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.
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.
Nonlinear optics and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Chen, C. H.
1990-08-01
The author was invited by the Institute of Atomic and Molecular Sciences, Academia Sinica, in Taiwan to give six lectures on nonlinear optics. The participants included graduate students, postdoctoral fellows, research staff, and professors from several research organizations and universities. Extensive discussion followed each lecture. Since both the Photophysics Group at Oak Ridge National Laboratory (ORNL) and Institute of Atomic and Molecular Sciences in Taiwan have been actively participating in nonlinear optics research, the discussions are very beneficial to ORNL programs. The author also visited several laboratories at IAMS to exchange research ideas on nonlinear optics.
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
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.
Nonlinear bubble dynamics of cavitation.
An, Yu
2012-01-01
For cavitation clouds generated in a standing sound wave driven by an ultrasonic horn, the nonlinear acoustic wave equation governing cavitation dynamics is numerically solved together with the bubble motion equation under an approximation. This conceptual calculation can qualitatively reproduce the observed characteristics of cavitation.
Nonlinear analysis of drought dynamics
NASA Astrophysics Data System (ADS)
Ma, M.
2015-12-01
Drought is an extreme natural hazard and becomes a severe problem in the world. It arises as a result of interactions between climate input and human activity, displaying the nonlinearity and complexity. Nonlinear time series analyses open a way to study the underlying dynamic characteristics of drought, and then provide the forward knowledge to understanding the physical mechanism of drought event. The rationale behind this idea is that information about the representation of nonlinear properties could be used as an additional quality indicator. To that end, the correlation dimension method, a powerful nonlinear time series analysis method based on the chaos theory, has been suggested to assess the intrinsic dimensionality or degree of freedom of time series according to Takens (1981). It can provide an assessment of the dominant processes that is required to map the observed dynamics. In this study, daily discharge and hourly groundwater level data of 63 catchments in Germany and China were investigated with correlation dimension method. The results indicated that the correlation dimension values of studied discharge exhibited none clear spatial patterns, but showed significant correlations with the spatial heterogeneity within the catchments. In contrast, the correlation dimension values of groundwater level displayed spatial patterns due to the different aquifer conditions (confined or unconfined). High correlation dimension values indicate partly confined conditions. In addition, Hurst analysis was involved to qualify the persistence of drought. It seems that drought mechanisms can be learnt from the data themselves in an inverse manner.
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
2008-11-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain poorly understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in considerable detail, both theoretically and experimentally. Instability in viscous jets leads to regular periodic coiling of the jet, which exhibits a non-trivial frequency dependence with the height of the fall. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities. We observe complex nonlinear spatio-temporal dynamics of the jet, and uncover a transition from periodic to quasi-periodic to a multi-frequency, broad-spectrum dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo'' or the Kaye effect. We examine different dynamical regimes in terms of scaling variables, which depend on the geometry (dimensionless height), kinematics (dimensionless flow rate), and the fluid properties (elasto-gravity number) and present a regime map of the dynamics of the jet in terms of these dimensionless variables.
Nonlinear Dynamics in Viscoelastic Jets
NASA Astrophysics Data System (ADS)
Majmudar, Trushant; Varagnat, Matthieu; McKinley, Gareth
2009-03-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain poorly understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in considerable detail, both theoretically and experimentally. Instability in viscous jets leads to regular periodic coiling of the jet, which exhibits a non-trivial frequency dependence with the height of the fall. Here we present a systematic study of the effect of viscoelasticity on the dynamics of continuous jets of worm-like micellar surfactant solutions of varying viscosities and elasticities. We observe complex nonlinear spatio-temporal dynamics of the jet, and uncover a transition from periodic to quasi-periodic to a multi-frequency, broad-spectrum dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the ``leaping shampoo'' or the Kaye effect. We examine different dynamical regimes in terms of scaling variables, which depend on the geometry (dimensionless height), kinematics (dimensionless flow rate), and the fluid properties (elasto-gravity number) and present a regime map of the dynamics of the jet in terms of these dimensionless variables.
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
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 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.
Taming Explosive Growth through Dynamic Random Links
NASA Astrophysics Data System (ADS)
Choudhary, Anshul; Kohar, Vivek; Sinha, Sudeshna
2014-03-01
We study the dynamics of a collection of nonlinearly coupled limit cycle oscillators relevant to a wide class of systems, ranging from neuronal populations to electrical circuits, over network topologies varying from a regular ring to a random network. We find that for sufficiently strong coupling strengths the trajectories of the system escape to infinity in the regular ring network. However when a fraction of the regular connections are dynamically randomized, the unbounded growth is suppressed and the system remains bounded. Further, we find a scaling relation between the critical fraction of random links necessary for successful prevention of explosive behavior and the network rewiring time-scale. These results suggest a mechanism by which blow-ups may be controlled in extended oscillator systems.
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 aspects of modern storage rings
Helleman, R.H.G.; Kheifets, S.A.
