It is demonstrated that the obtained principal modes capture more part of SST variability than principal components (PCs) constructed by either EOF decomposition or its spatio-temporal extension. Relation of these modes to various climate phenomena is shown and discussed in the report. The application of the approach to data-driven forecast of climate bahavior is also discussed.
The dynamics of interacting nonlinearities governing long wavelength driftwave turbulence
Newman, D.E.
1993-09-01
Because of the ubiquitous nature of turbulence and the vast array of different systems which have turbulent solutions, the study of turbulence is an area of active research. Much present day understanding of turbulence is rooted in the well established properties of homogeneous Navier-Stokes turbulence, which, due to its relative simplicity, allows for approximate analytic solutions. This work examines a group of turbulent systems with marked differences from Navier-Stokes turbulence, and attempts to quantify some of their properties. This group of systems represents a variety of drift wave fluctuations believed to be of fundamental importance in laboratory fusion devices. From extensive simulation of simple local fluid models of long wavelength drift wave turbulence in tokamaks, a reasonably complete picture of the basic properties of spectral transfer and saturation has emerged. These studies indicate that many conventional notions concerning directions of cascades, locality and isotropy of transfer, frequencies of fluctuations, and stationarity of saturation are not valid for moderate to long wavelengths. In particular, spectral energy transfer at long wavelengths is dominated by the E {times} B nonlinearity, which carries energy to short scale in a manner that is highly nonlocal and anisotropic. In marked contrast to the canonical self-similar cascade dynamics of Kolmogorov, energy is efficiently passed between modes separated by the entire spectrum range in a correlation time. At short wavelengths, transfer is dominated by the polarization drift nonlinearity. While the standard dual cascade applies in this subrange, it is found that finite spectrum size can produce cascades that are reverse directed and are nonconservative in enstrophy and energy similarity ranges. In regions where both nonlinearities are important, cross-coupling between the nolinearities gives rise to large no frequency shifts as well as changes in the spectral dynamics.
A nonlinear dynamical analogue model of geomagnetic activity
NASA Technical Reports Server (NTRS)
Klimas, A. J.; Baker, D. N.; Roberts, D. A.; Fairfield, D. H.; Buechner, J.
1992-01-01
Consideration is given to the solar wind-magnetosphere interaction within the framework of deterministic nonlinear dynamics. An earlier dripping faucet analog model of the low-dimensional solar wind-magnetosphere system is reviewed, and a plasma physical counterpart to that model is constructed. A Faraday loop in the magnetotail is considered, and the relationship of electric potentials on the loop to changes in the magnetic flux threading the loop is developed. This approach leads to a model of geomagnetic activity which is similar to the earlier mechanical model but described in terms of the geometry and plasma contents of the magnetotail. The model is characterized as an elementary time-dependent global convection model. The convection evolves within a magnetotail shape that varies in a prescribed manner in response to the dynamical evolution of the convection. The result is a nonlinear model capable of exhibiting a transition from regular to chaotic loading and unloading. The model's behavior under steady loading and also some elementary forms of time-dependent loading is discussed.
Nonlinear dynamics of specific DNA-protein interactions
NASA Astrophysics Data System (ADS)
Dwiputra, D.; Hidayat, W.; Khairani, R.; Zen, F. P.
2016-03-01
Interactions between DNA binding protein and specific base pairs of nucleic acid is critical for biological process. We propose a new model of DNA-protein interactions to depict the dynamics of specific DNA-protein interactions. Hydrogen bonds (H-bonds) are, among the other intermolecular interactions in DNA, the most distinctive in term of specificity of molecular bonds. As H-bonds account for specificity, we only consider the dynamics affected by H-bonds between DNA base pairs and H-bonds connecting protein side chains and DNA. The H-bonds are modelled by Morse potentials and coupling terms in the Hamiltonian of coupled oscillators resembling a coupling between planar DNA chain and a protein molecule. In this paper we give a perturbative approach as an attempt for a soliton solution. The solution is in the form of nonlinear travelling wave having the amplitudes satisfying coupled nonlinear Schrodinger equations and is interpreted as the mediator for nonlocal transmittance of biological information in DNA.
Linear and nonlinear dynamics of liquid planetary cores
NASA Astrophysics Data System (ADS)
Lathrop, D. P.
2013-12-01
This is the 50th anniversary of Ed Lorenz brilliant paper "Deterministic Nonperiodic Flow.'' Lorenz's work, along with many other founders' efforts, gave rise to the study of nonlinear dynamics. That field has allowed us to move beyond simple linear characterizations of nature, and to open up a deeper understanding of the Earth, other planets, and stars. Of the many things that make the Earth a habitable home, one is the existence of a planetary magnetic field generated in our liquid iron outer core. The generation process is known to be strongly nonlinear, and thereby almost certainly turbulent. Yet it is not a simple homogeneous isotropic turbulent flow, but is instead heavily modified by rotation and magnetic forces. We attempt to better understand the Earth's core using a three-meter liquid sodium laboratory model of the core. Our work in sodium in this system has just begun. The system exhibits a variety of behaviors with at least twelve different states, drawing different amounts of power, and causing varying levels of magnetic field amplification. In some states, rotation and magnetic fields cause the dynamics to simplify relative to more general turbulent flows in comparable conditions. Acknowledgements: I gratefully acknowledge my collaborators Daniel Zimmerman, Santiago Triana, Donald Martin, Nolan Balew, Henri-Claude Nataf, and Barbara Brawn-Cinani, and funding from the National Science Foundation Earth Sciences Instrumentation and Geophysics programs.
Molecular dynamics simulation of complex plasmas: interaction of nonlinear waves
NASA Astrophysics Data System (ADS)
Durniak, Celine; Samsonov, Dmitry
2008-11-01
Complex plasmas consist of micron sized microspheres immersed into ordinary ion-electron plasmas. They exist in solid, liquid, gaseous states and exhibit a range of dynamic phenomena such as waves, solitons, phase transitions, heat transfer. These phenomena can be modelled in complex plasmas at the microscopic or ``molecular'' scale, which is almost impossible in ordinary solids and liquids. We simulate a monolayer complex plasma consisting of 3000 negatively-charged particles (or grains) with the help of molecular dynamics computer simulations. The equations of grain motion are solved using a 5^th order Runge Kutta method taking into account interaction of every grain with each other via a Yukawa potential. The grains are confined more strongly in the vertical direction than in the horizontal. After seeding the grains randomly the code is run until the equilibrium is reached as the grain kinetics energy reduces due to damping force equal to the neutral friction in the experiments and a monolayer crystal lattice is formed. Then we investigate interactions between nonlinear waves in a monolayer strongly coupled complex plasma moving in three dimensions. Different excitations are applied during a short time symmetrically on both sides of the lattice. Structural properties and nonlinear waves characteristics are examined as the pulses propagate across the complex plasma in opposite directions.
Nonlinear dynamics of a simplified engine-propeller system
NASA Astrophysics Data System (ADS)
Yu, S. D.; Warwick, S. A.; Zhang, X.
2009-07-01
This paper presents a procedure for studying dynamical behaviors of a simplified engine-propeller dynamical system consisting of a number of bodies of plane motions. The equation of motion of the complex system is obtained using the Lagrange equation and solved numerically using the 4th order Runge-Kutta method. Various simulations were performed to investigate the transient and steady state behaviors of the multiple body system while taking into consideration the engine pressure pulsations, nonlinear inertia of moving bodies, and nonlinear aerodynamic load. Sub-harmonics and super harmonics in the steady state responses for different power and propeller pitch settings are obtained using the fast Fourier transform. Numerical simulations indicate that the 1.5 order is the dominant order of harmonics in the steady state oscillatory motion of the crankshaft. The findings and procedure presented in the paper are useful to the aerospace industry in certifying reciprocating engines and propellers. The crankshaft oscillatory velocities obtained from the simplified rigid body model are in good agreement with the experimental data for a SAITO-450 engine and a SOLO propeller at a 6″ pitch setting.
Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings
NASA Astrophysics Data System (ADS)
Cunha, Americo; Soize, Christian; Sampaio, Rubens
2015-11-01
This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.
Classifying transient signals with nonlinear dynamic filter banks
Brush, J.S.
1996-06-01
In recent years, several specific advances in the study of chaotic processes have been made which appear to have immediate applicability to signal processing. This paper describes two applications of one of these advances, nonlinear modeling, to signal detection & classification, in particular for short-lived or transient or signals. The first method uses the coefficients from an adaptively fit model as a set of features for signal detection and classification. In the second method, a library of predictive nonlinear dynamic equations is used as a filter bank, and statistics on the prediction residuals are used to form feature vectors for input data segments. These feature vectors provide a mechanism for detecting and classifying model transients at signal-to-noise ratios as low as {minus}10 dB, even when the generating dynamics of the transient signals are not present in the filter bank. The second method and some validating experiments are described in detail. {copyright} {ital 1996 American Institute of Physics.}
Transient dynamics and nonlinear stability of spatially extended systems.
Handel, Andreas; Grigoriev, Roman O
2006-09-01
As studies of various systems have shown, the sole focus on the eigenvalues in a linear stability analysis can be misleading, especially when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilization process. The critical noise level leading to destabilization is often found to scale as a power of the magnitude of transient amplification. In what follows we show that the power law exponent sensitively depends on the type of nonlinear terms and their potential for generating self-sustaining noise amplification cycles (bootstrapping). We find, however, that the exponents are not universal and also depend on the more subtle details of the transient dynamics. We also show that the basin of attraction of a spatially uniform state is bounded by the stable manifold(s) of nearby saddle(s) which play a major role in the transition. PMID:17025738
Nonlinear damping calculation in cylindrical gear dynamic modeling
NASA Astrophysics Data System (ADS)
Guilbault, Raynald; Lalonde, Sébastien; Thomas, Marc
2012-04-01
The nonlinear dynamic problem posed by cylindrical gear systems has been extensively covered in the literature. Nonetheless, a significant proportion of the mechanisms involved in damping generation remains to be investigated and described. The main objective of this study is to contribute to this task. Overall, damping is assumed to consist of three sources: surrounding element contribution, hysteresis of the teeth, and oil squeeze damping. The first two contributions are considered to be commensurate with the supported load; for its part however, squeeze damping is formulated using expressions developed from the Reynolds equation. A lubricated impact analysis between the teeth is introduced in this study for the minimum film thickness calculation during contact losses. The dynamic transmission error (DTE) obtained from the final model showed close agreement with experimental measurements available in the literature. The nonlinear damping ratio calculated at different mesh frequencies and torque amplitudes presented average values between 5.3 percent and 8 percent, which is comparable to the constant 8 percent ratio used in published numerical simulations of an equivalent gear pair. A close analysis of the oil squeeze damping evidenced the inverse relationship between this damping effect and the applied load.
Force and Moment Approach for Achievable Dynamics Using Nonlinear Dynamic Inversion
NASA Technical Reports Server (NTRS)
Ostroff, Aaron J.; Bacon, Barton J.
1999-01-01
This paper describes a general form of nonlinear dynamic inversion control for use in a generic nonlinear simulation to evaluate candidate augmented aircraft dynamics. The implementation is specifically tailored to the task of quickly assessing an aircraft's control power requirements and defining the achievable dynamic set. The achievable set is evaluated while undergoing complex mission maneuvers, and perfect tracking will be accomplished when the desired dynamics are achievable. Variables are extracted directly from the simulation model each iteration, so robustness is not an issue. Included in this paper is a description of the implementation of the forces and moments from simulation variables, the calculation of control effectiveness coefficients, methods for implementing different types of aerodynamic and thrust vectoring controls, adjustments for control effector failures, and the allocation approach used. A few examples illustrate the perfect tracking results obtained.
Symplectic ray-tracing: a new approach for nonlinear ray tracings by Hamiltonian dynamics
NASA Astrophysics Data System (ADS)
Satoh, Tetsu R.
2003-05-01
This paper describes a method of symplectic ray tracing for calculating the flows of non-linear dynamical systems. Symplectic ray tracing method traces the path of photons moving along the orbit calculated by using Hamilton's canonical equation. Using this method, we can simulate non-linear dynamical systems with various dimensions, accurate calculation, and quick implementation of scientif visualization system. This paper also demonstrates some visualization results of non-linear dynamical systems computed by using symplectic ray tracing method.
Nonlinear dynamics in a microfluidic loop device: Chaos and Fractals
NASA Astrophysics Data System (ADS)
Maddala, Jeevan; Rengaswamy, Raghunathan
2012-11-01
Discrete decision making and resistive interactions between droplets in a microfluidic loop device induces fascinating nonlinear dynamics such as multi-stability and period doubling. Droplets entering the device at fixed time intervals can exit at different periods or chaotically. One of the periodic behaviors that is observed in a loop is the three-period behavior; this is consistent with the notion that three period behavior implies chaos. Switching between these different dynamical regimes is achieved by changing the inlet droplet feeding frequency. Chaotic behavior is observed between islands of periodic behavior. We show through simulations and experimental observations that the transitions between periods are indeed chaotic. Network model is used to study the dynamic behavior for different inlet feeding frequencies resulting in the development of a bifurcation map. The bifurcation map shows that the three period dynamics is preceded by chaos. A Lyapunov exponent is used to further validate these results. The exit droplet spacing shows several fascinating patterns when the model is simulated for a large number of droplets in the chaotic regime. One such chaotic regime produces a fractal that has a boundary of cardioid. The correlation dimension for a fractal pattern produced by this particular loop system is calculated to be 0.7.
The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.
Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin
2016-07-01
Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data. PMID:27262423
Nonlinear dynamics of coiling, and mounding in viscoelastic jets
NASA Astrophysics Data System (ADS)
Majmudar, Trushant; Ober, Thomas; McKinley, Gareth
2009-11-01
Free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes like bottle filling, remain poorly understood in terms of fundamental fluid dynamics. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities, and model yield-stress fluids. We systematically vary the height of the drop and the flow rate in order to study the effects of varying geometric and kinematic parameters. We observe that for fluids with higher elastic relaxation times, folding is the preferred mode. In contrast, for low elasticity fluids we observe complex nonlinear dynamics consisting of coiling, folding, and irregular meandering as the height of the fall increases. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo" or the Kaye effect. Upon increasing the flow rate to very high values, the ``leaping shampoo" state disappears and is replaced by a pronounced mounding or ``heaping". A subsequent increase in the flow rate results in finger-like protrusions to emerge out of the mound and climb up towards the nozzle. This novel transition is currently under investigation and remains a theoretical challenge.
Sequential reconstruction of driving-forces from nonlinear nonstationary dynamics
NASA Astrophysics Data System (ADS)
Güntürkün, Ulaş
2010-07-01
This paper describes a functional analysis-based method for the estimation of driving-forces from nonlinear dynamic systems. The driving-forces account for the perturbation inputs induced by the external environment or the secular variations in the internal variables of the system. The proposed algorithm is applicable to the problems for which there is too little or no prior knowledge to build a rigorous mathematical model of the unknown dynamics. We derive the estimator conditioned on the differentiability of the unknown system’s mapping, and smoothness of the driving-force. The proposed algorithm is an adaptive sequential realization of the blind prediction error method, where the basic idea is to predict the observables, and retrieve the driving-force from the prediction error. Our realization of this idea is embodied by predicting the observables one-step into the future using a bank of echo state networks (ESN) in an online fashion, and then extracting the raw estimates from the prediction error and smoothing these estimates in two adaptive filtering stages. The adaptive nature of the algorithm enables to retrieve both slowly and rapidly varying driving-forces accurately, which are illustrated by simulations. Logistic and Moran-Ricker maps are studied in controlled experiments, exemplifying chaotic state and stochastic measurement models. The algorithm is also applied to the estimation of a driving-force from another nonlinear dynamic system that is stochastic in both state and measurement equations. The results are judged by the posterior Cramer-Rao lower bounds. The method is finally put into test on a real-world application; extracting sun’s magnetic flux from the sunspot time series.
The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics
NASA Technical Reports Server (NTRS)
Zhu, Yanqiu; Cohn, Stephen E.; Todling, Ricardo
1999-01-01
The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
Noise in Nonlinear Dynamical Systems 3 Volume Paperback Set
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2011-11-01
Volume 1: List of contributors; Preface; Introduction to volume one; 1. Noise-activated escape from metastable states: an historical view Rolf Landauer; 2. Some Markov methods in the theory of stochastic processes in non-linear dynamical systems R. L. Stratonovich; 3. Langevin equations with coloured noise J. M. Sancho and M. San Miguel; 4. First passage time problems for non-Markovian processes Katja Lindenberg, Bruce J. West and Jaume Masoliver; 5. The projection approach to the Fokker-Planck equation: applications to phenomenological stochastic equations with coloured noises Paolo Grigolini; 6. Methods for solving Fokker-Planck equations with applications to bistable and periodic potentials H. Risken and H. D. Vollmer; 7. Macroscopic potentials, bifurcations and noise in dissipative systems Robert Graham; 8. Transition phenomena in multidimensional systems - models of evolution W. Ebeling and L. Schimansky-Geier; 9. Coloured noise in continuous dynamical systems: a functional calculus approach Peter Hanggi; Appendix. On the statistical treatment of dynamical systems L. Pontryagin, A. Andronov and A. Vitt; Index. Volume 2: List of contributors; Preface; Introduction to volume two; 1. Stochastic processes in quantum mechanical settings Ronald F. Fox; 2. Self-diffusion in non-Markovian condensed-matter systems Toyonori Munakata; 3. Escape from the underdamped potential well M. Buttiker; 4. Effect of noise on discrete dynamical systems with multiple attractors Edgar Knobloch and Jeffrey B. Weiss; 5. Discrete dynamics perturbed by weak noise Peter Talkner and Peter Hanggi; 6. Bifurcation behaviour under modulated control parameters M. Lucke; 7. Period doubling bifurcations: what good are they? Kurt Wiesenfeld; 8. Noise-induced transitions Werner Horsthemke and Rene Lefever; 9. Mechanisms for noise-induced transitions in chemical systems Raymond Kapral and Edward Celarier; 10. State selection dynamics in symmetry-breaking transitions Dilip K. Kondepudi; 11. Noise in a
Perturbation and nonlinear dynamic analysis of different singing styles.
Butte, Caitlin J; Zhang, Yu; Song, Huangqiang; Jiang, Jack J
2009-11-01
Previous research has used perturbation analysis methods to study the singing voice. Using perturbation and nonlinear dynamic analysis (NDA) methods in conjunction may provide more accurate information on the singing voice and may distinguish vocal usage in different styles. Acoustic samples from different styles of singing were compared using nonlinear dynamic and perturbation measures. Twenty-six songs from different musical styles were obtained from an online music database (Rhapsody, RealNetworks, Inc., Seattle, WA). One-second samples were selected from each song for analysis. Perturbation analyses of jitter, shimmer, and signal-to-noise ratio and NDA of correlation dimension (D(2)) were performed on samples from each singing style. Percent jitter and shimmer median values were low normal for country (0.32% and 3.82%), musical theater (MT) (0.280% and 2.80%), jazz (0.440% and 2.34%), and soul (0.430% and 6.42%). The popular style had slightly higher median jitter and shimmer values (1.13% and 6.78%) than other singing styles, although this was not statistically significant. The opera singing style had median jitter of 0.520%, and yielded significantly high shimmer (P=0.001) of 7.72%. All six singing styles were measured reliably using NDA, indicating that operatic singing is notably more chaotic than other singing styles. Median correlation dimension values were low to normal, compared to healthy voices, in country (median D(2)=2.14), jazz (median D(2)=2.24), pop (median D(2)=2.60), MT (median D(2)=2.73), and soul (mean D(2)=3.26). Correlation dimension was significantly higher in opera (P<0.001) with median D(2)=6.19. In this study, acoustic analysis in opera singing gave significantly high values for shimmer and D(2), suggesting that it is more irregular than other singing styles; a previously unknown quality of opera singing. Perturbation analysis also suggested significant differences in vocal output in different singing styles. This preliminary study
Moderately nonlinear diffuse-charge dynamics under an ac voltage
NASA Astrophysics Data System (ADS)
Stout, Robert F.; Khair, Aditya S.
2015-09-01
The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of Vo/(kBT /e ) , where Vo is the amplitude of the driving voltage and kBT /e is the thermal voltage with kB as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D /λDL , where D is the ion diffusivity, λD is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O (Vo3) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in Vo. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing Vo. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.
Nonlinear Dynamic Causal Models for fMRI
Stephan, Klaas Enno; Kasper, Lars; Harrison, Lee M.; Daunizeau, Jean; den Ouden, Hanneke E.M.; Breakspear, Michael; Friston, Karl J.
2009-01-01
Models of effective connectivity characterize the influence that neuronal populations exert over each other. Additionally, some approaches, for example Dynamic Causal Modelling (DCM) and variants of Structural Equation Modelling, describe how effective connectivity is modulated by experimental manipulations. Mathematically, both are based on bilinear equations, where the bilinear term models the effect of experimental manipulations on neuronal interactions. The bilinear framework, however, precludes an important aspect of neuronal interactions that has been established with invasive electrophysiological recording studies; i.e., how the connection between two neuronal units is enabled or gated by activity in other units. These gating processes are critical for controlling the gain of neuronal populations and are mediated through interactions between synaptic inputs (e.g. by means of voltage-sensitive ion channels). They represent a key mechanism for various neurobiological processes, including top-down (e.g. attentional) modulation, learning and neuromodulation. This paper presents a nonlinear extension of DCM that models such processes (to second order) at the neuronal population level. In this way, the modulation of network interactions can be assigned to an explicit neuronal population. We present simulations and empirical results that demonstrate the validity and usefulness of this model. Analyses of synthetic data showed that nonlinear and bilinear mechanisms can be distinguished by our extended DCM. When applying the model to empirical fMRI data from a blocked attention to motion paradigm, we found that attention-induced increases in V5 responses could be best explained as a gating of the V1→V5 connection by activity in posterior parietal cortex. Furthermore, we analysed fMRI data from an event-related binocular rivalry paradigm and found that interactions amongst percept-selective visual areas were modulated by activity in the middle frontal gyrus. In both
Pseudo-nonlinear dynamic analysis of buckled pipes
NASA Astrophysics Data System (ADS)
Gültekin Sınır, B.