1986-01-01
It is argued that the nonlinearity of storage rings becomes an essential problem as the design parameters of each new machine are pushed further and further. Yet the familiar methods of classical mechanics do not allow determination of single particle orbits over reasonable lengths of time. It is also argued that the single particle dynamics of a storage ring is possibly one of the cleanest and simplest nonlinear dynamical systems available with very few degrees of freedom. Hence, reasons are found for accelerator physicists to be interested in nonlinear dynamics and for researchers in nonlinear dynamics to be interested in modern storage rings. The more familiar methods of treating nonlinear systems routinely used in acclerator theory are discussed, pointing out some of their limitations and pitfalls. 39 refs., 1 fig. (LEW)
Interfacial Nonlinear Dynamics, Phenomena, and Devices
NASA Astrophysics Data System (ADS)
Zhou, Ping
The dynamics of an optical switch based on a dielectric -clad nonlinear film is presented. Two transition processes of the optical switching, from total internal reflection (TIR) to transmission (Tr) and from Tr to TIR, are investigated in theory as well as experiment. Nonlinear dynamic layered transfer matrix theory is developed to study the transition process from TIR to Tr at a nonlinear thin film due to the optically induced refractive index change. A simple theoretical model based on a dynamic nonlinear Fabry-Perot etalon is given for the analysis of the switching process from Tr to TIR. The quantitative analysis can be used for the design and optimization of an optical sensor protector and other devices. Experiments have been done on both the processes of TIR to Tr and Tr to TIR switching for visible as well as infrared wavelengths. A theory for the design of an optimal anti-reflection coating is proposed in order to aid the design and optimization of a nonlinear interfacial switch. Furthermore, a detailed study of the dynamic optical tunneling through the nonlinear interface indicates that the reflected wave would undergo an additional dynamic nonlinear phase shift which is a novel nonlinear interfacial phenomenon, first revealed by this study.
Nonlinear and nonequilibrium dynamics in geomaterials.
TenCate, James A; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A
2004-08-01
The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.
Dynamical fermions with fat links
NASA Astrophysics Data System (ADS)
Knechtli, Francesco; Hasenfratz, Anna
2001-06-01
We present and test a new method for simulating dynamical fermions with fat links. Our construction is based on the introduction of auxiliary but dynamical gauge fields and works with any fermionic action and can be combined with any fermionic updating. In our simulation we use an overrelaxation step which makes it effective. For four flavors of staggered fermions the first results indicate that flavor symmetry at a lattice spacing a~0.2 fm is restored to a few percent. With the standard action this amount of flavor symmetry restoration is achieved at a~0.07 fm. We estimate that the overall computational cost is reduced by at least a factor of 10.
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.
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.
Nonlinear Dynamic Model Explains The Solar Dynamic
NASA Astrophysics Data System (ADS)
Kuman, Maria
Nonlinear mathematical model in torus representation describes the solar dynamic. Its graphic presentation shows that without perturbing force the orbits of the planets would be circles; only perturbing force could elongate the circular orbits into ellipses. Since the Hubble telescope found that the planetary orbits of other stars in the Milky Way are also ellipses, powerful perturbing force must be present in our galaxy. Such perturbing force is the Sagittarius Dwarf Galaxy with its heavy Black Hole and leftover stars, which we see orbiting around the center of our galaxy. Since observations of NASA's SDO found that magnetic fields rule the solar activity, we can expect when the planets align and their magnetic moments sum up, the already perturbed stars to reverse their magnetic parity (represented graphically as periodic looping through the hole of the torus). We predict that planets aligned on both sides of the Sun, when their magnetic moments sum-up, would induce more flares in the turbulent equatorial zone, which would bulge. When planets align only on one side of the Sun, the strong magnetic gradient of their asymmetric pull would flip the magnetic poles of the Sun. The Sun would elongate pole-to-pole, emit some energy through the poles, and the solar activity would cease. Similar reshaping and emission was observed in stars called magnetars and experimentally observed in super-liquid fast-spinning Helium nanodroplets. We are certain that NASA's SDO will confirm our predictions.
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 Dynamics of Parametrically Excited Gyroscopic Systems
Namachchivaya. N.S.
2001-06-01
The primary objective of this project is to determine how some of the powerful geometric methods of dynamical systems can be applied to study nonlinear gyroscopic systems. We proposed to develop techniques to predict local and global behavior and instability mechanisms and to analyze the interactions between noise, stability, and nonlinearities inherent in gyroscopic systems. In order to obtain these results we use the method of normal forms, global bifurcation techniques, and various other dynamical systems tools.
Nonlinear wave dynamics in honeycomb lattices
Bahat-Treidel, Omri; Segev, Mordechai
2011-08-15
We study the nonlinear dynamics of wave packets in honeycomb lattices and show that, in quasi-one-dimensional configurations, the waves propagating in the lattice can be separated into left-moving and right-moving waves, and any wave packet composed of only left (or only right) movers does not change its intensity structure in spite of the nonlinear evolution of its phase. We show that the propagation of a general wave packet can be described, within a good approximation, as a superposition of left- and right-moving self-similar (nonlinear) wave packets. Finally, we find that Klein tunneling is not suppressed by nonlinearity.
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 Structures with Material Degradation
NASA Astrophysics Data System (ADS)
Soltani, P.; Wagg, D. J.; Pinna, C.; Whear, R.; Briody, C.