2013-02-01
In this study, the post-divergence behavior of fluid-conveying pipes supported at both ends is investigated using the nonlinear equations of motion. The governing equation exhibits a cubic nonlinearity arising from mid-plane stretching. Exact solutions for post-buckling configurations of pipes with fixed-fixed, fixed-hinged, and hinged-hinged boundary conditions are investigated. The pipe is stable at its original static equilibrium position until the flow velocity becomes high enough to cause a supercritical pitchfork bifurcation, and the pipe loses stability by static divergence. In the supercritical fluid velocity regime, the equilibrium configuration becomes unstable and bifurcates into multiple equilibrium positions. To investigate the vibrations that occur in the vicinity of a buckled equilibrium position, the pseudo-nonlinear vibration problem around the first buckled configuration is solved precisely using a new solution procedure. By solving the resulting eigenvalue problem, the natural frequencies and the associated mode shapes of the pipe are calculated. The dynamic stability of the post-buckling configurations obtained in this manner is investigated. The first buckled shape is a stable equilibrium position for all boundary conditions. The buckled configurations beyond the first buckling mode are unstable equilibrium positions. The natural frequencies of the lowest vibration modes around each of the first two buckled configurations are presented. Effects of the system parameters on pipe behavior as well as the possibility of a subcritical pitchfork bifurcation are also investigated. The results show that many internal resonances might be activated among the vibration modes around the same or different buckled configurations.
Weakly nonlinear dynamics of near-CJ detonation waves
Bdzil, J.B.; Klein, R.
1993-02-01
The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature are running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.
Weakly nonlinear dynamics of near-CJ detonation waves
Bdzil, J.B. ); Klein, R. . Inst. fuer Technische Mechanik)
1993-01-01
The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature are running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance.
Intertwined Hamiltonians in two-dimensional curved spaces
Aghababaei Samani, Keivan . E-mail: samani@cc.iut.ac.ir; Zarei, Mina
2005-04-01
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS{sub 2}), de Sitter plane (dS{sub 2}), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.
Temporal and spatial structures of nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Purwins, Hans-Georg; Klempt, Günter; Berkemeier, Jürgen
The present article contains the description of simple experiments mounted for a demonstration of temporal and spatial structures of dissipative nonlinear dynamical systems. The systematic approach possible to systems with few degrees of freedom is described on an elementary level showing experiments on a rotating nonlinear oscillator. The temporal structure elements are those contained in the stationary, periodic, quasi-periodic, and chaotic motion. Structures of systems with many degrees of freedom are demonstrated by showing experiments on real spatially extended electronic circuits and gas discharge systems both described by reaction diffusion equations. Such systems have a complexity and richness of structures far beyond what can be described systematically by current techniques. However, for special cases a quantitative understanding is possible. Also filaments of rather well defined size and shape observed in our experiments can be considered as simple elements building up a variety of spatial patterns. We also show that noise is decisive in many cases for the formation and the nonreproducibility of stationary structures. Finally, we stress some features common to reaction diffusion systems and living beings.
Guidance of Nonlinear Nonminimum-Phase Dynamic Systems
NASA Technical Reports Server (NTRS)
Devasia, Santosh
1996-01-01
The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.
Efficient Nonlinear Low-Order Models in Atmospheric Dynamics
NASA Astrophysics Data System (ADS)
Grady, K.; Gluhovsky, A.
2014-12-01
Following the pioneering work of Kolmogorov, Lorenz, and Obukhov, low-order models (LOMs) have been widely employed in studies of atmospheric and climate dynamics for reducing hydrodynamic equations to a small number of modes in order to understand the interplay of principal mechanisms. However, arbitrary truncations in the Galerkin method commonly used to derive LOMs can lead to systems that lack fundamental physical properties, such as energy conservation in the dissipationless limit. The presentation will address this problem by constructing efficient LOMs as coupled 3-mode nonlinear dynamical systems known in mechanics as Volterra gyrostats. Such systems guarantee energy conservation in the dissipationless limit, and their modular nature allows the creation of new LOMs through the addition or removal of gyrostats in existing models (resulting in, for example, Hamiltonian LOMs). In fact, all physically sound models that have appeared in recent publications can be written as coupled gyrostats. These and new LOMs developed by the authors will be discussed in the talk, suggesting that coupled gyrostats may offer a general framework for developing efficient LOMs for atmospheric dynamics.
A nonlinear model for top fuel dragster dynamic performance assessment
NASA Astrophysics Data System (ADS)
Spanos, P. D.; Castillo, D. H.; Kougioumtzoglou, I. A.; Tapia, R. A.
2012-02-01
The top fuel dragster is the fastest and quickest vehicle in drag racing. This vehicle is capable of travelling a quarter mile in less than 4.5 s, reaching a final speed in excess of 330 miles per hour. The average power delivered by its engine exceeds 7000 Hp. To analyse and eventually increase the performance of a top fuel dragster, a dynamic model of the vehicle is developed. Longitudinal, vertical, and pitching chassis motions are considered, as well as drive-train dynamics. The aerodynamics of the vehicle, the engine characteristics, and the force due to the combustion gases are incorporated into the model. Further, a simplified model of the traction characteristics of the rear tyres is developed where the traction is calculated as a function of the slip ratio and the velocity. The resulting nonlinear, coupled differential equations of motion are solved using a fourth-order Runge-Kutta numerical integration scheme. Several simulation runs are made to investigate the effects of the aerodynamics and of the engine's initial torque in the performance of the vehicle. The results of the computational simulations are scrutinised by comparisons with data from actual dragster races. Ultimately, the proposed dynamic model of the dragster can be used to improve the aerodynamics, the engine and clutch set-ups of the vehicle, and possibly facilitate the redesign of the dragster.
Nonlinear dynamics of global atmospheric and Earth system processes
NASA Technical Reports Server (NTRS)
Saltzman, Barry
1993-01-01
During the past eight years, we have been engaged in a NASA-supported program of research aimed at establishing the connection between satellite signatures of the earth's environmental state and the nonlinear dynamics of the global weather and climate system. Thirty-five publications and four theses have resulted from this work, which included contributions in five main areas of study: (1) cloud and latent heat processes in finite-amplitude baroclinic waves; (2) application of satellite radiation data in global weather analysis; (3) studies of planetary waves and low-frequency weather variability; (4) GCM studies of the atmospheric response to variable boundary conditions measurable from satellites; and (5) dynamics of long-term earth system changes. Significant accomplishments from the three main lines of investigation pursued during the past year are presented and include the following: (1) planetary atmospheric waves and low frequency variability; (2) GCM studies of the atmospheric response to changed boundary conditions; and (3) dynamics of long-term changes in the global earth system.
NASA Astrophysics Data System (ADS)
Fu, Yiming; Chen, Yang; Zhong, Jun
2014-10-01
The nonlinear dynamic response problems of fiber-metal laminated beams with delamination are studied in this paper. Basing on the Timoshenko beam theory, and considering geometric nonlinearity, transverse shear deformation, temperature effect and contact effect, the nonlinear governing equations of motion for fiber-metal laminated beams under unsteady temperature field are established, which are solved by the differential quadrature method, Nermark-β method and iterative method. In numerical examples, the effects of delamination length, delamination depth, temperature field, geometric nonlinearity and transverse shear deformation on the nonlinear dynamic response of the glass reinforced aluminum laminated beam with delamination are discussed in details.
Quantised consensus of multi-agent systems with nonlinear dynamics
NASA Astrophysics Data System (ADS)
Zhu, Yunru; Zheng, Yuanshi; Wang, Long
2015-08-01
This paper studies the consensus problem of first-order and second-order multi-agent systems with nonlinear dynamics and quantised interactions. Continuous-time and impulsive control inputs are designed for the multi-agent systems on the logarithmic quantised relative state measurements of agents, respectively. By using nonsmooth analysis tools, we get some sufficient conditions for the consensus of multi-agent systems under the continuous-time inputs. Compared with continuous-time control inputs, impulsive distributed control inputs just use the state variables of the systems at discrete-time instances. Based on impulsive control theory, we prove that the multi-agent systems can reach consensus by choosing proper control gains and impulsive intervals. The simulation results are given to verify the effectiveness of the theoretical results.
Modeling of Nonlinear Dynamics of a Powered Paraglider
NASA Astrophysics Data System (ADS)
Watanabe, Masahito; Ochi, Yoshimasa
This paper presents a nonlinear dynamic model of a powered paraglider (PPG). The PPG is composed of a canopy and a payload with a propelling unit. The canopy is connected with the payload at two points. The model has been derived as a state vector equation under the assumption that the canopy has six degrees of freedom (DOF) and the payload has two DOF of pitching and yawing motions relative to the canopy. Friction at the connecting points between the canopy and the payload is taken into account. Time responses of the PPG without thrust have been computed using the model and the results are compared with flight experiment data. Simulation of a level flight with thrust has also been conducted.
Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness
NASA Astrophysics Data System (ADS)
Kaushik, Anshul; Ramani, Anand
2014-04-01
Crashworthiness of automotive structures is most often engineered after an optimal topology has been arrived at using other design considerations. This study is an attempt to incorporate crashworthiness requirements upfront in the topology synthesis process using a mathematically consistent framework. It proposes the use of equivalent linear systems from the nonlinear dynamic simulation in conjunction with a discrete-material topology optimizer. Velocity and acceleration constraints are consistently incorporated in the optimization set-up. Issues specific to crash problems due to the explicit solution methodology employed, nature of the boundary conditions imposed on the structure, etc. are discussed and possible resolutions are proposed. A demonstration of the methodology on two-dimensional problems that address some of the structural requirements and the types of loading typical of frontal and side impact is provided in order to show that this methodology has the potential for topology synthesis incorporating crashworthiness requirements.
Nonlinear Dynamic Inversion Baseline Control Law: Architecture and Performance Predictions
NASA Technical Reports Server (NTRS)
Miller, Christopher J.
2011-01-01
A model reference dynamic inversion control law has been developed to provide a baseline control law for research into adaptive elements and other advanced flight control law components. This controller has been implemented and tested in a hardware-in-the-loop simulation; the simulation results show excellent handling qualities throughout the limited flight envelope. A simple angular momentum formulation was chosen because it can be included in the stability proofs for many basic adaptive theories, such as model reference adaptive control. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as basic as possible to simplify the addition of the adaptive elements. Those design choices are explained, along with their predicted impact on the handling qualities.
Nonlinear Dynamics of Ionization Fronts in HII Regions
Mizuta, A; Kane, J O; Pound, M W; Remington, B A; Ryutov, D D; Takabe, H
2006-04-20
Hydrodynamic instability of an accelerating ionization front (IF) is investigated with 2D hydrodynamic simulations, including absorption of incident photoionizing photons, recombination in the HII region, and radiative molecular cooling. When the amplitude of the perturbation is large enough, nonlinear dynamics of the IF triggered by the separation of the IF from the cloud surface is observed. This causes the second harmonic of the imposed perturbation to appear on the cloud surfaces, whereas the perturbation in density of ablated gas in the HII region remains largely single mode. This mismatch of modes between the IF and the density perturbation in the HII region prevents the strong stabilization effect seen in the linear regime. Large growth of the perturbation caused by Rayleigh-Taylor-like instability is observed late in time.
One-Time Pad as a nonlinear dynamical system
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin
2012-11-01
The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding - a scheme for joint compression and encryption.
Nonlinear dynamic model of a solar stream generator
NASA Astrophysics Data System (ADS)
Ray, A.
1981-01-01
A thermal-hydraulic model of a once-through subcritical steam generator has been developed for predicting dynamic characteristics of solar thermal power plants as well as for control system design. The purpose of the model is to evaluate the overall system performance and component interaction with sufficient accuracy for controller design, rather than to describe the microscopic details occurring within the steam generator. The three-section (compressed water, two-phase mixture, and superheated steam) model with time-varying phase boundaries is described by a set of nonlinear differential equations derived from conservation of mass, momentum and energy. Local stability of the model has been examined at different levels of insolation. Transient response of six plant variables due to independent step disturbances in three input variables are presented as typical results.
NASA Astrophysics Data System (ADS)
Gupta, Samit Kumar; Sarma, Amarendra K.
2016-07-01
In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Ablowitz and Musslimani, (2013) [31]) continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrödinger system with PT-symmetric nonlinearity also admits Peregrine soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.
The Intertwining of Enterprise Strategy and Requirements
NASA Astrophysics Data System (ADS)
Loucopoulos, Pericles; Garfield, Joy
Requirements Engineering techniques need to focus not only on the target technical system, as has traditionally been the case, but also on the interplay between business and system functionality. Whether a business wishes to exploit advances in technology to achieve new strategic objectives or to organise work in innovative ways, the process of Requirements Engineering could and should present opportunities for modelling and evaluating the potential impact that technology can bring about to the enterprise.This chapter discusses a co-designing process that offers opportunities of change to both the business and its underlying technical systems, in a synergistic manner. In these design situations some of the most challenging projects involve multiple stakeholders from different participating organisations, subcontractors, divisions etc who may have a diversity of expertise, come from different organisational cultures and often have competing goals. Stakeholders are faced with many different alternative future ‘worlds’ each one demanding a possibly different development strategy.There are acute questions about the potential structure of the new business system and how key variables in this structure could impact on the dynamics of the system. This chapter presents a framework which enables the evaluation of requirements through (a) system dynamics modelling, (b) ontology modelling, (c) scenario modelling and (d) rationale modelling. System dynamics modelling is used to define the behaviour of an enterprise system in terms of four perspectives. Ontology modelling is used to formally define invariant components of the physical and social world within the enterprise domain. Scenario modelling is used to identify critical variables and by quantitatively analyzing the effects of these variables through simulation to better understand the dynamic behaviour of the possible future structures. Rationale modelling is used to assist collaborative discussions when considering
Failed eruptions of two intertwining small-scale filaments
NASA Astrophysics Data System (ADS)
Xue, Zhike; Yan, Xiaoli; Zhao, Li; Xiang, Yongyuan; Yang, Liheng; Guo, Yang
2016-02-01
Using multi-wavelength observations of the New Vacuum Solar Telescope (NVST), the Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO), we study the topology and evolutions of two filaments observed in NOAA active region (AR) 12031 on 2014 April 7. Before their eruptions, the two filaments (F1 and F2) were sinistral filaments, and the left part of F1 (LP) was located above F2, the right part of F1 (RP) under F2. They show an overall intertwining structure. LP erupted first and rotated clockwise. The total rotation angle was about 470° (≈2.61π). With its rotation, most of the plasma fell back, and thus it was a failed eruption. Meanwhile, when LP erupted to a higher altitude, the overlying magnetic loops were partially pushed from the northeast to the southwest with projected speeds from 36 to 105 km s-1. Next, F2 began to erupt and, when reaching a certain height, the plasma of F2 started to fall down to their footpoints. Using the potential-field source-surface (PFSS) model, the decay indexes at five positions along the polarity inversion line of AR 12031 were calculated to be from 1.03 to 1.25 with an average value of 1.20 that was lower than the critical value for torus instability. These results imply that the kink instability was the main triggering mechanism for the eruption of F1, and the eruption of F2 was due to the decreasing of overlying magnetic loops caused by the eruption of F1. The eruptions of two filaments were confined by the large-scale overlying magnetic loops.
BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns
NASA Astrophysics Data System (ADS)
Grammaticos, B.
2004-02-01
When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like `verify the relation 14.81'. Others are less so, such as `prepare a write-up on a) frequency-locking and b) devil
NASA Astrophysics Data System (ADS)
Renaud, G.; Le Bas, P.; Ten Cate, J. A.; Ulrich, T. J.; Carey, J. W.; Han, J.; Darling, T. W.; Johnson, P. A.
2011-12-01
Unraveling the physics of the earthquake source, reliable sequestration of CO2, predicting wellbore breakout in oil and gas reservoirs, monitoring thermal damage to rock in nuclear waste storage, and probing cement integrity require new approaches to material characterization and imaging. The elastic nonlinear material response is extremely promising in this regard. A persistent problem has been the direct relation between elastic nonlinearity and mechanical damage, because a reliable physics-based theory does not yet exist; however, recent work in medical nonlinear acoustics has led to an experimental breakthrough in measuring material nonlinear response. The breakthrough, termed Dynamic Acousto-Elasticity Testing (e.g., Renaud et al, 2008), has significant implication to development of a physics based theory, and thus ultimately to our ability to directly relate nonlinear material behavior to damage. The method provides the means to dynamically study the velocity-pressure and attenuation-pressure behaviors through the full wave cycle in contrast to most methods that measure average response (e.g., Nonlinear Resonance Ultrasound Spectroscopy [e.g., Guyer and Johnson, 2009]). The method relies on exciting a sample with a low frequency vibration in order to cycle it through stress-strain multiple times. Simultaneously, a high frequency ultrasonic source applies pulses and the change in wavespeed as a function of the low frequency stress is measured. In crystalline rock, we expect that the elastic nonlinearity arises from the microcracks and dislocations contained within individual crystals. In contrast, sandstones, limestones and other sedimentary rocks may have other origin(s) of elastic nonlinearity that are currently under debate. Thus we can use a crystalline sample as a point of reference from which to extrapolate to other sources of nonlinear mechanisms. We report results from our preliminary studies applying a number of room-dry rock samples of differing rock
Nonlinear dynamics of quantum cascade lasers with optical feedback
NASA Astrophysics Data System (ADS)
Jumpertz, L.; Ferré, S.; Schires, K.; Carras, M.; Grillot, F.
2015-01-01
Quantum Cascade (QC) lasers are widely used in optical communications, high-resolution spectroscopy, imaging, and remote sensing due to their wide spectral range, going from mid-infrared to the terahertz regime. The dynamics of QClasers are dominated by their ultrafast carrier lifetime, typically of the order of a few picoseconds. The combination of optical nonlinearities and ultrafast dynamics is an interesting feature of QC-lasers, and investigating the dynamical properties of such lasers gives unprecedented insights into the underlying physics of the components, which is of interest for the next generation of QC devices. A particular feature of QC-lasers is the absence of relaxation oscillations, which is the consequence of the relatively short carrier lifetime compared to photon lifetime. Optical feedback (i.e. self-injection) is known to be a robust technique for stabilizing or synchronizing a free-running laser, however its effect on QC-lasers remains mostly unexplored. This work aims at discussing the dynamical properties of QC-lasers operating under optical feedback by employing a novel set of rate equations taking into account the upper and lower lasing levels, the bottom state as well as the gain stage's cascading. This work analyzes the static laser properties subject to optical feedback and provides a comparison with experiments. Spectral analysis reveals that QC-lasers undergo distinct feedback regimes depending on the phase and amplitude of the reinjected field, and that the coherence-collapse regime only appears in a very narrow range of operation, making such lasers much more stable than their interband counterparts.
A new method of modelling and numerical simulation of nonlinear dynamical systems
Colosi, T.; Codreanu, S.
1996-06-01
This work presents the most significant aspects of an original method of modelling and numerical simulation of nonlinear (linear) dynamical systems (1) it assures the local-iterative linearization (LIL) of nonlinear (linear) differential equations and transforms them, in the close proximity of a pivot moment, into algebraic equations. The use of this method is illustrated in the study of a particular nonlinear dynamical systems. The conclusions highlight the advantages of the proposed procedure. {copyright} {ital 1996 American Institute of Physics.}
Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems
Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...
Lifespan Differences in Nonlinear Dynamics during Rest and Auditory Oddball Performance
ERIC Educational Resources Information Center
Muller, Viktor; Lindenberger, Ulman
2012-01-01
Electroencephalographic recordings (EEG) were used to assess age-associated differences in nonlinear brain dynamics during both rest and auditory oddball performance in children aged 9.0-12.8 years, younger adults, and older adults. We computed nonlinear coupling dynamics and dimensional complexity, and also determined spectral alpha power as an…
NASA Technical Reports Server (NTRS)
Hsieh, Shang-Hsien
1993-01-01
The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.
Nonlinear magnetic dynamics in a nanomagnet-topological insulator heterostructure
NASA Astrophysics Data System (ADS)
Duan, Xiaopeng; Li, Xi-Lai; Semenov, Yuriy G.; Kim, Ki Wook
2015-09-01
Magnetization dynamics of a nanomagnet, when strongly coupled with a topological insulator (TI) via the proximity interaction, is examined theoretically in the presence of electrical current on the TI surface under realistic transport conditions. Due to the spin-momentum interlock, the magnetic state and TI electron transport depend significantly on each other. Such an interdependence leads to a variety of nonlinear dynamical responses in all transport regimes including the scattering dominant diffusive cases. Generation of the anomalous Hall current, in particular, is found to be a key to the unique features that have not been observed previously. For instance, the anomalous Hall current can result in antiparallel alignment of the final magnetization state in reference to the effective driving magnetic field by inducing an extra term that counters the damping effect. Similarly the calculation also reveals steady oscillation of the magnetization under a broad range of conditions, offering a robust mechanism for highly efficient magnetization reversal and/or spin wave excitation under a dc bias.
Nonlinear fluctuation effects in dynamics of freely suspended films
NASA Astrophysics Data System (ADS)
Kats, E. I.; Lebedev, V. V.
2015-03-01
Long-scale dynamic fluctuation phenomena in freely suspended films is analyzed. We consider isotropic films that, say, can be pulled from bulk smectic-A liquid crystals. The key feature of such objects is possibility of bending deformations of the film. The bending (also known as flexular) mode turns out to be anomalously weakly attenuated. In the harmonic approximation there is no viscous-like damping of the bending mode, proportional to q2 (q is the wave vector of the mode), since it is forbidden by the rotational symmetry. Therefore, the bending mode is strongly affected by nonlinear dynamic fluctuation effects. We calculate the dominant fluctuation contributions to the damping of the bending mode due to its coupling to the inplane viscous mode, which restores the viscous-like q2 damping of the bending mode. Our calculations are performed in the framework of the perturbation theory where the coupling of the modes is assumed to be small, then the bending mode damping is relatively weak. We discuss our results in the context of existing experiments and numeric simulations of the freely suspended films and propose possible experimental observations of our predictions.
Macrosimulation of nonlinear dynamic systems for wave-shaping applications
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2014-11-01
Macromodeling is a technique widely used in circuits simulation. Macromodels usually describe complex, repetitive parts of large systems. They are often created on the base of original circuits by their simplification, e.g. macromodels of operational amplifiers. Another group of macromodels makes use of the circuit response approximation. This approach is called behavioral macromodeling. Low numerical complexity of behavioral macromodels is especially useful in CAD systems where circuit simulation must be run many times. In this paper the behavioral macromodeling technique has been applied to the whole circuit not to its part. This technique may be understood as shaping of the circuit output response and so belongs to a class of wave-shaping methods. We have used it to nonlinear, dynamic circuits with periodic signals of finite spectra, as e.g. in audio systems. The macromodels shape their frequency and spectral characteristics with a sufficient simplicity to omit unwanted distortions and with a sufficient efficiency to run the simulator in real time. Elaboration of this wave-shaping simulator is based on dynamic circuits identification, Fourier approximation of signals and harmonic balance technique. The obtained macromodel can be run as a software substitute for a hardware audio system.
Simulations of energetic particles interacting with nonlinear anisotropic dynamical turbulence
NASA Astrophysics Data System (ADS)
Heusen, M.; Shalchi, A.
2016-09-01
We investigate test-particle diffusion in dynamical turbulence based on a numerical approach presented before. For the turbulence we employ the nonlinear anisotropic dynamical turbulence model which takes into account wave propagation effects as well as damping effects. We compute numerically diffusion coefficients of energetic particles along and across the mean magnetic field. We focus on turbulence and particle parameters which should be relevant for the solar system and compare our findings with different interplanetary observations. We vary different parameters such as the dissipation range spectral index, the ratio of the turbulence bendover scales, and the magnetic field strength in order to explore the relevance of the different parameters. We show that the bendover scales as well as the magnetic field ratio have a strong influence on diffusion coefficients whereas the influence of the dissipation range spectral index is weak. The best agreement with solar wind observations can be found for equal bendover scales and a magnetic field ratio of δ B / B0 = 0.75.
Nonlinear dynamical analysis for displaced orbits above a planet
NASA Astrophysics Data System (ADS)
Xu, Ming; Xu, Shijie
2008-12-01
Nonlinear dynamical analysis and the control problem for a displaced orbit above a planet are discussed. It is indicated that there are two equilibria for the system, one hyperbolic (saddle) and one elliptic (center), except for the degenerate h {/z max}, a saddle-node bifurcation point. Motions near the equilibria for the nonresonance case are investigated by means of the Birkhoff normal form and dynamical system techniques. The Kolmogorov Arnold Moser (KAM) torus filled with quasiperiodic trajectories is measured in the τ 1 and τ 2 directions, and a rough algorithm for calculating τ 1 and τ 2 is proposed. A general iterative algorithm to generate periodic Lyapunov orbits is also presented. Transitions in the neck region are demonstrated, respectively, in the nonresonance, resonance, and degradation cases. One of the important contributions of the paper is to derive necessary and sufficiency conditions for stability of the motion near the equilibria. Another contribution is to demonstrate numerically that the critical KAM torus of nontransition is filled with the (1,1)-homoclinic orbits of the Lyapunov orbit.
Probabilistic evaluation approach for nonlinear vehicle-bridge dynamic performances
NASA Astrophysics Data System (ADS)
Jin, Zhibin; Pei, Shiling; Li, Xiaozhen; Qiang, Shizhong
2015-03-01
Railroad vehicle and bridge coupled lateral vibration problems are traditionally solved through detailed nonlinear models in time domain using limited samples to represent rail irregularity. Ideally, a random vibration and reliability based approach should be implemented because of the random nature of the excitation process. In this study, vehicle-bridge coupled dynamic equation was derived using the principle of virtual work utilizing a linearized wheel-rail contact equation. This simplification enables the calculation of the system random lateral responses through the pseudo-excitation method. By applying rail irregularity as random excitations to the system, this study utilized an explicit linearization method to avoid iterative solution at each time step of the integration. The results from the linearized method were validated through comparison with results obtained from Monte-Carlo simulations. By applying the linearized approach to probabilistic assessment of the vehicle-bridge system reliability, it was shown that system probability of exceedance of admissible limits increases with train speed and reduces with increased bridge self-weight. It is concluded that the proposed approach provides a viable efficient alternative to investigate the random dynamic characteristics of vehicle-bridge system especially in the lateral direction, which is dominated by the random rail irregularities.
Nonlinear dynamics of cosmic strings with nonscaling loops
Vanchurin, Vitaly
2010-09-15
At early stages the dynamics of cosmic string networks is expected to be influenced by an excessive production of small loops at the scales of initial conditions l{sub min}. To understand the late time behavior we propose a very simple analytical model of strings with a nonscaling population of loops. The complicated nonlinear dynamics is described by only a single parameter N{approx}2/(1-C(l{sub min})) where C(l) is a correlation function of the string tangent vectors. The model predicts an appearance of two new length scales: the coherence length {xi}{approx}t/N{sup 2} and the cross-correlation length {chi}{approx}t/N. At the onset of evolution N{approx}10 and at late times N is expected to grow logarithmically due to cosmological stretching and emission of small loops. The very late time evolution might be modified further when the gravitational back-reaction scale grows larger than l{sub min}.
Numerical simulation of nonlinear dynamical systems driven by commutative noise
Carbonell, F. Biscay, R.J.; Jimenez, J.C.; Cruz, H. de la
2007-10-01
The local linearization (LL) approach has become an effective technique for the numerical integration of ordinary, random and stochastic differential equations. One of the reasons for this success is that the LL method achieves a convenient trade-off between numerical stability and computational cost. Besides, the LL method reproduces well the dynamics of nonlinear equations for which other classical methods fail. However, in the stochastic case, most of the reported works has been focused in Stochastic Differential Equations (SDE) driven by additive noise. This limits the applicability of the LL method since there is a number of interesting dynamics observed in equations with multiplicative noise. On the other hand, recent results show that commutative noise SDEs can be transformed into a random differential equation (RDE) by means of a random diffeomorfism (conjugacy). This paper takes advantages of such conjugacy property and the LL approach for defining a LL scheme for SDEs driven by commutative noise. The performance of the proposed method is illustrated by means of numerical simulations.
The nonlinear dynamics of the Oklo natural reactor
Bilanovic, Z.; Harms, A.A.
1985-11-01
An analysis of the Oklo natural reactor, a self-sustaining and self-regulating critical assembly that existed some 2 billion years ago in Gabon, Africa, is presented. Nonlinear continuous dif ferential and nonlinear discrete iterative formulations are established and selected parameter characterizations identified. Conceivable power oscillations are calculated and discussed. Some implications of nonlinear mappings for nuclear simulation are suggested.
Nonlinear dynamics of heart rate variability in cocaine-exposed neonates during sleep.
Garde, S; Regalado, M G; Schechtman, V L; Khoo, M C
2001-06-01
The aim of this study was to determine the effects of prenatal cocaine exposure (PCE) on the dynamics of heart rate variability in full-term neonates during sleep. R-R interval (RRI) time series from 9 infants with PCE and 12 controls during periods of stable quiet sleep and active sleep were analyzed using autoregressive modeling and nonlinear dynamics. There were no differences between the two groups in spectral power distribution, approximate entropy, correlation dimension, and nonlinear predictability. However, application of surrogate data analysis to these measures revealed a significant degree of nonlinear RRI dynamics in all subjects. A parametric model, consisting of a nonlinear delayed-feedback system with stochastic noise as the perturbing input, was employed to estimate the relative contributions of linear and nonlinear deterministic dynamics in the data. Both infant groups showed similar proportional contributions in linear, nonlinear, and stochastic dynamics. However, approximate entropy, correlation dimension, and nonlinear prediction error were all decreased in active versus quiet sleep; in addition, the parametric model revealed a doubling of the linear component and a halving of the nonlinear contribution to overall heart rate variability. Spectral analysis indicated a shift in relative power toward lower frequencies. We conclude that 1) RRI dynamics in infants with PCE and normal controls are similar; and 2) in both groups, sympathetic dominance during active sleep produces primarily periodic low-frequency oscillations in RRI, whereas in quiet sleep vagal modulation leads to RRI fluctuations that are broadband and dynamically more complex. PMID:11356653
Moderately nonlinear diffuse-charge dynamics under an ac voltage.
Stout, Robert F; Khair, Aditya S
2015-09-01
The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer. PMID:26465471
Small-scale nonlinear dynamics of K-mouflage theories
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2014-12-01
We investigate the small-scale static configurations of K-mouflage models defined by a general function K (χ ) of the kinetic terms. The fifth force is screened by the nonlinear K-mouflage mechanism if K'(χ ) grows sufficiently fast for large negative χ . In the general nonspherically symmetric case, the fifth force is not aligned with the Newtonian force. For spherically symmetric static matter density profiles, we show that the results depend on the potential function W-(y )=y K'(-y2/2 ) ; i.e., W-(y ) must be monotonically increasing to +∞ for y ≥0 to guarantee the existence of a single solution throughout space for any matter density profile. Small radial perturbations around these static profiles propagate as travelling waves with a velocity greater than the speed of light. Starting from vanishing initial conditions for the scalar field and for a time-dependent matter density corresponding to the formation of an overdensity, we numerically check that the scalar field converges to the static solution. If W- is bounded, for high-density objects there are no static solutions throughout space, but one can still define a static solution restricted to large radii. Our dynamical study shows that the scalar field relaxes to this static solution at large radii, whereas spatial gradients keep growing with time at smaller radii. If W- is not bounded but nonmonotonic, there is an infinite number of discontinuous static solutions. However, the Klein-Gordon equation is no longer a well-defined hyperbolic equation, which leads to complex characteristic speeds and exponential instabilities. Therefore, these discontinuous static solutions are not physical, and these models are not theoretically sound. Such K-mouflage scenarios provide an example of theories that can appear viable at the cosmological level, for the cosmological background and perturbative analysis, while being meaningless at a nonlinear level for small-scale configurations. This shows the importance of
NASA Astrophysics Data System (ADS)
Fredette, Luke; Dreyer, Jason T.; Rook, Todd E.; Singh, Rajendra
2016-06-01
The dynamic stiffness properties of automotive hydraulic bushings exhibit significant amplitude sensitivity which cannot be captured by linear time-invariant models. Quasi-linear and nonlinear models are therefore proposed with focus on the amplitude sensitivity in magnitude and loss angle spectra (up to 50 Hz). Since production bushing model parameters are unknown, dynamic stiffness tests and laboratory experiments are utilized to extract model parameters. Nonlinear compliance and resistance elements are incorporated, including their interactions in order to improve amplitude sensitive predictions. New solution approximations for the new nonlinear system equations refine the multi-term harmonic balance term method. Quasi-linear models yield excellent accuracy but cannot predict trends in amplitude sensitivity since they rely on available dynamic stiffness measurements. Nonlinear models containing both nonlinear resistance and compliance elements yield superior predictions to those of prior models (with a single nonlinearity) while also providing more physical insight. Suggestion for further work is briefly mentioned.
NASA Astrophysics Data System (ADS)
Driben, R.; Konotop, V. V.; Meier, T.
2016-03-01
Nonlinearity is the driving force for numerous important effects in nature typically showing transitions between different regimes, regular, chaotic or catastrophic behavior. Localized nonlinear modes have been the focus of intense research in areas such as fluid and gas dynamics, photonics, atomic and solid state physics etc. Due to the richness of the behavior of nonlinear systems and due to the severe numerical demands of accurate three-dimensional (3D) numerical simulations presently only little knowledge is available on the dynamics of complex nonlinear modes in 3D. Here, we investigate the dynamics of 3D non-coaxial matter wave vortices that are trapped in a parabolic potential and interact via a repulsive nonlinearity. Our numerical simulations demonstrate the existence of an unexpected and fascinating nonlinear regime that starts immediately when the nonlinearity is switched-on and is characterized by a smooth dynamics representing torque-free precession with nutations. The reported motion is proven to be robust regarding various effects such as the number of particles, dissipation and trap deformations and thus should be observable in suitably designed experiments. Since our theoretical approach, i.e., coupled nonlinear Schrödinger equations, is quite generic, we expect that the obtained novel dynamical behavior should also exist in other nonlinear systems.
Driben, R.; Konotop, V. V.; Meier, T.
2016-01-01
Nonlinearity is the driving force for numerous important effects in nature typically showing transitions between different regimes, regular, chaotic or catastrophic behavior. Localized nonlinear modes have been the focus of intense research in areas such as fluid and gas dynamics, photonics, atomic and solid state physics etc. Due to the richness of the behavior of nonlinear systems and due to the severe numerical demands of accurate three-dimensional (3D) numerical simulations presently only little knowledge is available on the dynamics of complex nonlinear modes in 3D. Here, we investigate the dynamics of 3D non-coaxial matter wave vortices that are trapped in a parabolic potential and interact via a repulsive nonlinearity. Our numerical simulations demonstrate the existence of an unexpected and fascinating nonlinear regime that starts immediately when the nonlinearity is switched-on and is characterized by a smooth dynamics representing torque-free precession with nutations. The reported motion is proven to be robust regarding various effects such as the number of particles, dissipation and trap deformations and thus should be observable in suitably designed experiments. Since our theoretical approach, i.e., coupled nonlinear Schrödinger equations, is quite generic, we expect that the obtained novel dynamical behavior should also exist in other nonlinear systems. PMID:26964759
PCI-SS: MISO dynamic nonlinear protein secondary structure prediction
Green, James R; Korenberg, Michael J; Aboul-Magd, Mohammed O
2009-01-01
Background Since the function of a protein is largely dictated by its three dimensional configuration, determining a protein's structure is of fundamental importance to biology. Here we report on a novel approach to determining the one dimensional secondary structure of proteins (distinguishing α-helices, β-strands, and non-regular structures) from primary sequence data which makes use of Parallel Cascade Identification (PCI), a powerful technique from the field of nonlinear system identification. Results Using PSI-BLAST divergent evolutionary profiles as input data, dynamic nonlinear systems are built through a black-box approach to model the process of protein folding. Genetic algorithms (GAs) are applied in order to optimize the architectural parameters of the PCI models. The three-state prediction problem is broken down into a combination of three binary sub-problems and protein structure classifiers are built using 2 layers of PCI classifiers. Careful construction of the optimization, training, and test datasets ensures that no homology exists between any training and testing data. A detailed comparison between PCI and 9 contemporary methods is provided over a set of 125 new protein chains guaranteed to be dissimilar to all training data. Unlike other secondary structure prediction methods, here a web service is developed to provide both human- and machine-readable interfaces to PCI-based protein secondary structure prediction. This server, called PCI-SS, is available at . In addition to a dynamic PHP-generated web interface for humans, a Simple Object Access Protocol (SOAP) interface is added to permit invocation of the PCI-SS service remotely. This machine-readable interface facilitates incorporation of PCI-SS into multi-faceted systems biology analysis pipelines requiring protein secondary structure information, and greatly simplifies high-throughput analyses. XML is used to represent the input protein sequence data and also to encode the resulting
Nonlinear dynamics of drops and bubbles and chaotic phenomena
NASA Technical Reports Server (NTRS)
Trinh, Eugene H.; Leal, L. G.; Feng, Z. C.; Holt, R. G.
1994-01-01
Nonlinear phenomena associated with the dynamics of free drops and bubbles are investigated analytically, numerically and experimentally. Although newly developed levitation and measurement techniques have been implemented, the full experimental validation of theoretical predictions has been hindered by interfering artifacts associated with levitation in the Earth gravitational field. The low gravity environment of orbital space flight has been shown to provide a more quiescent environment which can be utilized to better match the idealized theoretical conditions. The research effort described in this paper is a closely coupled collaboration between predictive and guiding theoretical activities and a unique experimental program involving the ultrasonic and electrostatic levitation of single droplets and bubbles. The goal is to develop and to validate methods based on nonlinear dynamics for the understanding of the large amplitude oscillatory response of single drops and bubbles to both isotropic and asymmetric pressure stimuli. The first specific area on interest has been the resonant coupling between volume and shape oscillatory modes isolated gas or vapor bubbles in a liquid host. The result of multiple time-scale asymptotic treatment, combined with domain perturbation and bifurcation methods, has been the prediction of resonant and near-resonant coupling between volume and shape modes leading to stable as well as chaotic oscillations. Experimental investigations of the large amplitude shape oscillation modes of centimeter-size single bubbles trapped in water at 1 G and under reduced hydrostatic pressure, have suggested the possibility of a low gravity experiment to study the direct coupling between these low frequency shape modes and the volume pulsation, sound-radiating mode. The second subject of interest has involved numerical modeling, using the boundary integral method, of the large amplitude shape oscillations of charged and uncharged drops in the presence
Nonlinear magnetic vortex dynamics in a circular nanodot excited by spin-polarized current
2014-01-01
We investigate analytically and numerically nonlinear vortex spin torque oscillator dynamics in a circular magnetic nanodot induced by a spin-polarized current perpendicular to the dot plane. We use a generalized nonlinear Thiele equation including spin-torque term by Slonczewski for describing the nanosize vortex core transient and steady orbit motions and analyze nonlinear contributions to all forces in this equation. Blue shift of the nano-oscillator frequency increasing the current is explained by a combination of the exchange, magnetostatic, and Zeeman energy contributions to the frequency nonlinear coefficient. Applicability and limitations of the standard nonlinear nano-oscillator model are discussed. PMID:25147490
Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics.
Linnemann, D; Strobel, H; Muessel, W; Schulz, J; Lewis-Swan, R J; Kheruntsyan, K V; Oberthaler, M K
2016-07-01
We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies. PMID:27419565
Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
Linnemann, D.; Strobel, H.; Muessel, W.; Schulz, J.; Lewis-Swan, R. J.; Kheruntsyan, K. V.; Oberthaler, M. K.
2016-07-01
We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.
NASA Astrophysics Data System (ADS)
Bentaallah, Abderrahim; Massoum, Ahmed; Benhamida, Farid; Meroufel, Abdelkader
2012-03-01
This paper studies the nonlinear adaptive control of an induction motor with natural dynamic complete nonlinear observer. The aim of this work is to develop a nonlinear control law and adaptive performance for an asynchronous motor with two main objectives: to improve the continuation of trajectories and the stability, robustness to parametric variations and disturbances rejection. This control law will independently control the speed and flux into the machine by restricting supply. A complete nonlinear observer for dynamic nature ensuring closed loop stability of the entire control and observer has been developed. Several simulations have also been carried out to demonstrate system performance.
Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised
NASA Technical Reports Server (NTRS)
Devasia, Santosh
1999-01-01
A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.
Nonlinear dynamical model and response of avian cranial kinesis.
Meekangvan, Preeda; A Barhorst, Alan; Burton, Thomas D; Chatterjee, Sankar; Schovanec, Lawrence
2006-05-01
All modern birds have kinetic skulls in which the upper bill can move relative to the braincase, but the biomechanics and motion dynamics of cranial kinesis in birds are poorly understood. In this paper, we model the dynamics of avian cranial kinesis, such as prokinesis and proximal rhynchokinesis in which the upper jaw pivots around the nasal-frontal (N-F) hinge. The purpose of this paper is to present to the biological community an approach that demonstrates the application of sophisticated predictive mathematical modeling tools to avian kinesis. The generality of the method, however, is applicable to the advanced study of the biomechanics of other skeletal systems. The paper begins with a review of the relevant biological literature as well as the essential morphology of avian kinesis, especially the mechanical coupling of the upper and lower jaw by the postorbital ligament. A planar model of the described bird jaw morphology is then developed that maintains the closed kinematic topology of the avian jaw mechanism. We then develop the full nonlinear equations of motion with the assumption that the M. protractor pterygoideus and M. depressor mandibulae act on the quadrate as a pure torque, and the nasal frontal hinge is elastic with damping. The mechanism is shown to be a single degree of freedom device due to the holonomic constraints present in the quadrate-jugal bar-upper jaw-braincase-quadrate kinematic chain as well as the quadrate-lower jaw-postorbital ligament-braincase-quadrate kinematic chain. The full equations are verified via simulation and animation using the parameters of a Grey Heron (Ardea cinerea). Next we develop a simplified analytical model of the equations by power series expansion. We demonstrate that this model reproduces the dynamics of the full model to a high degree of fidelity. We proceed to use the harmonic balance technique to develop the frequency response characteristics of the jaw mechanism. It is shown that this avian cranial
Advanced data assimilation in strongly nonlinear dynamical systems
NASA Technical Reports Server (NTRS)
Miller, Robert N.; Ghil, Michael; Gauthiez, Francois
1994-01-01
Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Nonlinear dynamics of wind waves: multifractal phase/time effects
NASA Astrophysics Data System (ADS)
Mellen, R. H.; Leykin, I. A.
In addition to the bispectral coherence method, phase/time analysis of analytic signals is another promising avenue for the investigation of phase effects in wind waves. Frequency spectra of phase fluctuations obtained from both sea and laboratory experiments follow an F-β power law over several decades, suggesting that a fractal description is appropriate. However, many similar natural phenomena have been shown to be multifractal. Universal multifractals are quantified by two additional parameters: the Lévy index 0 < α < 2 for the type of multifractal and the co-dimension 0 < C1 < 1 for intermittence. The three parameters are a full statistical measure the nonlinear dynamics. Analysis of laboratory flume data is reported here and the results indicate that the phase fluctuations are 'hard multifractal' (α > 1). The actual estimate is close to the limiting value α = 2, which is consistent with Kolmogorov's lognormal model for turbulent fluctuations. Implications for radar and sonar backscattering from the sea surface are briefly considered.
A new method for parameter estimation in nonlinear dynamical equations
NASA Astrophysics Data System (ADS)
Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao
2015-01-01
Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.
Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics
Alex J. Dragt; Filippo Neri; Govindan Rangarajan; David Douglas; Liam M. Healy; Robert D. Ryne
1988-12-01
The purpose of this paper is to present a summary of new methods, employing Lie algebraic tools, for characterizing beam dynamics in charged-particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics, by a certain operator. The operators for the various elements can then be concatenated, following well-defined rules, to obtain a resultant operator that characterizes the entire system. This paper deals mostly with accelerator design and charged-particle beam transport. The application of Lie algebraic methods to light optics and electron microscopes is described elsewhere (1, see also 44). To keep its scope within reasonable bounds, they restrict their treatment of accelerator design and charged-particle beam transport primarily to the use of Lie algebraic methods for the description of particle orbits in terms of transfer maps. There are other Lie algebraic or related approaches to accelerator problems that the reader may find of interest (2). For a general discussion of linear and nonlinear problems in accelerator physics see (3).
Nonlinear dynamics and breakup of free-surface flows
Eggers, J.
1997-07-01
Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems. {copyright} {ital 1997} {ital The American Physical Society}
Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1996-01-01
Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.
Dynamic Gaussian wake meandering in a restricted nonlinear simulation framework
NASA Astrophysics Data System (ADS)
Bretheim, Joel; Porte-Agel, Fernando; Gayme, Dennice; Meneveau, Charles
2015-11-01
Wake meandering can significantly impact the performance of large-scale wind farms. Simplified wake expansion (e.g., Jensen/PARK) models, which are commonly used in industry, lead to accurate predictions of certain wind farm performance characteristics (e.g., time- and row-averaged total power output). However, they are unable to capture certain temporal phenomena such as wake meandering, which can have profound effects on both power output and turbine loading. We explore a dynamic wake modeling framework based on the approach proposed by Larsen et al. (Wind Energy 11, 2008) whereby turbine ``wake elements'' are treated as passive tracers and advected by an averaged streamwise flow. Our wake elements are treated as Gaussian velocity deficit profiles (Bastankhah and Porte-Agel, Renew. Energy 70, 2014). A restricted nonlinear (RNL) model is used to capture the turbulent velocity fluctuations that are critical to the wake meandering phenomenon. The RNL system, which has been used in prior wall-turbulence studies, provides a computationally affordable way to model atmospheric turbulence, making it more reasonable for use in engineering models than the more accurate but computationally intensive approaches like large-eddy simulation. This work is supported by NSF (IGERT 0801471, SEP-1230788, and IIA-1243482, the WINDINSPIRE project).
Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives
Faybishenko, Boris
2002-11-27
The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.
Vibrational dynamics of vocal folds using nonlinear normal modes.
Pinheiro, Alan P; Kerschen, Gaëtan
2013-08-01
Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues. The results show very interesting and complex nonlinear phenomena including frequency-energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations. PMID:23218815
Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations
NASA Astrophysics Data System (ADS)
Zhang, Yu; Jiang, Jack J.
2008-09-01
Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.
Porta, Alberto; Bari, Vlasta; Marchi, Andrea; De Maria, Beatrice; Cysarz, Dirk; Van Leeuwen, Peter; Takahashi, Anielle C. M.; Catai, Aparecida M.; Gnecchi-Ruscone, Tomaso
2015-01-01
Two diverse complexity metrics quantifying time irreversibility and local prediction, in connection with a surrogate data approach, were utilized to detect nonlinear dynamics in short heart period (HP) variability series recorded in fetuses, as a function of the gestational period, and in healthy humans, as a function of the magnitude of the orthostatic challenge. The metrics indicated the presence of two distinct types of nonlinear HP dynamics characterized by diverse ranges of time scales. These findings stress the need to render more specific the analysis of nonlinear components of HP dynamics by accounting for different temporal scales. PMID:25806002
Intertwining operators for the central extension of the Yangian double
NASA Astrophysics Data System (ADS)
Khoroshkin, S.; Lebedev, D.; Pakuliak, S.
1996-02-01
We continue the investigation of the central extended Yangian double [S. Khoroshkin, Central extension of the Yangian double, in: Collection SMF, Colloque “Septièmes Rencontres du Contact Franco-Belge en Algèbre”, June 1995, Reims; preprint q-alg/9602031]. In this paper we study the intertwining operators for certain infinite dimensional representations of overlineDY( sl2) , which are deformed analogs of the highest weight representations of the affine algebra overlinesl2 at level 1. We give bosonized expressions for intertwining operators, and verify that they generate an algebra isomorphic to the Zamolodchikov-Faddeev algebra for the SU (2)-invariant Thirring model. We compose from them L-operators by Miki's prescription and verify that they coincide with L-operators constructed from the universal R-matrix.
Colloquium: Theory of intertwined orders in high temperature superconductors
NASA Astrophysics Data System (ADS)
Fradkin, Eduardo; Kivelson, Steven A.; Tranquada, John M.
2015-04-01
The electronic phase diagrams of many highly correlated systems, and, in particular, the cuprate high temperature superconductors, are complex, with many different phases appearing with similar (sometimes identical) ordering temperatures even as material properties, such as dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as "competing orders." However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative "pair-density wave," the general relation is better thought of in terms of "intertwined orders." Some of the experiments in the cuprates which suggest that essential aspects of the physics are reflected in the intertwining of multiple orders, not just in the nature of each order by itself, are selectively analyzed. Several theoretical ideas concerning the origin and implications of this complexity are also summarized and critiqued.
Theory of intertwined orders in high temperature superconductors
Fradkin, Eduardo; Tranquada, John M.; Kivelson, Steven A.
2015-03-26
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar—sometimes identical—ordering temperatures even as material properties, such as a dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as “competing orders.” However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative “pair-density-wave,” the general relation is better thought of in terms of “intertwined orders.” We selectively analyze some of the experiments in the cuprates which suggest that essentialmore » aspects of the physics are reflected in the intertwining of multiple orders—not just in the nature of each order by itself. We also summarize and critique several theoretical ideas concerning the origin and implications of this complexity.« less
Theory of intertwined orders in high temperature superconductors
Fradkin, Eduardo; Tranquada, John M.; Kivelson, Steven A.
2015-03-26
The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar—sometimes identical—ordering temperatures even as material properties, such as a dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as “competing orders.” However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative “pair-density-wave,” the general relation is better thought of in terms of “intertwined orders.” We selectively analyze some of the experiments in the cuprates which suggest that essential aspects of the physics are reflected in the intertwining of multiple orders—not just in the nature of each order by itself. We also summarize and critique several theoretical ideas concerning the origin and implications of this complexity.
NASA Technical Reports Server (NTRS)
Lan, C. Edward; Ge, Fuying
1989-01-01
Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.
INTRODUCTION: Introduction to Nonlinear Dynamics and Chaos Theory
NASA Astrophysics Data System (ADS)
McCauley, Joseph L.
1988-01-01
Chapters 1-3 of these lectures were given at the University of Oslo during my academic free half-year August l985-January 1986 which I spent at the Institute for Energy Technology (IFE). Chapter 4 was given by T Riste during my journeys to other Scandinavian institutions where I held seminars covering much of what is reflected in Chapter 5. That chapter represents a contribution to chaos theory that was carried out in collaboration with J Palmore. In place of the universal properties of unimodal maps, which are well-treated in the books by Cvitanovic and Schuster, I have instead based my elementary introduction to scaling and universality upon the damped driven pendulum and circle maps, which are of current interest to experimenters at IFE and elsewhere, as is reflected in the literature over the past year. Also, the circle map has not been so well-treated pedagogically in available texts. The discussion in Chapter 3 is not advanced, but it should prepare the reader for a better appreciation of the literature in that field. I should say that these lectures for the most part were written for students, for experimenters, and for curious theorists from other fields in physics, but not for the experts in nonlinear dynamics. For example, Chapter 3 ends where the hardest work begins. Tn preparing the lectures, I drew heavily upon the books by Arnol'd, Jorna, Jordan and Smith, Lichtenberg and Lieberman, and Schuster, and upon numerous journal articles. The level of the lectures is that of a second year graduate course at the University of Houston, but beginning with undergraduate-level topics in ordinary differential equations. Throughout, I have emphasized my interest in the connection of nonlinear dynamics to statistical mechanics, as well as my interest in "computer arithmetic". I hope that the reader will also find these subjects to be of interest since they have provided me with a great deal of intellectual enjoyment. My free-half-year at IFE would have been
Linear and Nonlinear Analysis of Brain Dynamics in Children with Cerebral Palsy
ERIC Educational Resources Information Center
Sajedi, Firoozeh; Ahmadlou, Mehran; Vameghi, Roshanak; Gharib, Masoud; Hemmati, Sahel
2013-01-01
This study was carried out to determine linear and nonlinear changes of brain dynamics and their relationships with the motor dysfunctions in CP children. For this purpose power of EEG frequency bands (as a linear analysis) and EEG fractality (as a nonlinear analysis) were computed in eyes-closed resting state and statistically compared between 26…
An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models
ERIC Educational Resources Information Center
Chow, Sy-Miin; Ferrer, Emilio; Nesselroade, John R.
2007-01-01
In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways:…
Is DNA a nonlinear dynamical system where solitary conformational waves are possible?
Yakushevich, L V
2001-09-01
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA's nonlinear properties. PMID:11568475
Nonlinear Dynamics of Extended Hydrologic Systems over long time scales
NASA Astrophysics Data System (ADS)
Lall, Upmanu
2014-05-01
We often view our knowledge of hydrology and hence of nature as intransient, at least over the time scales over which we study processes we wish to predict and understand. Over the last few decades, this assumption has come under question, largely because of the vocal expression of a changing climate, but also the recurrent demonstration of significant land use change, both of which significantly affect the boundary conditions for terrestrial hydrology that is our forte. Most recently, the concepts of hydromorphology and social hydrology have entered the discussion, and the notion that climate and hydrology influence human action, which in turn shapes hydrology, is being recognized. Finally, as a field, we seem to be coming to the conclusion that the hydrologic system is an open system, whose boundaries evolve in time, and that the hydrologic system, at many scales, has a profound effect on the systems that drive it -- whether they be the ecological and climatic systems, or the social system. What a mess! Complexity! Unpredictability! At a certain level of abstraction, one can consider the evolution of these coupled systems with nonlinear feedbacks and ask what types of questions are relevant in terms of such a coupled evolution? What are their implications at the planetary scale? What are their implications for a subsistence farmer in an arid landscape who may under external influence achieve a new transient hydro-ecological equilibrium? What are the implications for the economy and power of nations? In this talk, I will try to raise some of these questions and also provide some examples with very simple dynamical systems that suggest ways of thinking about some practical issues of feedback across climate, hydrology and human behavior.
On the dynamics of approximating schemes for dissipative nonlinear equations
NASA Technical Reports Server (NTRS)
Jones, Donald A.
1993-01-01
Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.
Nonlinear Compliance Modulates Dynamic Bronchoconstriction in a Multiscale Airway Model
Hiorns, Jonathan E.; Jensen, Oliver E.; Brook, Bindi S.
2014-01-01
The role of breathing and deep inspirations (DI) in modulating airway hyperresponsiveness remains poorly understood. In particular, DIs are potent bronchodilators of constricted airways in nonasthmatic subjects but not in asthmatic subjects. Additionally, length fluctuations (mimicking DIs) have been shown to reduce mean contractile force when applied to airway smooth muscle (ASM) cells and tissue strips. However, these observations are not recapitulated on application of transmural pressure (PTM) oscillations (that mimic tidal breathing and DIs) in isolated intact airways. To shed light on this paradox, we have developed a biomechanical model of the intact airway, accounting for strain-stiffening due to collagen recruitment (a large component of the extracellular matrix (ECM)), and dynamic actomyosin-driven force generation by ASM cells. In agreement with intact airway studies, our model shows that PTM fluctuations at particular mean transmural pressures can lead to only limited bronchodilation. However, our model predicts that moving the airway to a more compliant point on the static pressure-radius relationship (which may involve reducing mean PTM), before applying pressure fluctuations, can generate greater bronchodilation. This difference arises from competition between passive strain-stiffening of ECM and force generation by ASM yielding a highly nonlinear relationship between effective airway stiffness and PTM, which is modified by the presence of contractile agonist. Effectively, the airway at its most compliant may allow for greater strain to be transmitted to subcellular contractile machinery. The model predictions lead us to hypothesize that the maximum possible bronchodilation of an airway depends on its static compliance at the PTM about which the fluctuations are applied. We suggest the design of additional experimental protocols to test this hypothesis. PMID:25517167
Summary report of the group on single-particle nonlinear dynamics
Axinescu, S.; Bartolini, R.; Bazzani, A.
1996-10-01
This report summarizes the research on single-particle nonlinear beam dynamics. It discusses the following topics: analytical and semi-analytical tools; early prediction of the dynamic aperture; how the results are commonly presented; Is the mechanism of the dynamic aperture understand; ripple effects; and beam-beam effects.
Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary
Chattopadhyay, S.; Audy, P.; Courant, E.D.; Forest, E.; Guignard, G.; Hagel, J.; Heifets, S.; Keil, E.; Kheifets, S.; Mais, H.; Moshammer, H.; Pellegrini, C.; Pilat, F.; Suzuki, T.; Turchetti, G.; Warnock, R.L.
1988-07-01
A summary and commentary of the available theoretical and analytical tools and recent advances in the nonlinear dynamics, stability and aperture issues in storage rings are presented. 11 refs., 4 figs.
Infectious diseases in space and time: noise and nonlinearity in epidemiological dynamics
NASA Astrophysics Data System (ADS)
Grenfell, Bryan
2005-03-01
I illustrate the impact of noise and nonlinearity on the spatio-temporal dynamics and evolution of epidemics using mathematical models and analyses of detailed epidemiological data from childhood infections, such as measles.
Modelling Nonlinear Dynamic Textures using Hybrid DWT-DCT and Kernel PCA with GPU
NASA Astrophysics Data System (ADS)
Ghadekar, Premanand Pralhad; Chopade, Nilkanth Bhikaji
2016-06-01
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.
The effect of problem perturbations on nonlinear dynamical systems and their reduced order models
Serban, R; Homescu, C; Petzold, L
2005-03-03
Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: 'What is the effect of perturbations in the problem parameters on the output functional of a nonlinear dynamical system?' and 'To what extent does the reduced order model capture this effect?'
Identification of nonlinear dynamic systems using functional link artificial neural networks.
Patra, J C; Pal, R N; Chatterji, B N; Panda, G
1999-01-01
We have presented an alternate ANN structure called functional link ANN (FLANN) for nonlinear dynamic system identification using the popular backpropagation algorithm. In contrast to a feedforward ANN structure, i.e., a multilayer perceptron (MLP), the FLANN is basically a single layer structure in which nonlinearity is introduced by enhancing the input pattern with nonlinear functional expansion. With proper choice of functional expansion in a FLANN, this network performs as good as and in some cases even better than the MLP structure for the problem of nonlinear system identification. PMID:18252296
On the nonlinear dissipative dynamics of weakly overdamped oscillators
Brezhnev, Yu. V.; Sazonov, S. V.
2014-11-15
We consider the motion of weakly overdamped linear oscillators. Weak overdamping of an oscillator is defined as a slight excess of the damping decrement over its natural frequency. Exact solutions are obtained for a certain relation between the decrement and the natural frequency and qualitatively different regimes of motion are analyzed. The threshold conditions corresponding to changes of regimes are established; one-component models with an arbitrary degree of nonlinearity are analyzed, and quadratic and cubic nonlinearities are considered in detail. If the nonlinearity in a multicomponent model is determined by a homogeneous function, transformations of the Kummer-Liouville type can be reduced to an autonomous system of second-order differential equations in the case when the relation between the decrement and the natural frequency has been established. Some integrable multicomponent models with quadratic and cubic nonlinearities are analyzed.
On the nonlinear dissipative dynamics of weakly overdamped oscillators
NASA Astrophysics Data System (ADS)
Brezhnev, Yu. V.; Sazonov, S. V.
2014-11-01
We consider the motion of weakly overdamped linear oscillators. Weak overdamping of an oscillator is defined as a slight excess of the damping decrement over its natural frequency. Exact solutions are obtained for a certain relation between the decrement and the natural frequency and qualitatively different regimes of motion are analyzed. The threshold conditions corresponding to changes of regimes are established; one-component models with an arbitrary degree of nonlinearity are analyzed, and quadratic and cubic nonlinearities are considered in detail. If the nonlinearity in a multicomponent model is determined by a homogeneous function, transformations of the Kummer-Liouville type can be reduced to an autonomous system of second-order differential equations in the case when the relation between the decrement and the natural frequency has been established. Some integrable multicomponent models with quadratic and cubic nonlinearities are analyzed.
Nonlinear Dynamic Modeling and Social Contagion: Reply to Stoolmiller (1998).
ERIC Educational Resources Information Center
Rodgers, Joseph Lee; Rowe, David C.; Buster, Maury
1998-01-01
Reviews and comments on Stoolmiller's (1998) criticisms of an epidemic model of the onset of social activities (EMOSA) and about nonlinear modeling in general. Discusses the idea of social contagion as a general theoretical tool. (Author)
An investigation on vibration energy harvesting using nonlinear dynamic principles inspired by trees
NASA Astrophysics Data System (ADS)
Harne, R. L.; Sun, A.; Wang, K. W.
2015-04-01
Trees exploit intriguing mechanisms such as multimodal frequency distributions and nonlinearities to distribute and dampen the aerodynamically-induced vibration energies to which they are subjected. In dynamical systems, these mechanisms are comparable to the internal resonance phenomenon. In recent years, researchers have harnessed strong nonlinearities, including internal resonance, to induce energetic dynamics that enhance performance of vibration energy harvesting systems. For trees, the internal resonance-like dynamics are evidently useful damping mechanisms in spite of the high variation associated with excitation and structural parameters. Yet for dynamic systems, studies show narrow operating regimes which exhibit internal resonance-based behaviors, suggesting that the energetic dynamics may be deactivated if stochastic inputs corrupt ideal excitation properties. To address these issues, this research evaluates the opportunities enabled by exploiting nonlinear, multimodal motions in an L-shaped energy harvester platform. The system dynamics are probed analytically, numerically, and experimentally for comprehensive insights on the versatility of internal resonance-based behaviors for energy harvesting. It is found that although activating the high amplitude nonlinear dynamics to enhance power generation is robust to significant additive noise in the harmonic excitations, parameter sensitivities may pose practical challenges in application. Discussion is provided on means to address such concerns and on future strategies that may favorably exploit nonlinearity and multimodal dynamics for robust energy harvesting performance.
A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors
NASA Technical Reports Server (NTRS)
Shi, H.; Yang, B.; Thomson, M.; Fang, H.
2011-01-01
This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.
NASA Astrophysics Data System (ADS)
Mukai, Y.; Hirori, H.; Yamamoto, T.; Kageyama, H.; Tanaka, K.
2016-01-01
We report on the nonlinear magnetization dynamics of a HoFeO3 crystal induced by a strong terahertz magnetic field resonantly enhanced with a split ring resonator and measured with magneto-optical Kerr effect microscopy. The terahertz magnetic field induces a large change (˜40%) in the spontaneous magnetization. The frequency of the antiferromagnetic resonance decreases in proportion to the square of the magnetization change. A modified Landau-Lifshitz-Gilbert equation with a phenomenological nonlinear damping term quantitatively reproduced the nonlinear dynamics.
X-ray third-order nonlinear dynamical diffraction in a crystal
Balyan, M. K.
2015-12-15
The dynamic diffraction of an X-ray wave in a crystal with a third-order nonlinear response to external field strength has been theoretically investigated. General equations for the wave propagation in crystal and nonlinear Takagi equations for both ideal and deformed crystals are derived. Integrals of motion are determined for the nonlinear problem of dynamic diffraction. The results of the numerical calculations of reflectivity in the symmetric Laue geometry for an incident plane wave and the intensity distributions on the output crystal surface for a point source are reported as an example.
NASA Astrophysics Data System (ADS)
Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin
2016-08-01
This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.
Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems
NASA Technical Reports Server (NTRS)
Murthy, V. R.; Shultz, Louis A.
1994-01-01
The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.
Resting State Networks' Corticotopy: The Dual Intertwined Rings Architecture
Mesmoudi, Salma; Perlbarg, Vincent; Rudrauf, David; Messe, Arnaud; Pinsard, Basile; Hasboun, Dominique; Cioli, Claudia; Marrelec, Guillaume; Toro, Roberto; Benali, Habib; Burnod, Yves
2013-01-01
How does the brain integrate multiple sources of information to support normal sensorimotor and cognitive functions? To investigate this question we present an overall brain architecture (called “the dual intertwined rings architecture”) that relates the functional specialization of cortical networks to their spatial distribution over the cerebral cortex (or “corticotopy”). Recent results suggest that the resting state networks (RSNs) are organized into two large families: 1) a sensorimotor family that includes visual, somatic, and auditory areas and 2) a large association family that comprises parietal, temporal, and frontal regions and also includes the default mode network. We used two large databases of resting state fMRI data, from which we extracted 32 robust RSNs. We estimated: (1) the RSN functional roles by using a projection of the results on task based networks (TBNs) as referenced in large databases of fMRI activation studies; and (2) relationship of the RSNs with the Brodmann Areas. In both classifications, the 32 RSNs are organized into a remarkable architecture of two intertwined rings per hemisphere and so four rings linked by homotopic connections. The first ring forms a continuous ensemble and includes visual, somatic, and auditory cortices, with interspersed bimodal cortices (auditory-visual, visual-somatic and auditory-somatic, abbreviated as VSA ring). The second ring integrates distant parietal, temporal and frontal regions (PTF ring) through a network of association fiber tracts which closes the ring anatomically and ensures a functional continuity within the ring. The PTF ring relates association cortices specialized in attention, language and working memory, to the networks involved in motivation and biological regulation and rhythms. This “dual intertwined architecture” suggests a dual integrative process: the VSA ring performs fast real-time multimodal integration of sensorimotor information whereas the PTF ring performs multi
Resting state networks' corticotopy: the dual intertwined rings architecture.
Mesmoudi, Salma; Perlbarg, Vincent; Rudrauf, David; Messe, Arnaud; Pinsard, Basile; Hasboun, Dominique; Cioli, Claudia; Marrelec, Guillaume; Toro, Roberto; Benali, Habib; Burnod, Yves
2013-01-01
How does the brain integrate multiple sources of information to support normal sensorimotor and cognitive functions? To investigate this question we present an overall brain architecture (called "the dual intertwined rings architecture") that relates the functional specialization of cortical networks to their spatial distribution over the cerebral cortex (or "corticotopy"). Recent results suggest that the resting state networks (RSNs) are organized into two large families: 1) a sensorimotor family that includes visual, somatic, and auditory areas and 2) a large association family that comprises parietal, temporal, and frontal regions and also includes the default mode network. We used two large databases of resting state fMRI data, from which we extracted 32 robust RSNs. We estimated: (1) the RSN functional roles by using a projection of the results on task based networks (TBNs) as referenced in large databases of fMRI activation studies; and (2) relationship of the RSNs with the Brodmann Areas. In both classifications, the 32 RSNs are organized into a remarkable architecture of two intertwined rings per hemisphere and so four rings linked by homotopic connections. The first ring forms a continuous ensemble and includes visual, somatic, and auditory cortices, with interspersed bimodal cortices (auditory-visual, visual-somatic and auditory-somatic, abbreviated as VSA ring). The second ring integrates distant parietal, temporal and frontal regions (PTF ring) through a network of association fiber tracts which closes the ring anatomically and ensures a functional continuity within the ring. The PTF ring relates association cortices specialized in attention, language and working memory, to the networks involved in motivation and biological regulation and rhythms. This "dual intertwined architecture" suggests a dual integrative process: the VSA ring performs fast real-time multimodal integration of sensorimotor information whereas the PTF ring performs multi
Generation of linear dynamic models from a digital nonlinear simulation
NASA Technical Reports Server (NTRS)
Daniele, C. J.; Krosel, S. M.
1979-01-01
The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.
Weakly nonlinear dynamics and the σ{sub 8} parameter
Juszkiewicz, Roman; Feldman, Hume A.; Fry, J.N.; Jaffe, Andrew H. E-mail: feldman@ku.edu E-mail: a.jaffe@imperial.ac.uk
2010-02-01
The amplitude of cosmological density fluctuations, σ{sub 8}, has been studied and estimated by analysing many cosmological observations. The values of the estimates vary considerably between the various probes. However, different estimators probe the value of σ{sub 8} in different cosmological scales and do not take into account the nonlinear evolution of the parameter at late times. We show that estimates of the amplitude of cosmological density fluctuations derived from cosmic flows are systematically higher than those inferred at early epochs from the CMB because of nonlinear evolution at later times. We discuss the past and future evolution of linear and nonlinear perturbations, derive corrections to the value of σ{sub 8} and compare amplitudes after accounting for these differences.