2016-09-01
Structures usually experience deterioration during their working life. Oxidation, corrosion, UV exposure, and thermo-mechanical fatigue are some of the most well-known mechanisms that cause degradation. The phenomenon gradually changes structural properties and dynamic behaviour over their lifetime, and can be more problematic and challenging in the presence of nonlinearity. In this paper, we study how the dynamic behaviour of a nonlinear system changes as the thermal environment causes certain parameters to vary. To this end, a nonlinear lumped mass modal model is considered and defined under harmonic external force. Temperature dependent material functions, formulated from empirical test data, are added into the model. Using these functions, bifurcation parameters are defined and the corresponding nonlinear responses are observed by numerical continuation. A comparison between the results gives a preliminary insight into how temperature induced properties affects the dynamic response and highlights changes in stability conditions of the structure.
Nonlinear 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.
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...
Nonlinear dynamics in a SPEAR wiggler
NASA Astrophysics Data System (ADS)
Safranek, J.; Limborg, C.; Terebilo, A.; Blomqvist, K. I.; Elleaume, P.; Nosochkov, Y.
2002-01-01
BL11, the most recently installed wiggler in the SPEAR storage ring at the Stanford Synchrotron Radiation Laboratory, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and closed orbit shifts were used to characterize the nonlinear fields. Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different from the magnetic measurements made along a straight line with a stretched wire. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Because of the relatively large dispersion (1.2 m) at BL11, the nonlinearities particularly reduced the off-energy dynamic aperture. Because of the nature of these nonlinear fields, it is impossible, even theoretically, to cancel them completely with short multipole correctors. Magic finger corrector magnets were built, however, that partially correct the nonlinear perturbation, greatly improving the storage ring performance.
NASA Astrophysics Data System (ADS)
Perdigão, R. A. P.
2015-12-01
The dynamical evolution of complex coevolving systems is assessed in a novel nonlinear statistical-dynamical framework formally linking nonlinear statistical measures of codependence and emergence with fundamental dynamical interaction laws. The methodological developments are then used to shed light onto fundamental interactions underlying complex behaviour in hydroclimate dynamics. For that purpose, a dynamical model is presented predicting evolving hydroclimatic quantities and their distributions under nonlinearly coevolving geophysical processes. The functional model is based on first principles regulating the dynamics of each system constituent and their synergies, therefore its applicability is general and data-independent, not requiring local calibrations. Moreover, it enables the dynamical estimation of hydroclimatic variations in space and time from the given knowledge at different spatiotemporal conditions. This paves the way for a robust physically based prediction of hydroclimatic changes in unmonitored areas. Validation is achieved by producing, with the dynamical model, a comprehensive spatiotemporal legacy consistent with the observed distributions along with their dynamical and statistical properties and relations. The similarity between simulated and observed distributions is further assessed with robust information-theoretic diagnostics. This study ultimately brings to light emerging signatures of structural change in hydroclimate dynamics arising from nonlinear synergies across spatiotemporal scales, and contributes to a better dynamical understanding and prediction of spatiotemporal regimes, transitions and extremes. The study further sheds light onto a diversity of emerging properties from harmonic to hyper-chaotic dynamics in hydroclimatic systems.
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.
Nonlinear dynamics of cell orientation
NASA Astrophysics Data System (ADS)
Safran, S. A.; de, Rumi
2009-12-01
The nonlinear dependence of cellular orientation on an external, time-varying stress field determines the distribution of orientations in the presence of noise and the characteristic time, τc , for the cell to reach its steady-state orientation. The short, local cytoskeletal relaxation time distinguishes between high-frequency (nearly perpendicular) and low-frequency (random or parallel) orientations. However, τc is determined by the much longer, orientational relaxation time. This behavior is related to experiments for which we predict the angle and characteristic time as a function of frequency.
Galerkin Method for Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
Noack, Bernd R.; Schlegel, Michael; Morzynski, Marek; Tadmor, Gilead
A Galerkin method is presented for control-oriented reduced-order models (ROM). This method generalizes linear approaches elaborated by M. Morzyński et al. for the nonlinear Navier-Stokes equation. These ROM are used as plants for control design in the chapters by G. Tadmor et al., S. Siegel, and R. King in this volume. Focus is placed on empirical ROM which compress flow data in the proper orthogonal decomposition (POD). The chapter shall provide a complete description for construction of straight-forward ROM as well as the physical understanding and teste
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…
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.
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.
Slow dynamics and anomalous nonlinear fast dynamics in diverse solids.
Johnson, Paul; Sutin, Alexander
2005-01-01
Results are reported of the first systematic study of anomalous nonlinear fast dynamics and slow dynamics in a number of solids. Observations are presented from seven diverse materials showing that anomalous nonlinear fast dynamics (ANFD) and slow dynamics (SD) occur together, significantly expanding the nonlinear mesoscopic elasticity class. The materials include samples of gray iron, alumina ceramic, quartzite, cracked Pyrex, marble, sintered metal, and perovskite ceramic. In addition, it is shown that materials which exhibit ANFD have very similar ratios of amplitude-dependent internal-friction to the resonance-frequency shift with strain amplitude. The ratios range between 0.28 and 0.63, except for cracked Pyrex glass, which exhibits a ratio of 1.1, and the ratio appears to be a material characteristic. The ratio of internal friction to resonance frequency shift as a function of time during SD is time independent, ranging from 0.23 to 0.43 for the materials studied. PMID:15704405
Slow dynamics and anomalous nonlinear fast dynamics in diverse solids
NASA Astrophysics Data System (ADS)
Johnson, Paul; Sutin, Alexander
2005-01-01
Results are reported of the first systematic study of anomalous nonlinear fast dynamics and slow dynamics in a number of solids. Observations are presented from seven diverse materials showing that anomalous nonlinear fast dynamics (ANFD) and slow dynamics (SD) occur together, significantly expanding the nonlinear mesoscopic elasticity class. The materials include samples of gray iron, alumina ceramic, quartzite, cracked Pyrex, marble, sintered metal, and perovskite ceramic. In addition, it is shown that materials which exhibit ANFD have very similar ratios of amplitude-dependent internal-friction to the resonance-frequency shift with strain amplitude. The ratios range between 0.28 and 0.63, except for cracked Pyrex glass, which exhibits a ratio of 1.1, and the ratio appears to be a material characteristic. The ratio of internal friction to resonance frequency shift as a function of time during SD is time independent, ranging from 0.23 to 0.43 for the materials studied. .
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).
Relations between static and dynamic exponents in nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Badii, R.; Broggi, G.
1990-01-01
The rules governing the evolution of nonlinear dynamical systems are systematically detected by constructing a hierarchical tree of symbol sequences. Relations between local partial dimensions and Lyapunov exponents are obtained from equations for the probabilities of symbol sequences on the logic tree. These relations are nonlinear and involve an open hierarchy of equations, which shows that the dimension spectrum f(α) cannot be obtained in closed form from the sole knowledge of the local Lyapunov exponents.
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).
Nonlinear Dynamics of Single Bunch Instability
Stupakov, G.V.; Breizman, B.N.; Pekker, M.S.; /Texas U.
2011-09-09
A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations. Microwave single bunch instability in circular accelerators has been observed in many machines. The instability usually arises when the number of particles in the bunch exceeds some critical value, Nc, which varies depending on the parameters of the accelerating regime. Recent observations on the SLC damping rings at SLAC with a new low-impedance vacuum chamber revealed new interesting features of the instability. In some cases, after initial exponential growth, the instability eventually saturated at a level that remained constant through the accumulation cycle. In other regimes, relaxation-type oscillations were measured in nonlinear phase of the instability. In many cases, the instability was characterized by a frequency close to the second harmonic of the synchrotron oscillations. Several attempts have been made to address the nonlinear stage of the instability based on either computer simulations or some specific assumptions regarding the structure of the unstable mode. An attempt of a more general consideration of the problem is carried out in this paper. We adopt an approach recently developed in plasma physics for analysis of nonlinear behavior of weakly unstable modes in dynamic systems. Assuming that the growth rate of the instability is much smaller than its frequency, we find a time dependent solution to Vlasov equation and derive an equation for the complex amplitude of the oscillations valid in the nonlinear regime. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement
On Dynamic Nonlinear Elasticity and Small Strain
NASA Astrophysics Data System (ADS)
Johnson, P. A.; Sutin, A.; Guyer, R. A.; Tencate, J. A.
2002-12-01
We are addressing the question of whether or not there is a threshold strain behavior where anomalous nonlinear fast dynamics (ANFD) commences in rock and other similar solids, or if the elastic nonlinearity persists to the smallest measurable values. In qualitative measures of many rock types and other materials that behave in the same manner, we have not observed a threshold; however the only careful, small strain level study conducted under controlled conditions that we are aware of is that of TenCate et al. in Berea sandstone (Phys. Rev. Lett. 85, 1020-1024 (2000)). This work indicates that in Berea sandstone, the elastic nonlinearity persists to the minimum measured strains of at least 10-8. Recently, we have begun controlled experiments in other materials that exhibit ANFD in order to see whether or not they behave as Berea sandstone does. We are employing Young's mode resonance to study resonance peak shift and amplitude variations as a function of drive level and detected strain level. In this type of experiment, the time average amplitude is recorded as the sample is driven by a continuous wave source from below to above the fundamental mode resonance. The drive level is increased, and the measurement is repeated progressively over larger and larger drive levels. Experiments are conducted at ambient pressure. Pure alumina ceramic is a material that is highly, elastically-nonlinear and nonporous, and therefore the significant influence of relative humidity on elastic nonlinear response that rock suffers is avoided. Temperature is carefully monitored. Measurements on pure alumina ceramic show that, like Berea sandstone, there is no threshold of elastic nonlinearity within our measurement capability. We are now studying other solids that exhibit ANFD including rock and mixed phase metal. These results indicate that elastic nonlinearity influences all elastic measurments on these solids including modulus and Q at ambient conditions. There appears to be no
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.
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.
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 of cilia and flagella.
Hilfinger, Andreas; Chattopadhyay, Amit K; Jülicher, Frank
2009-05-01
Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally. PMID:19518491
Nonlinear dynamics of cilia and flagella
NASA Astrophysics Data System (ADS)
Hilfinger, Andreas; Chattopadhyay, Amit K.; Jülicher, Frank
2009-05-01
Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.
Nonlinear dynamic analysis of sandwich panels
NASA Technical Reports Server (NTRS)
Lush, A. M.