Edge localized mode rotation and the nonlinear dynamics of filaments
NASA Astrophysics Data System (ADS)
Morales, J. A.; Bécoulet, M.; Garbet, X.; Orain, F.; Dif-Pradalier, G.; Hoelzl, M.; Pamela, S.; Huijsmans, G. T. A.; Cahyna, P.; Fil, A.; Nardon, E.; Passeron, C.; Latu, G.
2016-04-01
Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.
Non-linear dynamic analysis of anisotropic cylindrical shells
Lakis, A.A.; Selmane, A.; Toledano, A.
1996-12-01
A theory to predict the influence of geometric non-linearities on the natural frequencies of an empty anisotropic cylindrical shell is presented in this paper. It is a hybrid of finite element and classical thin shell theories. Sanders-Koiter non-linear and strain-displacement relations are used. Displacement functions are evaluated using linearized equations of motion. Modal coefficients are then obtained for these displacement functions. Expressions for the mass, linear and non-linear stiffness matrices are derived through the finite element method. The uncoupled equations are solved with the help of elliptic functions. The period and frequency variations are first determined as a function of shell amplitudes and then compared with the results in the literature.
A Study on the Improvement of Dynamic Loudspeaker Nonlinear Distortion
NASA Astrophysics Data System (ADS)
Inuzuka, Takamasa; Kasahara, Misawa; Mori, Yasuchika
Recently, the distortion caused by signal transduction has been significantly reduced because of development of digital signal processing technology, so that sound quality has improved dramatically. However, speaker system located at the end of the sound reproduction has not changed since the basic principle of the invention, the non-linear distortion occurs mostly have been concerned about the deterioration of sound quality. It is important to eliminate this distortion in high fidelity music playback. In order to reduce the nonlinear distortion, we propose a system using disturbance observer and consider in this method.
Modeling of the carrier dynamics in nonlinear semiconductor nanoscale resonators
NASA Astrophysics Data System (ADS)
Moille, Gregory; Combrié, Sylvain; De Rossi, Alfredo
2016-08-01
The Green's function formalism is used in order to model the diffusion of free carriers in nonlinear semiconductor nanoscale resonators. In combination with the time-dependent coupled-mode equations, this leads to excellent agreement with measurements carried on a variety of samples and materials, using a minimal set of fitting parameters. The role of the geometry of the cavity is evidenced and the influence of linear and nonlinear absorption on the response of the resonator is discussed. This model can handle a broad range of phenomena: switching, self-pulsing, including resonant four-wave mixing.
The effect of nonlinearities on the dynamic response of a large shuttle payload
NASA Technical Reports Server (NTRS)
Sullivan, Timothy L.; Carney, Kelly S.
1987-01-01
The STS Centaur was designed to be a high energy upper stage for use with the Space Shuttle. Two versions were designed under development when the program was cancelled. The first version, designated G-prime, was for planetary missions. The second version, designated G, was to place spacecraft in geosynchronous orbit. As a part of the STS Centaur finite-element model verification effort, test articles of both versions were subjected to a series of static tests. In addition the Centaur G-prime test article was subjected to a series of dynamic tests including a modal survey. Both the static and dynamic tests showed that nonlinearities existed in the Centaur and its support system. The support system included flight-like latches. The nonlinearities were particularly apparent in tests that loaded the forward support structure of the Centaur. These test results were used to aid in the development of two improved finite-element models. The first was a linear model, while the second contained nonlinear elements at the boundaries. Results from both models were compared with the transient response obtained from a step-relaxation or twang test. The linear model was able to accurately match the low frequency response found in the test data. However, only the nonlinear model was able to match higher frequency response that was present in some of the test data. In addition the nonlinear model was able to predict other nonlinear behavior such as the dynamic jump that occurs in systems with nonlinear stiffness.
Nonlinear soil parameter effects on dynamic embedment of offshore pipeline on soft clay
NASA Astrophysics Data System (ADS)
Yu, Su Young; Choi, Han Suk; Lee, Seung Keon; Park, Kyu-Sik; Kim, Do Kyun
2015-06-01
In this paper, the effects of nonlinear soft clay on dynamic embedment of offshore pipeline were investigated. Seabed embedment by pipe-soil interactions has impacts on the structural boundary conditions for various subsea structures such as pipeline, riser, pile, and many other systems. A number of studies have been performed to estimate real soil behavior, but their estimation of seabed embedment has not been fully identified and there are still many uncertainties. In this regards, comparison of embedment between field survey and existing empirical models has been performed to identify uncertainties and investigate the effect of nonlinear soil parameter on dynamic embedment. From the comparison, it is found that the dynamic embedment with installation effects based on nonlinear soil model have an influence on seabed embedment. Therefore, the pipe embedment under dynamic condition by nonlinear parameters of soil models was investigated by Dynamic Embedment Factor (DEF) concept, which is defined as the ratio of the dynamic and static embedment of pipeline, in order to overcome the gap between field embedment and currently used empirical and numerical formula. Although DEF through various researches is suggested, its range is too wide and it does not consider dynamic laying effect. It is difficult to find critical parameters that are affecting to the embedment result. Therefore, the study on dynamic embedment factor by soft clay parameters of nonlinear soil model was conducted and the sensitivity analyses about parameters of nonlinear soil model were performed as well. The tendency on dynamic embedment factor was found by conducting numerical analyses using OrcaFlex software. It is found that DEF was influenced by shear strength gradient than other factors. The obtained results will be useful to understand the pipe embedment on soft clay seabed for applying offshore pipeline designs such as on-bottom stability and free span analyses.
Nonlinear Modeling of Dynamic Interactions within Neuronal Ensembles using Principal Dynamic Modes
Marmarelis, V. Z.; Shin, D. C.; Song, D.; Hampson, R. E.; Deadwyler, S.; Berger, T. W.
2012-01-01
A methodology for nonlinear modeling of multi-input multi-output (MIMO) neuronal systems is presented that utilizes the concept of Principal Dynamic Modes (PDM). The efficacy of this new methodology is demonstrated in the study of the dynamic interactions between neuronal ensembles in the Pre-Frontal Cortex (PFC) of a behaving non-human primate (NHP) performing a Delayed Match-to-Sample task. Recorded spike trains from Layer-2 and Layer-5 neurons were viewed as the “inputs” and “outputs”, respectively, of a putative MIMO system/model that quantifies the dynamic transformation of multi-unit neuronal activity between Layer-2 and Layer-5 of the PFC. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The PDM-based approach seeks to reduce the complexity of MIMO models of neuronal ensembles in order to enable the practicable modeling of large-scale neural systems incorporating hundreds or thousands of neurons, which is emerging as a preeminent issue in the study of neural function. The “scaling-up” issue has attained critical importance as multi-electrode recordings are increasingly used to probe neural systems and advance our understanding of integrated neural function. The initial results indicate that the PDM-based modeling methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance. Furthermore, the PDM-based approach offers the prospect of improved biological/physiological interpretation of the obtained MIMO models. PMID:23011343
Parallel processors and nonlinear structural dynamics algorithms and software
NASA Technical Reports Server (NTRS)
Belytschko, Ted
1990-01-01
Techniques are discussed for the implementation and improvement of vectorization and concurrency in nonlinear explicit structural finite element codes. In explicit integration methods, the computation of the element internal force vector consumes the bulk of the computer time. The program can be efficiently vectorized by subdividing the elements into blocks and executing all computations in vector mode. The structuring of elements into blocks also provides a convenient way to implement concurrency by creating tasks which can be assigned to available processors for evaluation. The techniques were implemented in a 3-D nonlinear program with one-point quadrature shell elements. Concurrency and vectorization were first implemented in a single time step version of the program. Techniques were developed to minimize processor idle time and to select the optimal vector length. A comparison of run times between the program executed in scalar, serial mode and the fully vectorized code executed concurrently using eight processors shows speed-ups of over 25. Conjugate gradient methods for solving nonlinear algebraic equations are also readily adapted to a parallel environment. A new technique for improving convergence properties of conjugate gradients in nonlinear problems is developed in conjunction with other techniques such as diagonal scaling. A significant reduction in the number of iterations required for convergence is shown for a statically loaded rigid bar suspended by three equally spaced springs.
Nonlinear Dynamics: Theoretical Perspectives and Application to Suicidology
ERIC Educational Resources Information Center
Schiepek, Gunter; Fartacek, Clemens; Sturm, Josef; Kralovec, Karl; Fartacek, Reinhold; Ploderl, Martin
2011-01-01
Despite decades of research, the prediction of suicidal behavior remains limited. As a result, searching for more specific risk factors and testing their predictive power are central in suicidology. This strategy may be of limited value because it assumes linearity to the suicidal process that is most likely nonlinear by nature and which can be…
Nonlinear dynamics of large amplitude modes in a magnetized plasma
Brodin, G.; Stenflo, L.
2014-12-15
We derive two equations describing the coupling between electromagnetic and electrostatic oscillations in one-dimensional geometry in a magnetized cold and non-relativistic plasma. The nonlinear interaction between the wave modes is studied numerically. The effects of the external magnetic field strength and the initial electromagnetic polarization are of particular interest here. New results can, thus, be identified.
Linear Stability and Nonlinear Dynamics of Fishbone in NSTX
NASA Astrophysics Data System (ADS)
Wang, Feng; Fu, Guoyong; Breslau, J. A.; Liu, Jinyuan; Liu, Deyong
2013-10-01
Plasms in spherical tokamaks such as NSTX, with a safety factor above unity and weakly reversed magnetic shear may be unstable to an ideal, non-resonant internal kink mode. This mode, termed the LLM in MAST, can saturate and persist. This indicates strong interaction of energetic beam ions with LLM. In this work, we perform linear and nonlinear simulations to investigate energetic particle effects on the non-resonant kink mode and excitation of fishbone for NSTX-like parameters and profiles. The global kinetic-MHD hybrid code M3D-K is used. Numerical results show that beam ions have a strong stabilizing effect on the kink mode at low values of qmin and beam beta. However, at higher beam ion pressure, a fishbone-like mode is excited. The results show that the fishbone is preferentially excited at higher qmin values, consistent with the observed appearance of fishbone before ``long-lived mode'' in NSTX and MAST experiments. Nonlinear simulations show that the fishbone saturates nonlinearly with strong downward frequency chirping, and beam distribution flattened. An m/n = 2/1 magnetic island is induced nonlinearly, which could provide a trigger for the 2/1 NTM sometime observed after fishbone instability in NSTX. This work is supported by U.S. Department of Energy under DE-AC02-76CH03073, and National Magnetic Confinement Fusion Science Program of China (NMCSFP) under contract No. 2013GB107003, 2013GB111001.
Dynamics of self-pumped double PC mirrors based on photorefractive nonlinearity
Voronov, Aleksandr V; Shuvalov, Vladimir V
2004-05-31
It is shown that apart from a dynamic hologram formed in the self-crossing region of input beams [the first phase-conjugation (PC) channel] in a single-crystal double PC mirror, additional refractive-index gratings spontaneously develop, which form the second PC channel with the interaction geometry typical of two-crystal PC mirrors. The competition between these channels leads to a complicated spatiotemporal dynamics of generated nonlinear waves. Depending on the experimental conditions, PC with the efficiency of up to 70 % - 80 % is possible and dynamic structures can be formed from thin soliton-like filaments. (nonlinear optical phenomena)
NASA Astrophysics Data System (ADS)
Volchenkov, D.
2009-03-01
Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magneto-hydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications.
Equations of nonlinear dynamics of elastic shells in cylindrical Eulerian coordinates
NASA Astrophysics Data System (ADS)
Zubov, L. M.
2016-05-01
The equations of dynamics of elastic shells subjected to large deformations are formulated. The Eulerian coordinates on a circular cylinder and time are accepted as independent variables, and one of the unknown functions is the distance from a point of the shell surface to the cylinder axis. The equations of dynamics of nonlinearly elastic shells in the Eulerian coordinates are convenient for exact formulation of the problem on the interaction of strongly deformable shells with moving fluids and gases. The equations obtained can be used for dynamic calculations of fluids and gases flowings in pipelines, blood vessels, hoses, and other nonlinearly deformable thin-walled tubular elements of constructions.
NASA Astrophysics Data System (ADS)
Nakamura, Kenji; Saito, Kenichi; Watanabe, Tadaaki; Ichinokura, Osamu
2005-04-01
Interior permanent magnet synchronous motors (IPMSMs) have high efficiency and torque, since the motors can utilize reluctance torque in addition to magnet torque. The IPMSMs are widely used for electric household appliances and electric bicycles and vehicles. A quantitative analysis method of dynamic characteristics of the IPMSMs, however, has not been clarified fully. For optimum design, investigation of dynamic characteristics considering magnetic nonlinearity is needed. This paper presents a new nonlinear magnetic circuit model of an IPMSM, and suggests a dynamic analysis method using the proposed magnetic circuit model.
Nonlinear model reduction for dynamical systems using sparse sensor locations from learned libraries
NASA Astrophysics Data System (ADS)
Sargsyan, Syuzanna; Brunton, Steven L.; Kutz, J. Nathan
2015-09-01
We demonstrate the synthesis of sparse sampling and dimensionality reduction to characterize and model nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper orthogonal decomposition in order to expose the dominant low-rank coherent structures. Here, libraries of the nonlinear terms are also constructed in order to take advantage of the discrete empirical interpolation method and projection that allows for the approximation of nonlinear terms from a sparse number of grid points. The selected grid points are shown to be effective sensing and measurement locations for characterizing the underlying dynamics, stability, and bifurcations of nonlinear dynamical systems. The use of empirical interpolation points and sparse representation facilitates a family of local reduced-order models for each physical regime, rather than a higher-order global model, which has the benefit of physical interpretability of energy transfer between coherent structures. The method advocated also allows for orders-of-magnitude improvement in computational speed and memory requirements. To illustrate the method, the discrete interpolation points and nonlinear modal libraries are used for sparse representation in order to classify and reconstruct the dynamic bifurcation regimes in the complex Ginzburg-Landau equation. It is also shown that point measurements of the nonlinearity are more effective than linear measurements when sensor noise is present.
Method and system for training dynamic nonlinear adaptive filters which have embedded memory
NASA Technical Reports Server (NTRS)
Rabinowitz, Matthew (Inventor)
2002-01-01
Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.
Sargsyan, Syuzanna; Brunton, Steven L; Kutz, J Nathan
2015-09-01
We demonstrate the synthesis of sparse sampling and dimensionality reduction to characterize and model nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper orthogonal decomposition in order to expose the dominant low-rank coherent structures. Here, libraries of the nonlinear terms are also constructed in order to take advantage of the discrete empirical interpolation method and projection that allows for the approximation of nonlinear terms from a sparse number of grid points. The selected grid points are shown to be effective sensing and measurement locations for characterizing the underlying dynamics, stability, and bifurcations of nonlinear dynamical systems. The use of empirical interpolation points and sparse representation facilitates a family of local reduced-order models for each physical regime, rather than a higher-order global model, which has the benefit of physical interpretability of energy transfer between coherent structures. The method advocated also allows for orders-of-magnitude improvement in computational speed and memory requirements. To illustrate the method, the discrete interpolation points and nonlinear modal libraries are used for sparse representation in order to classify and reconstruct the dynamic bifurcation regimes in the complex Ginzburg-Landau equation. It is also shown that point measurements of the nonlinearity are more effective than linear measurements when sensor noise is present. PMID:26465583
Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics.
Kashima, Kenji
2016-01-01
Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics. PMID:27264780
Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics
NASA Astrophysics Data System (ADS)
Kashima, Kenji
2016-06-01
Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics.
Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics
Kashima, Kenji
2016-01-01
Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics. PMID:27264780
Engine dynamic analysis with general nonlinear finite element codes
NASA Technical Reports Server (NTRS)
Adams, M. L.; Padovan, J.; Fertis, D. G.
1991-01-01
A general engine dynamic analysis as a standard design study computational tool is described for the prediction and understanding of complex engine dynamic behavior. Improved definition of engine dynamic response provides valuable information and insights leading to reduced maintenance and overhaul costs on existing engine configurations. Application of advanced engine dynamic simulation methods provides a considerable cost reduction in the development of new engine designs by eliminating some of the trial and error process done with engine hardware development.
Erem, B.; Hyde, D.E.; Peters, J.M.; Duffy, F.H.; Brooks, D.H.; Warfield, S.K.
2015-01-01
The dynamical structure of the brain’s electrical signals contains valuable information about its physiology. Here we combine techniques for nonlinear dynamical analysis and manifold identification to reveal complex and recurrent dynamics in interictal epileptiform discharges (IEDs). Our results suggest that recurrent IEDs exhibit some consistent dynamics, which may only last briefly, and so individual IED dynamics may need to be considered in order to understand their genesis. This could potentially serve to constrain the dynamics of the inverse source localization problem. PMID:26366250
Investigation of the spinfoam path integral with quantum cuboid intertwiners
NASA Astrophysics Data System (ADS)
Bahr, Benjamin; Steinhaus, Sebastian
2016-05-01
In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the spinfoam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov. To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-j limit. Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or nongeometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant α , which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however. Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have an exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations.
Terrier, Philippe; Dériaz, Olivier
2013-01-01
It has been observed that times series of gait parameters [stride length (SL), stride time (ST), and stride speed (SS)], exhibit long-term persistence and fractal-like properties. Synchronizing steps with rhythmic auditory stimuli modifies the persistent fluctuation pattern to anti-persistence. Another non-linear method estimates the degree of resilience of gait control to small perturbations, i.e., the local dynamic stability (LDS). The method makes use of the maximal Lyapunov exponent, which estimates how fast a non-linear system embedded in a reconstructed state space (attractor) diverges after an infinitesimal perturbation. We propose to use an instrumented treadmill to simultaneously measure basic gait parameters (time series of SL, ST, and SS from which the statistical persistence among consecutive strides can be assessed), and the trajectory of the center of pressure (from which the LDS can be estimated). In 20 healthy participants, the response to rhythmic auditory cueing (RAC) of LDS and of statistical persistence [assessed with detrended fluctuation analysis (DFA)] was compared. By analyzing the divergence curves, we observed that long-term LDS (computed as the reverse of the average logarithmic rate of divergence between the 4th and the 10th strides downstream from nearest neighbors in the reconstructed attractor) was strongly enhanced (relative change +73%). That is likely the indication of a more dampened dynamics. The change in short-term LDS (divergence over one step) was smaller (+3%). DFA results (scaling exponents) confirmed an anti-persistent pattern in ST, SL, and SS. Long-term LDS (but not short-term LDS) and scaling exponents exhibited a significant correlation between them (r = 0.7). Both phenomena probably result from the more conscious/voluntary gait control that is required by RAC. We suggest that LDS and statistical persistence should be used to evaluate the efficiency of cueing therapy in patients with neurological gait disorders. PMID
Nonlinear wave dynamics near phase transition in PT-symmetric localized potentials
NASA Astrophysics Data System (ADS)
Nixon, Sean; Yang, Jianke
2016-09-01
Nonlinear wave propagation in parity-time symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for a phase transition to occur are derived based on a generalization of the Krein signature. Using the multi-scale perturbation analysis, a reduced nonlinear ordinary differential equation (ODE) is derived for the amplitude of localized solutions near phase transition. Above the phase transition, this ODE predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below the phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
Manimala, James M; Sun, C T
2016-06-01
The amplitude-dependent dynamic response in acoustic metamaterials having nonlinear local oscillator microstructures is studied using numerical simulations on representative discrete mass-spring models. Both cubically nonlinear hardening and softening local oscillator cases are considered. Single frequency, bi-frequency, and wave packet excitations at low and high amplitude levels were used to interrogate the models. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range is found to correspond to the amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. A predominant shift in the propagated wave spectrum towards lower frequencies is observed. Moreover, the feasibility of amplitude and frequency-dependent selective filtering of composite signals consisting of individual frequency components which fall within propagating or attenuating regimes is demonstrated. Further enrichment of these wave manipulation mechanisms in acoustic metamaterials using different combinations of nonlinear microstructures presents device implications for acoustic filters and waveguides. PMID:27369163
Dynamics of a vertical riser with weak structural nonlinearity excited by wakes
NASA Astrophysics Data System (ADS)
Keber, Marko; Wiercigroch, Marian
2008-08-01
In this paper we investigate the effect of a weak structural nonlinearity on the dynamical behaviour of a vertical offshore riser subjected to vortex-induced vibration (VIV). Coupling of the riser dynamics with the flow of the surrounding fluid is achieved by attaching a wake oscillator to a reduced model of the structure, which is obtained through the application of the invariant manifold technique for the derivation of nonlinear normal modes. By comparing the free responses of the linear and the nonlinear structure, it was found that the structural nonlinearity has a stiffening effect on the oscillation of the riser, which becomes more pronounced when the internal flow is incorporated into the model. Consequently, in the coupled system, the response is considerably modified for the structure as well as for the fluid variable.
Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate in an optical cavity
NASA Astrophysics Data System (ADS)
Zhang, J. M.; Cui, F. C.; Zhou, D. L.; Liu, W. M.
2009-03-01
We investigate the nonlinear dynamics of a combined system which is composed of a cigar-shaped Bose-Einstein condensate and an optical cavity with the two sides coupled dispersively. This system is characterized by the cavity-induced nonlinearity; after integrating out the fast degree of freedom of the cavity mode, the potential felt by the condensate depends on the condensate itself. Adopting a discrete-mode approximation for the condensate, we map out the steady configurations of the system. It is found that due to the nonlinearity of the system, the nonlinear levels of the system may fold up in some parameter regimes. That will lead to the breakdown of adiabatic evolution of the system. Analysis of the dynamical stability of the steady states indicates that the same level structure also results in optical bistability.
Non-Linearity in Wide Dynamic Range CMOS Image Sensors Utilizing a Partial Charge Transfer Technique
Shafie, Suhaidi; Kawahito, Shoji; Halin, Izhal Abdul; Hasan, Wan Zuha Wan
2009-01-01
The partial charge transfer technique can expand the dynamic range of a CMOS image sensor by synthesizing two types of signal, namely the long and short accumulation time signals. However the short accumulation time signal obtained from partial transfer operation suffers of non-linearity with respect to the incident light. In this paper, an analysis of the non-linearity in partial charge transfer technique has been carried, and the relationship between dynamic range and the non-linearity is studied. The results show that the non-linearity is caused by two factors, namely the current diffusion, which has an exponential relation with the potential barrier, and the initial condition of photodiodes in which it shows that the error in the high illumination region increases as the ratio of the long to the short accumulation time raises. Moreover, the increment of the saturation level of photodiodes also increases the error in the high illumination region. PMID:22303133
Analysis of some large-scale nonlinear stochastic dynamic systems with subspace-EPC method
NASA Astrophysics Data System (ADS)
Er, GuoKang; Iu, VaiPan
2011-09-01
The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method. PMID:25420238
Nonlinear analysis of magnetization dynamics excited by spin Hall effect
NASA Astrophysics Data System (ADS)
Taniguchi, Tomohiro
2015-03-01
We investigate the possibility of exciting self-oscillation in a perpendicular ferromagnet by the spin Hall effect on the basis of a nonlinear analysis of the Landau-Lifshitz-Gilbert (LLG) equation. In the self-oscillation state, the energy supplied by the spin torque during a precession on a constant energy curve should equal the dissipation due to damping. Also, the current to balance the spin torque and the damping torque in the self-oscillation state should be larger than the critical current to destabilize the initial state. We find that these conditions in the spin Hall system are not satisfied by deriving analytical solutions of the energy supplied by the spin transfer effect and the dissipation due to the damping from the nonlinear LLG equation. This indicates that the self-oscillation of a perpendicular ferromagnet cannot be excited solely by the spin Hall torque.
Nonlinear dynamics of accretion disks with stochastic viscosity
Cowperthwaite, Philip S.; Reynolds, Christopher S.
2014-08-20
We present a nonlinear numerical model for a geometrically thin accretion disk with the addition of stochastic nonlinear fluctuations in the viscous parameter. These numerical realizations attempt to study the stochastic effects on the disk angular momentum transport. We show that this simple model is capable of reproducing several observed phenomenologies of accretion-driven systems. The most notable of these is the observed linear rms-flux relationship in the disk luminosity. This feature is not formally captured by the linearized disk equations used in previous work. A Fourier analysis of the dissipation and mass accretion rates across disk radii show coherence for frequencies below the local viscous frequency. This is consistent with the coherence behavior observed in astrophysical sources such as Cygnus X-1.
SOLITONS: Nonreciprocal dynamics of pulses in a nonlinear inhomogeneous fibre
NASA Astrophysics Data System (ADS)
Adamova, M. S.; Zolotovskii, Igor'O.; Sementsov, Dmitrii I.
2007-08-01
The conditions, under which the nonreciprocity of the frequency modulation rate and pulse duration as well as the spectral nonreciprocity in fibres with different types of inhomogeneity of nonlinearity and group-velocity dispersion appear, are studied for the Gaussian and hyperbolic secant frequency-modulated pulses. Strong compression nonreciprocity is found in fibres with an alternating group-velocity dispersion periodically changing over its length.
Andrianov, I.V.; Danishevsky, V.V.
1994-12-31
Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions.
Review of nonlinear dynamics of the unstable fluid interface: conservation laws and group theory
NASA Astrophysics Data System (ADS)
Abarzhi, Snezhana I.
2008-12-01
In this paper, we briefly overview some theoretical approaches and empirical modeling approaches of the nonlinear Rayleigh-Taylor instabilities, which have been developed over recent decades, summarize the results of the group theory analysis of the nonlinear coherent dynamics in Rayleigh-Taylor and Richtmyer-Meshkov flows, consider the issues of validation and verification of the theories and models, and outline some criteria for the estimate of the fidelity and information capacity of the experimental and numerical data sets.
Geomedium as a nonlinear dynamic system. An evolutionary concept of earthquake development
Makarov, Pavel V.
2014-11-14
An evolutionary approach to earthquake development is proposed. A medium under loading is treated as a multiscale nonlinear dynamic system. Its failure involves a number of stages typical of any dynamic system: dynamic chaos, self-organized criticality, and global stability loss in the final stage of its evolution. In the latter stage, the system evolves in a blow-up mode accompanied by catastrophic superfast movements of the elements of this geomedium.
Test-Analysis Correlation and Finite Element Model Updating for Nonlinear Transient Dynamics
Hemez, F.M.; Doebling, S.W.
1999-02-08
This research aims at formulating criteria for measuring the correlation between test data and finite element results for nonlinear, transient dynamics. After reviewing the linear case and illustrating the limitations of modal-based updating when it is applied to nonlinear experimental data, simple time-domain, test-analysis correlation metrics are proposed. Two implementations are compared: the conventional least-squares technique and the Principal Component Decomposition that correlates subspaces rather than individual time-domain responses. Illustrations and discussions are provided using the LANL 8-DOF system, an experimental testbed for validating nonlinear data correlation and model updating techniques.
Nonlinear dynamics of magnetically coupled beams for multi-modal vibration energy harvesting
NASA Astrophysics Data System (ADS)
Abed, I.; Kacem, N.; Bouhaddi, N.; Bouazizi, M. L.
2016-04-01
We investigate the nonlinear dynamics of magnetically coupled beams for multi-modal vibration energy harvesting. A multi-physics model for the proposed device is developed taking into account geometric and magnetic nonlinearities. The coupled nonlinear equations of motion are solved using the Galerkin discretization coupled with the harmonic balance method and the asymptotic numerical method. Several numerical simulations have been performed showing that the expected performances of the proposed vibration energy harvester are significantly promising with up to 130 % in term of bandwidth and up to 60 μWcm-3g-2 in term of normalized harvested power.
Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity.
Polesana, P; Dubietis, A; Porras, M A; Kucinskas, E; Faccio, D; Couairon, A; Di Trapani, P
2006-05-01
The near-field dynamics of a femtosecond Bessel beam propagating in a Kerr nonlinear medium (fused silica) is investigated both numerically and experimentally. We demonstrate that the input Bessel beam experiences strong nonlinear reshaping. Due to the combined action of self-focusing and nonlinear losses the reshaped beam exhibits a radial compression and reduced visibility of the Bessel oscillations. Moreover, we show that the reshaping process starts from the intense central core and gradually replaces the Bessel beam profile during propagation, highlighting the conical geometry of the energy flow. PMID:16803062
NASA Astrophysics Data System (ADS)
Fan, Guanghua; Chen, Minrui; Wu, Xingzhi; Han, Min; Song, Yinglin; Qu, Shiliang; Xie, Bo; Yang, Linpo; Gao, Renxi; Guo, Zhongyi; Liu, Jiaqi
2016-01-01
Pd nanoparticles are deposited on one surface of a quartz sheet. Their optical nonlinearity and ultrafast dynamics in air and in hydrogen environment are investigated. The Pd nanoparticles exhibit self focusing and saturable absorption in air. In hydrogen environment with increasing hydrogen, the NPs maintain self focusing, however their nonlinear refraction index increases; and their nonlinear absorption changes from saturable absorption to reverse saturable absorption. In hydrogen environment, the acoustic breathing movement of these NPs damps more obviously and the contact between the NPs and quartz sheet is looser, comparing to that in air.
NASA Astrophysics Data System (ADS)
Liu, Y. Z.; Hao, Y. X.; Zhang, W.; Chen, J.; Li, S. B.
2015-07-01
The nonlinear vibration of a simply supported FGM cylindrical shell with small initial geometric imperfection under complex loads is studied. The effects of radial harmonic excitation, compressive in-plane force combined with supersonic aerodynamic and thermal loads are considered. The small initial geometric imperfection of the cylindrical shell is characterized in the form of the sine-type trigonometric functions. The effective material properties of this FGM cylindrical shell are graded in the radial direction according to a simple power law in terms of the volume fractions. Based on Reddy's third-order shear deformation theory, von Karman-type nonlinear kinematics and Hamilton's principle, the nonlinear partial differential equation that controls the shell dynamics is derived. Both axial symmetric and driven modes of the cylindrical shell deflection pattern are included. Furthermore, the equations of motion can be reduced into a set of coupled nonlinear ordinary differential equations by applying Galerkin's method. In the study of the nonlinear dynamics responses of small initial geometric imperfect FGM cylindrical shell under complex loads, the 4th order Runge-Kutta method is used to obtain time history, phase portraits, bifurcation diagrams and Poincare maps with different parameters. The effects of external loads, geometric imperfections and volume fractions on the nonlinear dynamics of the system are discussed.
Silicon Microdisk Resonators for Nonlinear Optics and Dynamics
NASA Astrophysics Data System (ADS)
Johnson, Thomas
Silicon is incredibly well-studied as an electronic material. Since the out-migration of William Noyce, Gordon Moore, and the rest of the original Fairchild Semiconductor class from Shockley Semiconductor, silicon has only grown in prominence. Untold billions have been expended on research, development, and manufacture, and now silicon is perhaps the most well-controlled commercial material on Earth. For all that, the use of silicon as a mechanical material, though envisioned in the late 1950s, largely became viable only after the advent of large-scale silicon processing for microelectronics. As an optical material, silicon also has a long pedigree, with most of the positive focus on its excellent optical transparency and the enormous potential for improvement residing in its lack of effective emission. This thesis concerns an alternate route to the generation of light in silicon: the nonlinear route. Resonant elements play a critical role in making this viable. The ability to build up optical intensity in the confined volume of a microresonator reduces the input power required to achieve a given energy density. Silicon also has certain excellent nonlinear properties: a large Raman gain coefficient, for example, and an appreciable Kerr effect. Unfortunately, silicon also exhibits significant two-photon absorption (TPA) in the convenient telecommunications wavelength bands. As such, the build-up of optical energy in silion may also be accompanied by a build-up of TPA-induced free-carrier populations. These populations may serve to limit the efficiency of nonlinear processes or to generate additional nonlinear behavior in their interactions with optical fields. Thus two important stepping-stones on the way to the low-power, low-footprint use of silicon as an optical material are: the need to reduce optical losses in the optical elements, and to reduce or modify the populations of free carriers generated in the nonlinear optics regime. This thesis will present design
Real-Time Monitoring of Non-linear Suicidal Dynamics: Methodology and a Demonstrative Case Report
Fartacek, Clemens; Schiepek, Günter; Kunrath, Sabine; Fartacek, Reinhold; Plöderl, Martin
2016-01-01
In recent years, a number of different authors have stressed the usefulness of non-linear dynamic systems approach in suicide research and suicide prevention. This approach applies specific methods of time series analysis and, consequently, it requires a continuous and fine-meshed assessment of the processes under consideration. The technical means for this kind of process assessment and process analysis are now available. This paper outlines how suicidal dynamics can be monitored in high-risk patients by an Internet-based application for continuous self-assessment with integrated tools of non-linear time series analysis: the Synergetic Navigation System. This procedure is illustrated by data from a patient who attempted suicide at the end of a 90-day monitoring period. Additionally, future research topics and clinical applications of a non-linear dynamic systems approach in suicidology are discussed. PMID:26913016
A geometrical approach to control and controllability of nonlinear dynamical networks
Wang, Le-Zhi; Su, Ri-Qi; Huang, Zi-Gang; Wang, Xiao; Wang, Wen-Xu; Grebogi, Celso; Lai, Ying-Cheng
2016-01-01
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control. PMID:27076273
Nonlinear Dynamics of Bose-Einstein Condensates with Long-Range Interactions
Wunner, G.; Cartarius, H.; Fabcic, T.; Koeberle, P.; Main, J.; Schwidder, T.
2008-11-13
The motto of this paper is: Let's face Bose-Einstein condensation through nonlinear dynamics. We do this by choosing variational forms of the condensate wave functions (of given symmetry classes), which convert the Bose-Einstein condensates via the time-dependent Gross-Pitaevskii equation into Hamiltonian systems that can be studied using the methods of nonlinear dynamics. We consider in particular cold quantum gases where long-range interactions between the neutral atoms are present, in addition to the conventional short-range contact interaction, viz. gravity-like interactions, and dipole-dipole interactions. The results obtained serve as a useful guide in the search for nonlinear dynamics effects in numerically exact quantum calculations for Bose-Einstein condensates. A main result is the prediction of the existence of stable islands as well as chaotic regions for excited states of dipolar condensates, which could be checked experimentally.
Use of non-linear EEG analysis to study abnormal brain dynamics in deaf human subjects.
Micheloyannis, S; Stam, C J; Fountoulakis, E; Bourkas, M; Arvanitis, S; Papanikolaou, E
1998-06-19
We compared the cortical dynamics of deaf subjects to those of control subjects at rest with eyes closed and during reading with the help of a non-linear prediction statistic. This method is suitable for short-term noisy time series such as electroencephalographic signals. Furthermore, we used surrogate data to test for non-linear dynamics underlying the electroencephalographic time series recorded. Our results indicate that significant non-linearity accompanies cortical activation during reading. This is more diffuse in deaf subjects and could be due to the widespread reorganization of their cerebral cortex. Predictability was lower in deaf subjects at rest, which indicates their increased 'readiness' in the resting condition. Finally, our results indicate that normal and deaf subjects differ significantly in terms of cortical dynamics. PMID:9682843
A geometrical approach to control and controllability of nonlinear dynamical networks.
Wang, Le-Zhi; Su, Ri-Qi; Huang, Zi-Gang; Wang, Xiao; Wang, Wen-Xu; Grebogi, Celso; Lai, Ying-Cheng
2016-01-01
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control. PMID:27076273
NASA Astrophysics Data System (ADS)
Zhang, Ying-Yue; Yang, Qiu-Ying; Chen, Tian-Lun
2007-07-01
We introduce a modified small-world network adding new links with nonlinearly preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. We study several important structural properties of our network such as the distribution of link-degree, the maximum link-degree, and the length of the shortest path. We further argue several dynamical characteristics of the model such as the important critical value fc, the f0 avalanche, and the mutating condition, and find that those characteristics show particular behaviors.
Jaksic, V; Mandic, D P; Ryan, K; Basu, B; Pakrashi, V
2016-01-01
Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input. PMID:26909175
Mandic, D. P.; Ryan, K.; Basu, B.; Pakrashi, V.
2016-01-01
Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input. PMID:26909175
Nonlinear Dynamics of Complex Coevolutionary Systems in Historical Times
NASA Astrophysics Data System (ADS)
Perdigão, Rui A. P.
2016-04-01
A new theoretical paradigm for statistical-dynamical modeling of complex coevolutionary systems is introduced, with the aim to provide historical geoscientists with a practical tool to analyse historical data and its underlying phenomenology. Historical data is assumed to represent the history of dynamical processes of physical and socio-economic nature. If processes and their governing laws are well understood, they are often treated with traditional dynamical equations: deterministic approach. If the governing laws are unknown or impracticable, the process is often treated as if being random (even if it is not): statistical approach. Although single eventful details - such as the exact spatiotemporal structure of a particular hydro-meteorological incident - may often be elusive to a detailed analysis, the overall dynamics exhibit group properties summarized by a simple set of categories or dynamical regimes at multiple scales - from local short-lived convection patterns to large-scale hydro-climatic regimes. The overwhelming microscale complexity is thus conveniently wrapped into a manageable group entity, such as a statistical distribution. In a stationary setting whereby the distribution is assumed to be invariant, alternating regimes are approachable as dynamical intermittence. For instance, in the context of bimodal climatic oscillations such as NAO and ENSO, each mode corresponds to a dynamical regime or phase. However, given external forcings or longer-term internal variability and multiscale coevolution, the structural properties of the system may change. These changes in the dynamical structure bring about a new distribution and associated regimes. The modes of yesteryear may no longer exist as such in the new structural order of the system. In this context, aside from regime intermittence, the system exhibits structural regime change. New oscillations may emerge whilst others fade into the annals of history, e.g. particular climate fluctuations during
[Regular and chaotic dynamics with applications in nonlinear optics]. Final report
Kovacic, G.
1998-10-12
The following major pieces of work were completed under the sponsorship of this grant: (1) singular perturbation theory for dynamical systems; (2) homoclinic orbits and chaotic dynamics in second-harmonic generating, optically pumped, passive optical cavities; (3) chaotic dynamics in short ring-laser cavities; (4) homoclinic orbits in moderately-long ring-laser cavities; (5) finite-dimensional attractor in ring-laser cavities; (6) turbulent dynamics in long ring-laser cavities; (7) bifurcations in a model for a free-boundary problem for the heat equation; (8) weakly nonlinear dynamics of interface propagation; (9) slowly periodically forced planar Hamiltonian systems; and (10) soliton spectrum of the solutions of the nonlinear Schroedinger equation. A brief summary of the research is given for each project.
Non-linear dynamics of compound sawteeth in tokamaks
NASA Astrophysics Data System (ADS)
Ahn, J.-H.; Garbet, X.; Lütjens, H.; Marx, A.; Nicolas, T.; Sabot, R.; Luciani, J.-F.; Guirlet, R.; Février, O.; Maget, P.
2016-05-01
Compound sawteeth is studied with the XTOR-2F code. Non-linear full 3D magnetohydrodynamic simulations show that the plasma hot core is radially displaced and rotates during the partial crash, but is not fully expelled out of the q = 1 surface. Partial crashes occur when the radius of the q = 1 surface exceeds a critical value, at fixed poloidal beta. This critical value depends on the plasma elongation. The partial crash time is larger than the collapse time of an ordinary sawtooth, likely due to a weaker diamagnetic stabilization. This suggests that partial crashes result from a competition between destabilizing effects such as the q = 1 radius and diamagnetic stabilization.
Alternating-phase focusing: A model to study nonlinear dynamics
Sagalovsky, L.; Delayen, J.R.
1992-01-01
We discuss a new model to study alternating-phase focusing (APF). Our approach is based on representing the accelerating electric field with a continuous phase modulated traveling wave. The resulting nonlinear equations of motion can be solved analytically to predict the regions of stable APF motion. We also identify the key parameters which adequately describe the physics of APF. The model is believed to be applicable to low-{beta} ion linacs with short independently-controlled superconducting cavities being developed at ANL.
Alternating-phase focusing: A model to study nonlinear dynamics
Sagalovsky, L.; Delayen, J.R.
1992-09-01
We discuss a new model to study alternating-phase focusing (APF). Our approach is based on representing the accelerating electric field with a continuous phase modulated traveling wave. The resulting nonlinear equations of motion can be solved analytically to predict the regions of stable APF motion. We also identify the key parameters which adequately describe the physics of APF. The model is believed to be applicable to low-{beta} ion linacs with short independently-controlled superconducting cavities being developed at ANL.
Parallel processors and nonlinear structural dynamics algorithms and software
NASA Technical Reports Server (NTRS)
Belytschko, Ted; Gilbertsen, Noreen D.; Neal, Mark O.; Plaskacz, Edward J.
1989-01-01
The adaptation of a finite element program with explicit time integration to a massively parallel SIMD (single instruction multiple data) computer, the CONNECTION Machine is described. The adaptation required the development of a new algorithm, called the exchange algorithm, in which all nodal variables are allocated to the element with an exchange of nodal forces at each time step. The architectural and C* programming language features of the CONNECTION Machine are also summarized. Various alternate data structures and associated algorithms for nonlinear finite element analysis are discussed and compared. Results are presented which demonstrate that the CONNECTION Machine is capable of outperforming the CRAY XMP/14.
Non-stationary resonance dynamics of a nonlinear sonic vacuum with grounding supports
NASA Astrophysics Data System (ADS)
Koroleva (Kikot), I. P.; Manevitch, L. I.; Vakakis, Alexander F.
2015-11-01
In a recent work [L.I. Manevitch, A.F.Vakakis, Nonlinear oscillatory acoustic vacuum, SIAM Journal of Applied Mathematics 74(6) (2014), 1742-1762] it was shown that a periodic chain of linearly coupled particles performing low-energy in-plane transverse oscillations behaves as a strongly nonlinear sonic vacuum (with corresponding speed of sound equal to zero). In this work we consider the grounded version of this system by coupling each particle to the ground through lateral springs in order to study the effect of the grounding stiffness on the strongly nonlinear dynamics. In that context we consider the simplest possible such system consisting of two coupled particles and present analytical and numerical studies of the non-stationary planar dynamics. The most significant limiting case corresponding to predominant low energy transversal excitations is considered by taking into account leading order geometric nonlinearities. Then we show that the grounded system behaves as a nonlinear sonic vacuum due to the purely cubic stiffness nonlinearities in the governing equations of motion and the complete absence of any linear stiffness terms. Under certain assumptions the nonlinear normal modes (i.e., the time-periodic nonlinear oscillations) in the configuration space of this system coincide with those of the corresponding linear one, so they obey the same orthogonality relations. Moreover, we analytically find that there are two transitions in the dynamics of this system, with the parameter governing these transitions being the relation between the lateral (grounding) and the interchain stiffnesses. The first transition concerns a bifurcation of one of the nonlinear normal modes (NNMs), whereas the second provides conditions for intense energy transfers and mixing between the NNMs. The drastic effects of these bifurcations on the non-stationary resonant dynamics are discussed. Specifically, the second transition relates to strongly non-stationary dynamics, and signifies
Influence of the nonlinear dynamic plasma screening on the electron-dust collision in dusty plasmas
Ki, Dae-Han; Jung, Young-Dae
2012-05-07
The nonlinear dynamic plasma screening effects on the elastic electron-dust grain collision are investigated in dusty plasmas. The results show that the nonlinear dynamic screening effect significantly increases the magnitude of the eikonal phase shift. It is also found that the magnitude of the phase shift decreases with an increase of the thermal energy. In addition, it is found that the differential eikonal cross section shows the oscillatory behavior, and the oscillating peaks approach to the collision center with increasing thermal energy. It is also found that the total eikonal cross section decreases with an increase of the thermal energy.
Kerr-lens-mediated dynamics of two nonlinearly coupled mode-locked laser oscillators
NASA Astrophysics Data System (ADS)
Wu, Song; Smith, Sandra L.; Fork, Richard L.
1992-02-01
The dynamics of two nonlinearly coupled femtosecond oscillators are investigated for the case where two distinct nonlinear mechanisms are balanced to determine the temporal relationship and properties of the pulses in the two oscillators. In the time domain the shared bleaching of a common absorber creates an attractive mechanism for the pulses, while interactive Kerr lens deflections create a repulsive mechanism. The interplay of these two mechanisms causes a variety of dynamical behaviors, including pulse synchronization, pulse duration switching, and a latching type of amplitude bistability.
NASA Astrophysics Data System (ADS)
Podbielski, Jan; Heitmann, Detlef; Grundler, Dirk
2007-11-01
We have studied the spin dynamics of microscopic permalloy rings at GHz frequencies. Increasing the irradiation power, we observe first nonlinear spin dynamics and second microwave-assisted switching (MAS). We explore the MAS phase diagram as a function of microwave power and frequency f and, in particular, extract the critical microwave field hc(f). Its frequency dependence reflects characteristic eigenfrequencies from both the linear and nonlinear spin-wave spectrum. By comparing hc(f) with the different susceptibilities, we gain insight into the microscopic processes which might be the basis of a predictive theory of MAS.
Application of non-linear dynamics to the characterization of cardiac electrical instability
NASA Technical Reports Server (NTRS)
Kaplan, D. T.; Cohen, R. J.
1987-01-01
Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.
NASA Astrophysics Data System (ADS)
Tene, Yair; Tene, Noam; Tene, G.