1984-01-01
Two analytical techniques applicable to large deflection dynamic response calculations for pressure loaded composite sandwich panels are demonstrated. One technique utilizes finite element modeling with a single equivalent layer representing the face sheets and core. The other technique utilizes the modal analysis computer code DEPROP which was recently modified to include transverse shear deformation in a core layer. The example problem consists of a simply supported rectangular sandwich panel. Included are comparisons of linear and nonlinear static response calculations, in addition to dynamic response calculations.
Dynamic Associations in Nonlinear Computing Arrays
NASA Astrophysics Data System (ADS)
Huberman, B. A.; Hogg, T.
1985-10-01
We experimentally show that nonlinear parallel arrays can be made to compute with attractors. This leads to fast adaptive behavior in which dynamical associations can be made between different inputs which initially produce sharply distinct outputs. We first define a set of simple local procedures which allow a general computing structure to change its state in time so as to produce classical Pavlovian conditioning. We then examine the dynamics of coalescence and dissociation of attractors with a number of quantitative experiments. We also show how such arrays exhibit generalization and differentiation of inputs in their behavior.
Nonlinear robust control of integrated vehicle dynamics
NASA Astrophysics Data System (ADS)
He, Zhengyi; Ji, Xuewu
2012-02-01
A new methodology to design the vehicle GCC (global chassis control) nonlinear controller is developed in this paper. Firstly, to handle the nonlinear coupling between sprung and unsprung masses, the vehicle is treated as a mechanical system of two-rigid-bodies which has 6 DOF (degree of freedom), including longitudinal, lateral, yaw, vertical, roll and pitch dynamics. The system equation is built in the yaw frame based on Lagrange's method, and it has been proved that the derived system remains the important physical properties of the general mechanical system. Then the GCC design problem is formulated as the trajectory tracking problem for a cascade system, with a Lagrange's system interconnecting with a linear system. The nonlinear robust control design problem of this cascade interconnected system is divided into two H ∞ control problems with respect to the two sub-systems. The parameter uncertainties in the system are tackled by adaptive theory, while the external uncertainties and disturbances are dealt with the H ∞ control theory. And the passivity of the mechanical system is applied to construct the solution of nonlinear H ∞ control problem. Finally, the effectiveness of the proposed controller is validated by simulation results even during the emergency manoeuvre.
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.
Fractal dimension and nonlinear dynamical processes
NASA Astrophysics Data System (ADS)
McCarty, Robert C.; Lindley, John P.
1993-11-01
Mandelbrot, Falconer and others have demonstrated the existence of dimensionally invariant geometrical properties of non-linear dynamical processes known as fractals. Barnsley defines fractal geometry as an extension of classical geometry. Such an extension, however, is not mathematically trivial Of specific interest to those engaged in signal processing is the potential use of fractal geometry to facilitate the analysis of non-linear signal processes often referred to as non-linear time series. Fractal geometry has been used in the modeling of non- linear time series represented by radar signals in the presence of ground clutter or interference generated by spatially distributed reflections around the target or a radar system. It was recognized by Mandelbrot that the fractal geometries represented by man-made objects had different dimensions than the geometries of the familiar objects that abound in nature such as leaves, clouds, ferns, trees, etc. The invariant dimensional property of non-linear processes suggests that in the case of acoustic signals (active or passive) generated within a dispersive medium such as the ocean environment, there exists much rich structure that will aid in the detection and classification of various objects, man-made or natural, within the medium.
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.
Nonlinear dynamical model of human gait.
West, Bruce J; Scafetta, Nicola
2003-05-01
We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way. PMID:12786188
Nonlinear dynamical model of human gait
NASA Astrophysics Data System (ADS)
West, Bruce J.; Scafetta, Nicola
2003-05-01
We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.
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
Quantum dynamics of nonlinear cavity systems
NASA Astrophysics Data System (ADS)
Nation, Paul David
In this work we investigate the quantum dynamics of three different configurations of nonlinear cavity systems. We begin by carrying out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprising a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing an external flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal and noise response where it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state. Next, we consider the use of a superconducting transmission line formed from an array of dc-SQUIDs for investigating analogue Hawking radiation. We will show that biasing the array with a space-time varying flux modifies the propagation velocity of the transmission line, leading to an effective metric with a horizon. As a fundamentally quantum mechanical device, this setup allows for investigations of quantum effects such as backreaction and analogue space-time fluctuations on the Hawking process. Finally, we investigate a quantum parametric amplifier with dynamical pump mode, viewed as a zero-dimensional model of Hawking radiation from an evaporating black hole. The conditions are derived under which the spectrum of particles generated from vacuum fluctuations deviates from the thermal spectrum predicted for the conventional parametric amplifier. We find that significant deviation occurs once the pump mode (black hole) has released nearly half of its initial energy in the signal (Hawking radiation) and idler (in-falling particle) modes. As a model of black hole dynamics, this finding lends support to the view that late-time Hawking radiation contains information about the quantum state of the black hole and is entangled with the black hole's quantum
Entanglement, Nonlinear Dynamics, and the Heisenberg Limit
Pezze, Luca; Smerzi, Augusto
2009-03-13
We show that quantum Fisher information provides a sufficient condition to recognize multiparticle entanglement in an N qubit state. The same criterion gives a necessary and sufficient condition for sub-shot-noise phase sensitivity in the estimation of a collective rotation angle {theta}. The analysis therefore singles out the class of entangled states which are useful to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the nonlinear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.
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
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
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.
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.
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.