1993-08-01
An interactive data fusion methodology of video, audio, and nonlinear structural dynamic analysis for potential application in forensic engineering is presented. The methodology was developed and successfully demonstrated in the analysis of heavy transportable bridge collapse during preparation for testing. Multiple bridge elements failures were identified after the collapse, including fracture, cracks and rupture of high performance structural materials. Videotape recording by hand held camcorder was the only source of information about the collapse sequence. The interactive data fusion methodology resulted in extracting relevant information form the videotape and from dynamic nonlinear structural analysis, leading to full account of the sequence of events during the bridge collapse.
NASA Technical Reports Server (NTRS)
Ozguven, H. Nevzat
1991-01-01
A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.
Nonlinear Phase Dynamics in a Driven Bosonic Josephson Junction
Boukobza, Erez; Moore, Michael G.; Cohen, Doron; Vardi, Amichay
2010-06-18
We study the collective dynamics of a driven two-mode Bose-Hubbard model in the Josephson interaction regime. The classical phase space is mixed, with chaotic and regular components, which determine the dynamical nature of the fringe visibility. For a weak off-resonant drive, where the chaotic component is small, the many-body dynamics corresponds to that of a Kapitza pendulum, with the relative phase {phi} between the condensates playing the role of the pendulum angle. Using a master equation approach we show that the modulation of the intersite potential barrier stabilizes the {phi}={pi} 'inverted pendulum' coherent state, and protects the fringe visibility.
Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740
Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels
Steinacher, Arno; Bates, Declan G.; Akman, Ozgur E.; Soyer, Orkun S.
2016-01-01
Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for
Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.
Steinacher, Arno; Bates, Declan G; Akman, Ozgur E; Soyer, Orkun S
2016-01-01
Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for
Nonlinear dynamical behavior of thermionic low pressure discharges. I. Simulation
NASA Astrophysics Data System (ADS)
Greiner, F.; Klinger, T.; Piel, A.
1995-06-01
The discharge modes of a thermionic low pressure discharge (p<1Pa) are investigated with the one-dimensional particle-in-cell simulation codes PDP1 and XPDP1 [C. K. Birdsall, IEEE Trans. Plasma Sci. 19, 65 (1991)]. The simulation results provide a model approach for stable discharge modes, hysteresis, and for nonlinear relaxation-oscillations. During this potential-relaxation instability, nonlinear structures, e.g. electron holes and double layers, are observed. A Pierce-Buneman-mode is suggested as a trigger mechanism for the onset of the instability. The detailed oscillation process can be subdivided into three distinct phases: expansion phase, double layer phase, and relaxation phase. This allows one to explain the parameter dependencies of the oscillation frequency. For a periodically driven discharge, mode-locking in a period-2 state is found and explained by the model. The mode-locking phenomenon is studied systematically. The results of the simulations are well confirmed by experimental observations presented in Part II of this paper [T. Klinger et al., Phys. Plasmas 2, 1822 (1995)].
Nonlinear dynamical behavior of thermionic low pressure discharges. I. Simulation
Greiner, F.; Klinger, T.; Piel, A.
1995-06-01
The discharge modes of a thermionic low pressure discharge ({ital p}{lt}1Pa) are investigated with the one-dimensional particle-in-cell simulation codes PDP1 and XPDP1 [C. K. Birdsall, IEEE Trans. Plasma Sci. {bold 19}, 65 (1991)]. The simulation results provide a model approach for stable discharge modes, hysteresis, and for nonlinear relaxation-oscillations. During this potential-relaxation instability, nonlinear structures, e.g. electron holes and double layers, are observed. A Pierce--Buneman-mode is suggested as a trigger mechanism for the onset of the instability. The detailed oscillation process can be subdivided into three distinct phases: expansion phase, double layer phase, and relaxation phase. This allows one to explain the parameter dependencies of the oscillation frequency. For a periodically driven discharge, mode-locking in a period-2 state is found and explained by the model. The mode-locking phenomenon is studied systematically. The results of the simulations are well confirmed by experimental observations presented in Part II of this paper [T. Klinger {ital et} {ital al}., Phys. Plasmas {bold 2}, 1822 (1995)]. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Nonlinear dynamical effects on reaction rates in thermally fluctuating environments.
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2010-07-21
A framework to calculate the rate constants of condensed phase chemical reactions of manybody systems is presented without relying on the concept of transition state. The theory is based on a framework we developed recently adopting a multidimensional underdamped Langevin equation in the region of a rank-one saddle. The theory provides a reaction coordinate expressed as an analytical nonlinear functional of the position coordinates and velocities of the system (solute), the friction constants, and the random force of the environment (solvent). Up to moderately high temperature, the sign of the reaction coordinate can determine the final destination of the reaction in a thermally fluctuating media, irrespective of what values the other (nonreactive) coordinates may take. In this paper, it is shown that the reaction probability is analytically derived as the probability of the reaction coordinate being positive, and that the integration with the Boltzmann distribution of the initial conditions leads to the exact reaction rate constant when the local equilibrium holds and the quantum effect is negligible. Because of analytical nature of the theory taking into account all nonlinear effects and their combination with fluctuation and dissipation, the theory naturally provides us with the firm mathematical foundation of the origin of the reactivity of the reaction in a fluctuating media. PMID:20544104
Adiabatic nonlinear waves with trapped particles. III. Wave dynamics
Dodin, I. Y.; Fisch, N. J.
2012-01-15
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter S, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At S < 1/2, a wave is stable and exhibits group velocity splitting. At S > 1/2, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schroedinger equation, which is traditionally considered as a universal model of wave self-action but misses the trapped-particle oscillation-center inertia.
Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.
Zausner, Tobi
2011-04-01
Artists create their work in conditions of disequilibrium, states of creative chaos that may appear turbulent but are capable of bringing forth new order. By absorbing information from the environment and discharging it negentropically as new work, artists can be modeled as dissipative systems. A characteristic of chaotic systems is a heightened sensitivity to stimuli, which can generate either positive experiences or negative ones that can lead some artists to substance abuse and misguided searches for a creative chaos. Alcohol and drug use along with inadequately addressed co-occurring emotional disorders interfere with artists' quest for the nonlinearity of creativity. Instead, metaphorically modeled by a limit cycle of addiction and then a spiral to disorder, the joys of a creative chaos become an elusive chimera for them rather than a fulfilling experience. Untreated mental illness and addiction to substances have shortened the lives of artists such as Vincent Van Gogh, Frida Kahlo, Henri de Toulouse-Lautrec, and Jackson Pollock, all of whom committed suicide. In contrast Edvard Munch and John Callahan, who chose to address their emotional problems and substance abuse, continued to live and remain creative. Choosing to access previously avoided moments of pain can activate the nonlinear power of self-transformation. PMID:21382261
Efficient fully nonlinear data assimilation for geophysical fluid dynamics
NASA Astrophysics Data System (ADS)
van Leeuwen, Peter Jan; Ades, Melanie
2013-06-01
A potential problem with Ensemble Kalman Filter is the implicit Gaussian assumption at analysis times. Here we explore the performance of a recently proposed fully nonlinear particle filter on a high-dimensional but simplified ocean model, in which the Gaussian assumption is not made. The model simulates the evolution of the vorticity field in time, described by the barotropic vorticity equation, in a highly nonlinear flow regime. While common knowledge is that particle filters are inefficient and need large numbers of model runs to avoid degeneracy, the newly developed particle filter needs only of the order of 10-100 particles on large scale problems. The crucial new ingredient is that the proposal density can not only be used to ensure all particles end up in high-probability regions of state space as defined by the observations, but also to ensure that most of the particles have similar weights. Using identical twin experiments we found that the ensemble mean follows the truth reliably, and the difference from the truth is captured by the ensemble spread. A rank histogram is used to show that the truth run is indistinguishable from any of the particles, showing statistical consistency of the method.
Hu, Eric Y.; Bouteiller, Jean-Marie C.; Song, Dong; Baudry, Michel; Berger, Theodore W.
2015-01-01
Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations. PMID:26441622
NASA Astrophysics Data System (ADS)
Chen, Yun; Yang, Hui
2016-06-01
Many real-world systems are evolving over time and exhibit dynamical behaviors. In order to cope with system complexity, sensing devices are commonly deployed to monitor system dynamics. Online sensing brings the proliferation of big data that are nonlinear and nonstationary. Although there is rich information on nonlinear dynamics, significant challenges remain in realizing the full potential of sensing data for system control. This paper presents a new approach of heterogeneous recurrence analysis for online monitoring and anomaly detection in nonlinear dynamic processes. A partition scheme, named as Q-tree indexing, is firstly introduced to delineate local recurrence regions in the multi-dimensional continuous state space. Further, we design a new fractal representation of state transitions among recurrence regions, and then develop new measures to quantify heterogeneous recurrence patterns. Finally, we develop a multivariate detection method for on-line monitoring and predictive control of process recurrences. Case studies show that the proposed approach not only captures heterogeneous recurrence patterns in the transformed space, but also provides effective online control charts to monitor and detect dynamical transitions in the underlying nonlinear processes.
Revisiting nonlinearity in meandering river planform dynamics using Gradual Wavelet Reconstruction
NASA Astrophysics Data System (ADS)
Schwenk, J.; Foufoula-Georgiou, E.; Lanzoni, S.
2014-12-01
Characterizing the intrinsic nonlinearity in meandering river dynamics is important because it dictates river evolution response to perturbations such as bank armoring or channel straightening. Meandering river dynamics have been described in terms of chaos or self-organized criticality—characterizations predicated on the presence of nonlinearity—yet recent studies have found only limited evidence for its existence. Standard nonlinearity tests are performed by generating a number of linearized surrogate series from a signal of interest. Inherent nonlinearities in the original signal are destroyed in the surrogates via phase randomization in the Fourier domain. Nonlinearity is inferred if a significant difference exists between the original and the surrogates in an appropriately determined phase space. These tests detect the presence or absence of nonlinearity but cannot identify which scales and locations are contributing most to the signal's nonlinearity. A new surrogate generation method called Gradual Wavelet Reconstruction (GWR) has two key advantages over the standard methodology. First, GWR quantifies the degree of nonlinearity rather than simply detecting its presence or absence, providing a basis for comparisons between river planforms and models of meander migration. Second, because the GWR methodology relies on localized transformations, it can determine the scales and locations primarily contributing to the observed complexity. As a result of those advantages too, GWR has been shown to detect the presence of nonlinearity in signals where standard tests have failed. We apply GWR methodology to time series of channel sinuosity predicted by two established models of long-time meander migration: a HIPS-type model and that of Zolezzi and Seminara (2001). Although the former model has been shown to capture first-order meander dynamics, it fails to fully couple sediment and flow dynamics; nor does it account for the resonance phenomenon. Using GWR, we show
Spatial patterns in nonlinear sea-level dynamics inferred from global satellite altimetry data
NASA Astrophysics Data System (ADS)
Radebach, Alexander; Donges, Jonathan F.; Donner, Reik V.; Barbosa, Susana; Lange, Holger; Kurths, Jürgen
2013-04-01
Since the advent of the satellite era, global sea-level altimetry data sets are available. To study complex oceanographic processes and their coupling to atmospheric dynamics it is necessary to advance beyond analyzing global mean sea-level rise or local trends. We apply a wide range of methods from linear and nonlinear time series analysis for investigating the complex dynamics of observed sea-level altimetry time series at different locations around the globe. Employing this toolkit, linear and nonlinear autodependencies (autocorrelation and auto-mutual information functions), deterministic structure (recurrence quantification and recurrence network analysis), time-reversibility characteristics (visibility graph analysis) and the relative importance of stochastic vs. deterministic dynamics (complexity-entropy plane) are studied. Combining the complimentary information from all metrics, consistent spatial patterns of sea-level dynamics are detected. Classical statistical properties such as variance, skewness and Shannon entropy of the probability distribution of sea-level reveal the special importance of western boundary currents as well as parts of the Antarctic Circumpolar Current as regions of particularly complex sea-level dynamics. In turn, the nonlinear dynamics characteristics present a somewhat different pattern exhibiting particularly high complexity in the tropics as well as the Gulf Stream and Kuroshio regions. Notably, these are also the areas where missing values due to atmospheric processes are most prominent. Further research is required to fully disentangle the dynamic complexity of sea-level from potential artifacts in the underlying altimetry data.
Nonlinear Dynamic Behavior of Functionally Graded Truncated Conical Shell Under Complex Loads
NASA Astrophysics Data System (ADS)
Yang, S. W.; Hao, Y. X.; Zhang, W.; Li, S. B.
Nonlinear dynamic behaviors of ceramic-metal graded truncated conical shell subjected to complex loads are investigated. The shell is modeled by first-order shear deformation theory. The nonlinear partial differential governing equation in terms of transverse displacements of the FGM truncated conical shell is derived from the Hamilton's principle. Galerkin's method is then utilized to discretize the partial governing equations to a two-degree-of-freedom nonlinear ordinary differential equation. The temperature-dependent materials properties of the constituents are graded in the radial direction in accordance with a power-law distribution. The aerodynamic pressure can be calculated by using the first-order piston theory. The temperature field is assumed to be a steady-state constant-temperature distribution. Bifurcation diagrams, the maximum Lyapunov exponents, wave forms and phase portraits are obtained by numerical simulation to demonstrate the complex nonlinear dynamics response of the FGM truncated conical shell. The influences of the semi-vertex angle, the material gradient index, in-plane and aerodynamic load on the nonlinear dynamics are studied.
NASA Astrophysics Data System (ADS)
Moradi, Hamed; Movahhedy, Mohammad R.; Vossoughi, Gholamreza
2012-07-01
In this paper, internal resonance and nonlinear dynamics of regenerative chatter in milling process is investigated. An extended dynamic model of the peripheral milling process including both structural and cutting force nonlinearities is presented. Closed form expressions for the nonlinear cutting forces are derived through their Fourier series components. In the presence of the large vibration amplitudes, the loss of contact effect is included in this model. Using the multiple-scales approach, analytical approximate response of the delayed nonlinear system is obtained. Considering the internal resonance dynamics (i.e. mode coupling), the energy transfer between the coupled x-y modes is studied. The results show that during regenerative chatter under specific cutting conditions, one mode can decay. Furthermore, it is possible to adjust the rate at which the x-mode (or y-mode) decays by implementation of the internal resonance. Therefore, under both internal resonance and regenerative chatter conditions, it is possible to suppress the undesirable vibration of one mode (direction) in which accurate surface finish is required. Under the steady-state motion, jump phenomenon is investigated for the process with regenerative chatter under various cutting conditions. Moreover, the effects of structural and cutting force nonlinearities on the stability lobes diagram of the process are investigated.
Fully nonlinear dynamics of stochastic thin-film dewetting.
Nesic, S; Cuerno, R; Moro, E; Kondic, L
2015-12-01
The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation. Within a stochastic lubrication framework, we show that thermal noise substantially influences the process of droplets formation. Stochastic systems feature a smaller number of droplets with a larger variability in size and space distribution, when compared to their deterministic counterparts. Finally, we discuss the influence of stochasticity on droplet coarsening for asymptotically long times. PMID:26764623
Observation of chaotic dynamics of coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
van Buskirk, R.; Jeffries, C.
1985-05-01
Experimental data are employed as bases for theoretically modelling the behavior of a finite number of driven nonlinear coupled oscillators. Attention is focused on Si p-n junction resonators exposed to an external inductance. A junction oscillator displays period doubling, Hopf figuracions to quasi-periodicity, entrainment horns and breakup of the invariant torus. Calculated and measured data are compared, with favorable results, by means of Poincare' sections, bifurcation diagrams and parameter phase space diagrams for the drive voltage and frequency. Fractal dimensions 2.03 and 2.33 are expressed in Poincare' sections to illustrate the behavior of single and dual coupled resonators which experience a breakup of the strange attractor.
Fully nonlinear dynamics of stochastic thin-film dewetting
NASA Astrophysics Data System (ADS)
Nesic, S.; Cuerno, R.; Moro, E.; Kondic, L.
2015-12-01
The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows materials nanostructuring. Often, it is crucial to be able to control the evolution, and to produce patterns characterized by regularly spaced droplets. While thermal fluctuations are expected to play a role in the dewetting process, their relevance has remained poorly understood, particularly during the nonlinear stages of evolution that involve droplet formation. Within a stochastic lubrication framework, we show that thermal noise substantially influences the process of droplets formation. Stochastic systems feature a smaller number of droplets with a larger variability in size and space distribution, when compared to their deterministic counterparts. Finally, we discuss the influence of stochasticity on droplet coarsening for asymptotically long times.
Adaptive methods for nonlinear structural dynamics and crashworthiness analysis
NASA Technical Reports Server (NTRS)
Belytschko, Ted
1993-01-01
The objective is to describe three research thrusts in crashworthiness analysis: adaptivity; mixed time integration, or subcycling, in which different timesteps are used for different parts of the mesh in explicit methods; and methods for contact-impact which are highly vectorizable. The techniques are being developed to improve the accuracy of calculations, ease-of-use of crashworthiness programs, and the speed of calculations. The latter is still of importance because crashworthiness calculations are often made with models of 20,000 to 50,000 elements using explicit time integration and require on the order of 20 to 100 hours on current supercomputers. The methodologies are briefly reviewed and then some example calculations employing these methods are described. The methods are also of value to other nonlinear transient computations.
Measurements of impulsive reconnection driven by nonlinear Hall dynamics
Tharp, T. D.; Almagri, A. F.; Miller, M. C.; Mirnov, V. V.; Prager, S. C.; Sarff, J. S.; Kim, C. C.
2010-12-15
The magnetic fields associated with reconnection in the edge of the reversed field pinch configuration have been measured in the Madison Symmetric Torus. The measured magnetic field structure is compared with theoretical predictions computed in both toroidal and cylindrical geometries. The summation of multiple modes has been accomplished to reveal a complex but still coherent edge structure. Key terms of relevant Ohm's law are accessible from magnetic field measurement and reveal the ordering [(1/ne)JxB>>E>{eta}J], which implies that two fluid effects are important in the physics governing this reconnection. Further, it is seen that the nonlinear three-wave coupling of the Hall term acts as a driving mechanism for this linearly stable mode.
Dynamics of cubic–quintic nonlinear Schrödinger equation with different parameters
NASA Astrophysics Data System (ADS)
Wei, Hua; Xue-Shen, Liu; Shi-Xing, Liu
2016-05-01
We study the dynamics of the cubic–quintic nonlinear Schrödinger equation by the symplectic method. The behaviors of the equation are discussed with harmonically modulated initial conditions, and the contributions from the quintic term are discussed. We observe the elliptic orbit, homoclinic orbit crossing, quasirecurrence, and stochastic motion with different nonlinear parameters in this system. Numerical simulations show that the changing processes of the motion of the system and the trajectories in the phase space are various for different cubic nonlinear parameters with the increase of the quintic nonlinear parameter. Project supported by the National Natural Science Foundation of China (Grant Nos. 11301350, 11472124, and 11271158) and the Doctor Start-up Fund in Liaoning Province, China (Grant No. 20141050).
Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice
Abdullaev, F. Kh.; Tomio, Lauro; Gammal, A.; Luz, H. L. F. da
2007-10-15
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.
NASA Technical Reports Server (NTRS)
Oakley, David R.; Knight, Norman F., Jr.
1994-01-01
A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for nonlinear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly nonlinear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly nonlinear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the nonlinear static response of two and three dimensional hyperelastic systems involving contact. Impressive relative speedups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.
Dynamic nonlinearity in epitaxial BaTi O3 films
NASA Astrophysics Data System (ADS)
Tyunina, M.; Savinov, M.
2016-08-01
Dynamic dielectric and piezoelectric constants of ferroelectrics increase proportionally to the amplitude of alternating electric field as a result of hysteretic Rayleigh-type motion of domain walls. Here a hysteresis-free quadratic field dependence of the dynamic dielectric response is experimentally demonstrated in the absence of domain walls in epitaxial BaTi O3 films. This extraordinary behavior is related to polar entities, whose presence is confirmed by the Vogel-Fulcher relaxation. The polar entities are ascribed to polarization fluctuations associated with lattice inhomogeneity.
Nonlinear dynamics of the blood flow studied by Lyapunov exponents.
Bracic, M; Stefanovska, A
1998-05-01
In order to gain an insight into the dynamics of the cardiovascular system throughout which the blood circulates, the signals measured from peripheral blood flow in humans were analyzed by calculating the Lyapunov exponents. Over a wide range of algorithm parameters, paired values of both the global and the local Lyapunov exponents were obtained, and at least one exponent equaled zero within the calculation error. This may be an indication of the deterministic nature and finite number of degrees of freedom of the cardiovascular system governing the blood-flow dynamics on a time scale of minutes. A difference was observed in the Lyapunov dimension of controls and athletes. PMID:9608852
Mitsis, G D; Zhang, R; Levine, B D; Marmarelis, V Z
2002-04-01
Dynamic autoregulation of cerebral hemodynamics in healthy humans is studied using the novel methodology of the Laguerre-Volterra network for systems with fast and slow dynamics (Mitsis, G. D., and V. Z. Marmarelis, Ann. Biomed. Eng. 30:272-281, 2002). Since cerebral autoregulation is mediated by various physiological mechanisms with significantly different time constants, it is used to demonstrate the efficacy of the new method. Results are presented in the time and frequency domains and reveal that cerebral autoregulation is a nonlinear and dynamic (frequency-dependent) system with considerable nonstationarities. Quantification of the latter reveals greater variability in specific frequency bands for each subject in the low and middle frequency range (below 0.1 Hz). The nonlinear dynamics are prominent also in the low and middle frequency ranges, where the frequency response of the system exhibits reduced gain. PMID:12086006
NASA Astrophysics Data System (ADS)
Qiu, Zhiping; Ma, Lihong; Wang, Xiaojun
2009-01-01
Effects of uncertainties on the dynamic response of the nonlinear vibration systems with general form are investigated. Based on interval mathematics, modeling the uncertain parameters as interval numbers, a non-probabilistic interval analysis method, which estimates the range of the nonlinear dynamic response with the help of Taylor series expansion, is presented, where the partial derivatives of the dynamic response with respect to uncertain parameters are considered to be interval numbers. The sensitivity matrices of dynamic response with the uncertain parameters are derived. For the presented method, only the bounds on uncertain parameters are needed, instead of probabilistic density distribution or statistical quantities. Numerical examples are used to illustrate the validity and feasibility of the presented method.
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
Huffaker, Ray; Bittelli, Marco
2015-01-01
Wind-energy production may be expanded beyond regions with high-average wind speeds (such as the Midwest U.S.A.) to sites with lower-average speeds (such as the Southeast U.S.A.) by locating favorable regional matches between natural wind-speed and energy-demand patterns. A critical component of wind-power evaluation is to incorporate wind-speed dynamics reflecting documented diurnal and seasonal behavioral patterns. Conventional probabilistic approaches remove patterns from wind-speed data. These patterns must be restored synthetically before they can be matched with energy-demand patterns. How to accurately restore wind-speed patterns is a vexing problem spurring an expanding line of papers. We propose a paradigm shift in wind power evaluation that employs signal-detection and nonlinear-dynamics techniques to empirically diagnose whether synthetic pattern restoration can be avoided altogether. If the complex behavior of observed wind-speed records is due to nonlinear, low-dimensional, and deterministic system dynamics, then nonlinear dynamics techniques can reconstruct wind-speed dynamics from observed wind-speed data without recourse to conventional probabilistic approaches. In the first study of its kind, we test a nonlinear dynamics approach in an application to Sugarland Wind-the first utility-scale wind project proposed in Florida, USA. We find empirical evidence of a low-dimensional and nonlinear wind-speed attractor characterized by strong temporal patterns that match up well with regular daily and seasonal electricity demand patterns. PMID:25617767
Nonlinear Dynamics of Electronic Systems - Proceedings of the Workshop Ndes '93
NASA Astrophysics Data System (ADS)
Davies, A. C.; Schwarz, W.
1994-04-01
The Table of Contents for the book is as follows: * Editors' Preface * CHUA'S CIRCUIT -- ANALYSIS AND APPLICATIONS * Recent Generalisations of Chua's Circuit * Realisations of Chua's Circuit * From Chua's Circuit to Chua's Oscillator: A Picture Book of Attractors * A Simple Explanation of the Physical Behaviour of Chua's Circuit or A Route to the Hearts of Chua's Circuit * Chaos Control Techniques: A Study Using Chua's Circuit * Stochastic Properties of Signals Generated by Chua's Circuit * ANALYSIS AND METHODS * Contemporary Problems in Dynamical Chaos * Methods of Global Bifurcation Analysis and Applications to Nonlinear Circuits * Geometrical Analysis of the Behaviour of Third-Order Digital Filters * Identification of the Irregular Behaviour in Nonlinear Electrical Circuits by the Time Series Method * Investigations to the Influence of Noise on the Irregular Behaviour of Nonlinear Dynamical Circuits and Systems * On Integration of Nonlinear Dynamics of Large Electrical Power Systems * NEURAL NETWORKS * Complex Dynamics in Cellular Neural Networks * Polynomial Cellular Neural Network: A New Dynamical Circuit for Pattern Recognition * Wave Propagation in Arrays of Active Nonlinear Circuits * A Noise Generator Based on Chaos for a Neural Network Application * PHENOMENA AND APPLICATIONS * Synchronization of Chaotic Signals * Experimental Demonstration of Binary Chaos-Shift-Keying Using Self-Synchronising Chua's Circuits * Two Simulation Experiments in Chaotic Synchronization * Chaotic Bridges -- A New Concept for High Sensitive Devices * Hyperchaos and Related Phenomena from Odd-Dimensional Hysteresis System * The Role of Chaos in a Gyrotron-Type of Interaction * Chaos and Regularity in a Ferroelectric Duffing-Like Oscillator * Acquisition Properties and Chaotic Behaviour of the Sampling Phase-Locked Loop * Generating Low Frequency Noise Using a Chaotic Circuit * DESIGN OF CHAOTIC SYSTEMS * Chaos and Pseudorandomness * Digital Counters and Pseudorandom Number
Ferman, M.A.
1994-12-31
A collection of some highlights of the Author`s experiences with nonlinear dynamics in analyses and tests of Panels and Membranes encountered over the past 40 years is given. The primary focus is placed on a major block of his work since the early 70`s, involving work with fluid-structure interaction with Panels and Membranes, and with efforts in Acoustic Fatigue of Panels. While the Author had encountered nonlinear problems throughout Ins career involving flutter, vibration in general, and dynamic thrust instability; it was the more recent work with panels and membranes that greatly expanded his experience. This was triggered by the advent of highly maneuverable aircraft, powered by large powerful, noisy engines, and new materials in the mid 70`s. The significance of nonlinearity for these applications is most obvious from the results shown here-it simply cannot be ignored for optimal, safe design.
Klonowski, Wlodzimierz
2007-01-01
Methods of contemporary physics are increasingly important for biomedical research but, for a multitude of diverse reasons, most practitioners of biomedicine lack access to a comprehensive knowledge of these modern methodologies. This paper is an attempt to describe nonlinear dynamics and its methods in a way that could be read and understood by biomedical professionals who usually are not trained in advanced mathematics. After an overview of basic concepts and vocabulary of nonlinear dynamics, deterministic chaos, and fractals, application of nonlinear methods of biosignal analysis is discussed. In particular, five case studies are presented: 1. Monitoring the depth of anaesthesia and of sedation; 2. Bright Light Therapy and Seasonal Affective Disorder; 3. Analysis of posturographic signals; 4. Evoked EEG and photo-stimulation; 5. Influence of electromagnetic fields generated by cellular phones. PMID:17908344
Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations
NASA Technical Reports Server (NTRS)
Hodges, D. H.
1985-01-01
Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.
Snyder, P.B.; Wilson, H.R.; Xu, X.Q.
2005-05-15
Nonlinear three-dimensional electromagnetic simulations are employed to study the dynamics of edge localized modes (ELMs) driven by intermediate wavelength peeling-ballooning modes. It is found that the early behavior of the modes is similar to expectations from linear, ideal peeling-ballooning mode theory, with the modes growing linearly at a fraction of the Alfven frequency. In the nonlinear phase, the modes grow explosively, forming a number of extended filaments which propagate rapidly from the outer closed flux region into the open flux region toward the outboard wall. Similarities to nonlinear ballooning theory as well as additional complexities are observed. Comparison to observations reveals a number of similarities. Implications of the simulations and proposals for the dynamics of the full ELM crash are discussed.
Nonlinear Impact Dynamic Analysis and Comparison with Experimental Data for the Skid Gear
NASA Astrophysics Data System (ADS)
Kim, Dong-Hyun; Kim, Yu-Sung
In this study, nonlinear crash analyses have been conducted for the skid landing gear of helicopter. The realistic configuration of skid landing gear system is considered. Detailed three-dimensional finite element model with variable thickness and material nonlinearity is constructed for required impact design conditions. Advanced computational approach is used to conduct nonlinear transient impact dynamic analyses for different collision models. Characteristics of impact dynamic responses due to the ground crash are practically investigated in detail. It is also shown that the exact consideration of friction effect is very important to accurately predict the crash behavior of the skid type landing gear system. Finally, two typical landing conditions are analyzed and correlated with drop test results.
Huang, Ruimei; Du, Shouhong; Chen, Ziyi; Zhang, Zhen; Zhou, Yi
2014-02-01
Electroencephalogram (EEG) is the primary tool in investigation of the brain science. It is necessary to carry out a deepgoing study into the characteristics and information hidden in EEGs to meet the needs of the clinical research. In this paper, we present a wavelet-nonlinear dynamic methodology for analysis of nonlinear characteristic of EEGs and delta, theta, alpha, and beta sub-bands. We therefore studied the effectiveness of correlation dimension (CD), largest Lyapunov exponen, and approximate entropy (ApEn) in differentiation between the interictal EEG and ictal EEG based on statistical significance of the differences. The results showed that the nonlinear dynamic char acteristic of EEG and EEG subbands could be used as effective identification statistics in detecting seizures. PMID:24804477
Global Dynamics of a Parasite-Host Model with Nonlinear Incidence Rate
NASA Astrophysics Data System (ADS)
Tang, Yilei
The paper is concerned with the effect of a nonlinear incidence rate Sp Iq on dynamical behaviors of a parasite-host model. It is shown that the global attractor of the parasite-host model is an equilibrium if q = 1, which is similar to that of the parasite-host model with a nonlinear incidence rate of the fractional function (SI)/(S+I). However, when q is greater than one, more positive equilibria appear and limit cycles arise from Hopf bifurcations at the positive equilibria for the model with the incidence rate Sp Iq. It reveals that the nonlinear incidence rate of the exponential function Sp Iq for generic p and q can lead to more complicated and richer dynamics than the bilinear incidence rate or the fractional incidence rate for this model.
NASA Astrophysics Data System (ADS)
Gu, Guo-Ying; Gupta, Ujjaval; Zhu, Jian; Zhu, Li-Min; Zhu, Xiang-Yang
2015-07-01
In the practical applications of actuators, the control of their deformation or driving force is a key issue. Most of recent studies on dielectric elastomer actuators (DEAs) focus on issues of mechanics, physics, and material science, whereas less importance is given to the control of these soft actuators. In this paper, we underline the importance of a nonlinear dynamic model as the basis for a feedforward deformation control approach of a rubber-based DEA. Experimental evidence shows the effectiveness of the feedforward controller. The present study confirms that a DEA's trajectory can be finely controlled with a solid nonlinear dynamic model despite the presence of material nonlinearities and electromechanical coupling. The effective control of DEAs may pave the way for extensive emerging applications to soft robots.
Guidance of Nonlinear Nonminimum-Phase Dynamic Systems
NASA Technical Reports Server (NTRS)
Devasia, Santosh
1997-01-01
The first two years research work has advanced the inversion-based guidance theory for: (1) systems with non-hyperbolic internal dynamics; (2) systems with parameter jumps; (3) systems where a redesign of the output trajectory is desired; and (4) the generation of recovery guidance maneuvers.
Nonlinear dynamics of the rattleback: a nonholonomic model
NASA Astrophysics Data System (ADS)
Borisov, A. V.; Kazakov, A. O.; Kuznetsov, S. P.
2014-05-01
For a solid convex body moving on a rough horizontal plane - known in mechanics as a rattleback - numerical simulations are used to discuss and illustrate dynamical phenomena that are characteristic of the motion due to the nonholonomic nature of the mechanical system; the relevant feature is the nonconservation of the phase volume in the course of the dynamics? evolution. In such a system, a local compression of the phase volume can produce behavior features similar to those exhibited by dissipative systems, such as the presence of stable equilibrium points relevant to stationary rotations; limit cycles (rotations with oscillations), and strange chaotic attractors. A chart of dynamical regimes is plotted in a plane of parameters whose axes are the total mechanical energy and the angle of relative rotation of the geometric and dynamic principal axes of the body. The transition to chaos through a sequence of Feigenbaum period doubling bifurcations is demonstrated. A number of strange attractors are considered, for which phase portraits, Lyapunov exponents, and Fourier spectra are presented.
Linear-Nonlinear-Poisson Models of Primate Choice Dynamics
ERIC Educational Resources Information Center
Corrado, Greg S.; Sugrue, Leo P.; Seung, H. Sebastian; Newsome, William T.
2005-01-01
The equilibrium phenomenon of matching behavior traditionally has been studied in stationary environments. Here we attempt to uncover the local mechanism of choice that gives rise to matching by studying behavior in a highly dynamic foraging environment. In our experiments, 2 rhesus monkeys ("Macacca mulatta") foraged for juice rewards by making…
Spatiotemporal behavior and nonlinear dynamics in a phase conjugate resonator
NASA Technical Reports Server (NTRS)
Liu, Siuying Raymond
1993-01-01
The work described can be divided into two parts. The first part is an investigation of the transient behavior and stability property of a phase conjugate resonator (PCR) below threshold. The second part is an experimental and theoretical study of the PCR's spatiotemporal dynamics above threshold. The time-dependent coupled wave equations for four-wave mixing (FWM) in a photorefractive crystal, with two distinct interaction regions caused by feedback from an ordinary mirror, was used to model the transient dynamics of a PCR below threshold. The conditions for self-oscillation were determined and the solutions were used to define the PCR's transfer function and analyze its stability. Experimental results for the buildup and decay times confirmed qualitatively the predicted behavior. Experiments were carried out above threshold to study the spatiotemporal dynamics of the PCR as a function of Pragg detuning and the resonator's Fresnel number. The existence of optical vortices in the wavefront were identified by optical interferometry. It was possible to describe the transverse dynamics and the spatiotemporal instabilities by modeling the three-dimensional-coupled wave equations in photorefractive FWM using a truncated modal expansion approach.
[Nonlinear effects on population dynamics related to age structure and fishery impact].
Frisman, E Ia; Last, E V
2005-01-01
Population dynamics of commercial fish populations with an age structure was studied by the example of salmons. The relationship between the amount of catch on fishing efforts and total abundance of a stock fished is described by a nonlinear "trophic" function. Special attention is given to the analysis of population dynamics stability under conditions for maximum profit. Simulation results are compared to statistical data on the catch of Pacific salmon species in the Bering Sea. PMID:16240747
Ma, Rongfei
2015-01-01
In this paper, ammonia quantitative analysis based on miniaturized Al ionization gas sensor and non-linear bistable dynamic model was proposed. Al plate anodic gas-ionization sensor was used to obtain the current-voltage (I-V) data. Measurement data was processed by non-linear bistable dynamics model. Results showed that the proposed method quantitatively determined ammonia concentrations. PMID:25975362
Nonlinear dynamics and plasma transport. Progress report, September 15, 1991--September 14, 1992
Antonsen, T.M. Jr.; Drake, J.F.; Finn, J.M.; Guzdar, P.N.; Hassam, A.B.; Sagdeev, R.Z.
1992-06-01
In this paper we summarize the progress made over the last year in three different areas of research: (a) shear flow generation and reduced transport in fluids and plasma, (b) nonlinear dynamics and visualization of 3D flows, and (c) application of wavelet analysis to the study of fractal dimensions in experimental and numerical data.
Dynamics of a nonautonomous soliton in a generalized nonlinear Schroedinger equation
Yang Zhanying; Zhang Tao; Zhao Lichen; Feng Xiaoqiang; Yue Ruihong
2011-06-15
We solve a generalized nonautonomous nonlinear Schroedinger equation analytically by performing the Darboux transformation. The precise expressions of the soliton's width, peak, and the trajectory of its wave center are investigated analytically, which symbolize the dynamic behavior of a nonautonomous soliton. These expressions can be conveniently and effectively applied to the management of soliton in many fields.
NASA Technical Reports Server (NTRS)
Goldberger, A. L.; West, B. J.; Bhargava, V.
1985-01-01
The application of nonlinear analysis both to normal physiological dynamics and pathophysiological perturbations in a variety of different systems leads to observations not predicted by traditional models. Such analyses may have important implications for diagnostic and prognostic assessment as well as for therapeutics.
Social Contagion, Adolescent Sexual Behavior, and Pregnancy: A Nonlinear Dynamic EMOSA Model.
ERIC Educational Resources Information Center
Rodgers, Joseph Lee; Rowe, David C.; Buster, Maury
1998-01-01
Expands an existing nonlinear dynamic epidemic model of onset of social activities (EMOSA), motivated by social contagion theory, to quantify the likelihood of pregnancy for adolescent girls of different sexuality statuses. Compares five sexuality/pregnancy models to explain variance in national prevalence curves. Finds that adolescent girls have…
On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators
NASA Astrophysics Data System (ADS)
Alsaleem, Fadi M.; Younis, Mohammad I.; Ouakad, Hassen M.
2009-04-01
We present modeling, analysis and experimental investigation for nonlinear resonances and the dynamic pull-in instability in electrostatically actuated resonators. These phenomena are induced by exciting a microstructure with nonlinear forcing composed of a dc parallel-plate electrostatic load superimposed on an ac harmonic load. Nonlinear phenomena are investigated experimentally and theoretically including primary resonance, superharmonic and subharmonic resonances, dynamic pull-in and the escape-from-potential-well phenomenon. As a case study, a capacitive sensor made up of two cantilever beams with a proof mass attached to their tips is studied. A nonlinear spring-mass-damper model is utilized accounting for squeeze-film damping and the parallel-plate electrostatic force. Long-time integration and a global dynamic analysis are conducted using a finite-difference method combined with the Floquet theory to capture periodic orbits and analyze their stability. The domains of attraction (basins of attraction) for data points on the frequency-response curve are calculated numerically. Dover cliff integrity curves are calculated and the erosion of the safe basin of attraction is investigated as the frequency of excitation is swept passing primary resonance and dynamic pull-in. Conclusions are presented regarding the safety and integrity of MEMS resonators based on the simulated basin of attraction and the observed experimental data.
Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory
ERIC Educational Resources Information Center
Bloch, Deborah P.
2005-01-01
The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…
Aerodynamic and Nonlinear Dynamic Acoustic Analysis of Tension Asymmetry in Excised Canine Larynges
ERIC Educational Resources Information Center
Devine, Erin E.; Bulleit, Erin E.; Hoffman, Matthew R.; McCulloch, Timothy M.; Jiang, Jack J.
2012-01-01
Purpose: To model tension asymmetry caused by superior laryngeal nerve paralysis (SLNP) in excised larynges and apply perturbation, nonlinear dynamic, and aerodynamic analyses. Method: SLNP was modeled in 8 excised larynges using sutures and weights to mimic cricothyroid (CT) muscle function. Weights were removed from one side to create tension…
Rigatos, Gerasimos G; Rigatou, Efthymia G; Djida, Jean Daniel
2015-10-01
A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies). PMID:26280184
Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm
NASA Astrophysics Data System (ADS)
Kania, Adhe; Sidarto, Kuntjoro Adji
2016-02-01
Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.
A DYNAMIC NONLINEAR MODEL OF OZONE-INDUCED FEV1 RESPONSE UNDER CHANGING EXPOSURE CONDITIONS
A Dynamic Nonlinear Model of Ozone-induced FEV1 Response under Changing Exposure Conditions. 1WF McDonnell, 2PW Stewart, 3MV Smith. 1Human Studies Division, NHEERL, U.S. EPA, RTP, NC. 2University of North Carolina, Chapel Hill, NC. 3ASI, Durham, NC.
Ozone exposure result...
Cold atom dynamics in linear and nonlinear optical potentials
NASA Astrophysics Data System (ADS)
Williams, William
This dissertation has two major components. The first is theoretical work on using multiple optical fields to control atoms. Theoretical models for creating complex optical potentials for use in atomic lithography are explored and a proposal for serial writing of an atomic beam is presented. A proposal to compress a cloud of cold atoms to create a tightly confined cigar shaped cloud of dense atoms for use in atom optics experiments and quantum control is also presented. The second component focuses on the study of nonlinear self-focusing in cold Cesium atoms. Modulation instability is explored in a cold atom environment which produces novel effects such as red detuned modulational instability. Several experimental setups are explored and compared with theoretical models. The first is two-wave mixing which consists of a strong pump beam and a weak probe beam crossing in a MOT. The second is using a counter-propagating pump beam to balance the radiation force of the forward propagating pump beam. The third is retro-reflecting both the probe and the pump beam which creates a more complicated experimental setup with multiple atomic gratings. Energy transfer from the pump to the probe beam via atomic density redistribution for red detuning is presented.
Nonlinear dynamical model based control of in vitro hippocampal output
Hsiao, Min-Chi; Song, Dong; Berger, Theodore W.
2012-01-01
This paper describes a modeling-control paradigm to control the hippocampal output (CA1 response) for the development of hippocampal prostheses. In order to bypass a damaged hippocampal region (e.g., CA3), downstream hippocampal signal (e.g., CA1 responses) needs to be reinstated based on the upstream hippocampal signal (e.g., dentate gyrus responses) via appropriate stimulations to the downstream (CA1) region. In this approach, we optimize the stimulation signal to CA1 by using a predictive DG-CA1 nonlinear model (i.e., DG-CA1 trajectory model) and an inversion of the CA1 input–output model (i.e., inverse CA1 plant model). The desired CA1 responses are first predicted by the DG-CA1 trajectory model and then used to derive the optimal stimulation intensity through the inverse CA1 plant model. Laguerre-Volterra kernel models for random-interval, graded-input, contemporaneous-graded-output system are formulated and applied to build the DG-CA1 trajectory model and the CA1 plant model. The inverse CA1 plant model to transform desired output to input stimulation is derived from the CA1 plant model. We validate this paradigm with rat hippocampal slice preparations. Results show that the CA1 responses evoked by the optimal stimulations accurately replicate the CA1 responses recorded in the hippocampal slice with intact trisynaptic pathway. PMID:23429994
Nonlinear dynamics of capacitive charging and desalination by porous electrodes.
Biesheuvel, P M; Bazant, M Z
2010-03-01
The rapid and efficient exchange of ions between porous electrodes and aqueous solutions is important in many applications, such as electrical energy storage by supercapacitors, water desalination and purification by capacitive deionization, and capacitive extraction of renewable energy from a salinity difference. Here, we present a unified mean-field theory for capacitive charging and desalination by ideally polarizable porous electrodes (without Faradaic reactions or specific adsorption of ions) valid in the limit of thin double layers (compared to typical pore dimensions). We illustrate the theory for the case of a dilute, symmetric, binary electrolyte using the Gouy-Chapman-Stern (GCS) model of the double layer, for which simple formulae are available for salt adsorption and capacitive charging of the diffuse part of the double layer. We solve the full GCS mean-field theory numerically for realistic parameters in capacitive deionization, and we derive reduced models for two limiting regimes with different time scales: (i) in the "supercapacitor regime" of small voltages and/or early times, the porous electrode acts like a transmission line, governed by a linear diffusion equation for the electrostatic potential, scaled to the RC time of a single pore, and (ii) in the "desalination regime" of large voltages and long times, the porous electrode slowly absorbs counterions, governed by coupled, nonlinear diffusion equations for the pore-averaged potential and salt concentration. PMID:20365735
Robust Control Design for Uncertain Nonlinear Dynamic Systems
NASA Technical Reports Server (NTRS)
Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.
2012-01-01
Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
Nonlinear Bayesian cue integration explains the dynamics of vocal learning
NASA Astrophysics Data System (ADS)
Zhou, Baohua; Sober, Samuel; Nemenman, Ilya
The acoustics of vocal production in songbirds is tightly regulated during both development and adulthood as birds progressively refine their song using sensory feedback to match an acoustic target. Here, we perturb this sensory feedback using headphones to shift the pitch (fundamental frequency) of song. When the pitch is shifted upwards (downwards), birds eventually learn to compensate and sing lower (higher), bringing the experienced pitch closer to the target. Paradoxically, the speed and amplitude of this motor learning decrease with increases in the introduced error size, so that birds respond rapidly to a small sensory perturbation, while seemingly never correcting a much bigger one. Similar results are observed broadly across the animal kingdom, and they do not derive from a limited plasticity of the adult brain since birds can compensate for a large error as long as the error is imposed gradually. We develop a mathematical model based on nonlinear Bayesian integration of two sensory modalities (one perturbed and the other not) that quantitatively explains all of these observations. The model makes predictions about the structure of the probability distribution of the pitches sung by birds during the pitch shift experiments, which we confirm using experimental data. This work was supported in part by James S. McDonnell Foundation Grant # 220020321, NSF Grant # IOS/1208126, NSF Grant # IOS/1456912 and NIH Grants # R01NS084844.