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 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.
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.
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.
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
Nonlinear dynamics in combinatorial games: Renormalizing Chomp
NASA Astrophysics Data System (ADS)
Friedman, Eric J.; Landsberg, Adam Scott
2007-06-01
We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to transform a combinatorial game like Chomp into a type of dynamical system. Not only does this provide powerful insights into the game of Chomp (yielding a complete probabilistic description of optimal play in Chomp and an answer to a longstanding question about the nature of the winning opening move), but more generally, it offers a mathematical framework for exploring this unexpected relationship between combinatorial games and modern dynamical systems theory.
Linking dynamical heterogeneity to static amorphous order
NASA Astrophysics Data System (ADS)
Charbonneau, Patrick; Dyer, Ethan; Lee, Jaehoon; Yaida, Sho
2016-07-01
Glass-forming liquids grow dramatically sluggish upon cooling. This slowdown has long been thought to be accompanied by a growing correlation length. Characteristic dynamical and static length scales, however, have been observed to grow at different rates, which perplexes the relationship between the two and with the slowdown. Here, we show the existence of a direct link between dynamical sluggishness and static point-to-set correlations, holding at the local level as we probe different environments within a liquid. This link, which is stronger and more general than that observed with locally preferred structures, suggests the existence of an intimate relationship between structure and dynamics in a broader range of glass-forming liquids than previously thought.
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.
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 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.
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 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.
Nonlinearities in Magnetostrictive Transducer Dynamic Output
NASA Astrophysics Data System (ADS)
Flatau, Alison; Faidley, L. E.; Calkins, F. T.; Dapino, M. J.
1997-03-01
We have designed a magnetostrictive transducer for use in characterizing material properties of 11.5 cm long by 1.27 cm diameter cylindrical samples of the magnetostrictive material Terfenol-D. The material studied is a commercially available Terfenol-D, made using a modified Brigman manufacturing process. Output displacements in the stiffness controlled portion of the transducer's dynamic range (as loaded, up to 1000 Hz) were measured using a LVDT. Trends in output were observed as controlled changes in operating conditions were made. Excitation frequency, amplitude of magnetic excitation, and prestress were varied independently as other operating conditions (including temperature, mass load, and magnetic bias) were held fixed. Data are presented demonstrating distinct nonlinearities associated with a monotonic decrease in output with increased excitation frequency, a monotonic increase in output with increased excitation amplitude, and an initial increase followed by a decrease in output with increased prestress.
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.
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
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
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.
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
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.
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.
NASA Technical Reports Server (NTRS)
Graves, Philip L.
1989-01-01
A method of formulating the dynamical equations of a flexible, serial manipulator is presented, using the Method of Kinematic Influence. The resulting equations account for rigid body motion, structural motion due to link and joint flexibilities, and the coupling between these two motions. Nonlinear inertial loads are included in the equations. A finite order mode summation method is used to model flexibilities. The structural data may be obtained from experimental, finite element, or analytical methods. Nonlinear flexibilities may be included in the model.
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.
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 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.
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.
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 dynamics enabled systems design and control
NASA Astrophysics Data System (ADS)
Lacarbonara, Walter
2012-08-01
There is a growing interest towards design of high-performance structures and devices by seeking ways to exploit advantageously different nonlinearities at different scales rather than constraining operations to avoid nonlinear phenomena. Tools of robust nonlinear modeling and analysis are shown to be turned into design tools for achieving high levels of vibration control authority and synthesis of engineered systems and materials. A brief overview of methods and results on active resonance cancellation and passive nonlinear hysteretic vibration absorbers is illustrated. Recent results on the diffused hysteresis exhibited at the nano-microscale in nanocomposites due to the powerful nonlinear stick-slip mechanism exhibited by carbon nanotubes dispersed in a hosting matrix are discussed. The optimization of the main microstructural parameters is shown to lead to unprecedented levels of damping capacity in next-generation nanostructured materials tailored for wide-band vibrational energy dissipation.
Dynamic analysis and control of lightweight manipulators with flexible parallel link mechanisms
NASA Technical Reports Server (NTRS)
Lee, Jeh Won
1991-01-01
The flexible parallel link mechanism is designed for increased rigidity to sustain the buckling when it carries a heavy payload. Compared to a one link flexible manipulator, a two link flexible manipulator, especially the flexible parallel mechanism, has more complicated characteristics in dynamics and control. The objective of this research is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model. The step response of the analytical model and the TREETOPS model match each other well. The nonlinear dynamics is studied using a sinusoidal excitation. The actuator dynamic effect on a flexible robot was investigated. The effects are explained by the root loci and the Bode plot theoretically and experimentally. For the base performance for the advanced control scheme, a simple decoupled feedback scheme is applied.
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
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
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
NASA Astrophysics Data System (ADS)
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
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
Epistemological and Treatment Implications of Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
Stein, A. H.
The treatment implications of understanding mind as solely epiphenomenal to nonlinearly founded neurobiology are discussed. G. Klimovsky's epistemological understanding of psychoanalysis as a science is rejected and treatment approaches integrating W. R. Bion's and D. W. Winnicott's work are supported.
An experimental study of nonlinear dynamic system identification
NASA Astrophysics Data System (ADS)
Stry, Greselda I.; Mook, D. Joseph
1990-12-01
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.
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 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.
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.
Dynamic deformation of strongly nonlinear toroidal rubber elements
NASA Astrophysics Data System (ADS)
Lee, Chien-Wei; Nesterenko, Vitali F.
2013-08-01
Dynamic deformation of rubber toroidal elements (o-rings) was investigated under dynamic loading conditions at strain rates 102 s-1. The forces acting on o-rings were simultaneously monitored using an accelerometer and strain gauges, while global engineering strains were independently determined by a synchronized high speed camera. Dynamic non-linear stress-strain relation was compared with empirical relation obtained from static loading of o-rings. The paper presents first experimental results and analysis of dissipative properties of o-rings during dynamic compression and unloading. The strongly nonlinear force-strain and strain-rate dependent behavior was described using nonlinear viscoelastic relation with only one adjustable parameter.
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.
NASA Technical Reports Server (NTRS)
Lee, Jeh Won
1990-01-01
The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.
Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)
2002-01-01
The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.
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.
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.
Structural dynamics and resonance in plants with nonlinear stiffness.
Miller, Laura A
2005-06-21
Although most biomaterials are characterized by strong stiffness nonlinearities, the majority of studies of plant biomechanics and structural dynamics focus on the linear elastic range of their behavior. In this paper, the effects of hardening (elastic modulus increases with strain) and softening (elastic modulus decreases with strain) nonlinearities on the structural dynamics of plant stems are investigated. A number of recent studies suggest that trees, crops, and other plants often uproot or snap when they are forced by gusting winds or waves at their natural frequency. This can be attributed to the fact that the deflections of the plant, and hence mechanical stresses along the stem and root system, are greatest during resonance. To better understand the effect of nonlinear stiffness on the resonant behavior of plants, plant stems have been modeled here as forced Duffing oscillators with softening or hardening nonlinearities. The results of this study suggest that the resonant behavior of plants with nonlinear stiffness is substantially different from that predicted by linear models of plant structural dynamics. Parameter values were considered over a range relevant to most plants. The maximum amplitudes of deflection of the plant stem were calculated numerically for forcing frequencies ranging from zero to twice the natural frequency. For hardening nonlinearities, the resonant behavior was 'pushed' to higher frequencies, and the maximum deflection amplitudes were lower than for the linear case. For softening nonlinearities, the resonant behavior was pushed to lower frequencies, and the maximum deflection amplitudes were higher than for the linear case. These nonlinearities could be beneficial or detrimental to the stability of the plant, depending on the environment. Damping had the effect of drastically decreasing deflection amplitudes and reducing the effect of the nonlinearities.
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.
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.
Linked-List-Based Multibody Dynamics (MBDyn) Engine
NASA Technical Reports Server (NTRS)
MacLean, John; Brain, Thomas; Wuiocho, Leslie; Huynh, An; Ghosh, Tushar
2012-01-01
This new release of MBDyn is a software engine that calculates the dynamics states of kinematic, rigid, or flexible multibody systems. An MBDyn multibody system may consist of multiple groups of articulated chains, trees, or closed-loop topologies. Transient topologies are handled through conservation of energy and momentum. The solution for rigid-body systems is exact, and several configurable levels of nonlinear term fidelity are available for flexible dynamics systems. The algorithms have been optimized for efficiency and can be used for both non-real-time (NRT) and real-time (RT) simulations. Interfaces are currently compatible with NASA's Trick Simulation Environment. This new release represents a significant advance in capability and ease of use. The two most significant new additions are an application programming interface (API) that clarifies and simplifies use of MBDyn, and a link-list infrastructure that allows a single MBDyn instance to propagate an arbitrary number of interacting groups of multibody top ologies. MBDyn calculates state and state derivative vectors for integration using an external integration routine. A Trickcompatible interface is provided for initialization, data logging, integration, and input/output.
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.
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.
Nonlinear dynamics and quantum entanglement in optomechanical systems.
Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2014-03-21
To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.
Parameter and Structure Inference for Nonlinear Dynamical Systems
NASA Technical Reports Server (NTRS)
Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark
2006-01-01
A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.
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.
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
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.
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.
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
Nonlinear dynamics of microtubules —A longitudinal model
NASA Astrophysics Data System (ADS)
Zdravković, S.; Satarić, M. V.; Zeković, S.
2013-05-01
In the present letter we describe a model of nonlinear dynamics of microtubules (MTs) assuming a single longitudinal degree of freedom per tubulin dimer. This is a longitudinal displacement of a dimer at a certain position with respect to the neighbouring one. A nonlinear partial differential equation, describing dimer's dynamics within MT, is solved both analytically and numerically. It is shown that such a nonlinear model can lead to the existence of kink solitons moving along the MTs. The internal electrical field strength is calculated using two procedures and a perfect agreement between the results is demonstrated. This enabled the estimation of the total energy, kink velocity and kink width. To simplify the calculation of the total energy we stated and proved a useful auxiliary theorem.
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
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.
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.
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…
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.
Review of the study of nonlinear atmospheric dynamics in China (1999 2002)
NASA Astrophysics Data System (ADS)
Diao, Yina; Feng, Guolin; Liu, Shida; Liu, Shikuo; Luo, Dehai; Huang, Sixun; Lu, Weisong; Chou, Jifan
2004-06-01
Researches on nonlinear atmospheric dynamics in China (1999 2002) are briefly surveyed. This review includes the major achievements in the following branches of nonlinear dynamics: nonlinear stability theory, nonlinear blocking dynamics, 3D spiral structure in the atmosphere, traveling wave solution of the nonlinear evolution equation, numerical predictability in a chaotic system, and global analysis of climate dynamics. Some applications of nonlinear methods such as hierarchy structure of climate and scaling invariance, the spatial-temporal series predictive method, the nonlinear inverse problem, and a new difference scheme with multi-time levels are also introduced.
Linking shape dynamics and loop quantum gravity
NASA Astrophysics Data System (ADS)
Smolin, Lee
2014-08-01
Shape dynamics is a reformulation of general relativity, locally equivalent to Einstein's theory, in which the refoliation invariance of the older theory is traded for local scale invariance. Shape dynamics is here derived in a formulation related to the Ashtekar variables by beginning with a modification of the Plebanski action. The constraints of shape dynamics and their algebra are reproduced in terms of these new variables.
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.
Nonlinear dynamics in ecosystem response to climatic change: Case studies and policy implications
Burkett, Virginia R.; Wilcox, Douglas A.; Stottlemyer, Robert; Barrow, Wylie; Fagre, Dan; Baron, Jill; Price, Jeff; Nielsen, Jennifer L.; Allen, Craig D.; Peterson, David L.; Ruggerone, Greg; Doyle, Thomas
2005-01-01
Many biological, hydrological, and geological processes are interactively linked in ecosystems. These ecological phenomena normally vary within bounded ranges, but rapid, nonlinear changes to markedly different conditions can be triggered by even small differences if threshold values are exceeded. Intrinsic and extrinsic ecological thresholds can lead to effects that cascade among systems, precluding accurate modeling and prediction of system response to climate change. Ten case studies from North America illustrate how changes in climate can lead to rapid, threshold-type responses within ecological communities; the case studies also highlight the role of human activities that alter the rate or direction of system response to climate change. Understanding and anticipating nonlinear dynamics are important aspects of adaptation planning since responses of biological resources to changes in the physical climate system are not necessarily proportional and sometimes, as in the case of complex ecological systems, inherently nonlinear.
Non-linearity dynamics in ecosystem response to climate change: Case studies and policy implications
Burkett, V.R.; Wilcox, D.A.; Stottlemyer, R.; Barrow, W.; Fagre, D.; Baron, J.; Nielsen, J.L.; Allen, C.D.; Peterson, D.L.; Ruggerone, G.; Doyle, T.
2005-01-01
Many biological, hydrological, and geological processes are interactively linked in ecosystems. These ecological phenomena normally vary within bounded ranges, but rapid, nonlinear changes to markedly different conditions can be triggered by even small differences if threshold values are exceeded. Intrinsic and extrinsic ecological thresholds can lead to effects that cascade among systems, precluding accurate modeling and prediction of system response to climate change. Ten case studies from North America illustrate how changes in climate cna lead to rapid, threshold-type responses within ecological communities; the case studies also highlight the role of human activities that alter the rate or direction of system response to climate change. Understanding and anticipating nonlinear dynamics are important aspects of adaptation planning since responses of biological resources to changes in the physical climate system are not necessarily proportional and sometimes, as in the case of complex ecological systems, inherently nonlinear.
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 nonlinear thermal optical effects in coupled ring resonators
NASA Astrophysics Data System (ADS)
Huang, Chenguang; Fan, Jiahua; Zhu, Lin
2012-09-01
We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple "shark fins" and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.
Digit replacement: A generic map for nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
García-Morales, Vladimir
2016-09-01
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.
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.
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
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.
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.
Complex dynamics of a nonlinear voter model with contrarian agents
Tanabe, Shoma; Masuda, Naoki
2013-12-15
We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases with the number of other agents in the opposite state, as in the linear voter model and nonlinear majority voting models. Contrarians flip the state with a rate that increases with the number of other agents in the same state. The nonlinearity controls the strength of the majority voting and is used as a main bifurcation parameter. We show that the model undergoes a rich bifurcation scenario comprising the egalitarian equilibrium, two symmetric lopsided equilibria, limit cycle, and coexistence of different types of stable equilibria with intertwining attractive basins.
Nonlinearity of local dynamics promotes multi-chimeras.
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.
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
Treatment of material creep and nonlinearities in flexible mulitbody dynamics
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.
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.
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.
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.
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.
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).
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.
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.
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.
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 the SPEAR 3 Double-Waist Chicane
Safranek, J.A.; Huang, X.; Terebilo, A.; /SLAC
2007-08-08
One of the two 7.6 m long straight sections in SPEAR3 has been divided into two short straights to provide places for two new small-gap insertion devices (IDs). A chicane generates an angular separation of 10 mrad between the two straights. A quadrupole triplet has been added in the center of the 7.6 m long chicane to create a 'double-waist chicane' optics with {beta}{sub {gamma}}=1.6 m at the center of each of two future IDs. The new optics also reduces {beta}{sub {gamma}}to 2.5 m in the four 4.8 m straight sections. In this paper, the authors discuss nonlinear dynamic studies associated with design and implementation of the new optics. They present tracking results generated during the design stage and compare them to nonlinear dynamics measurements made with the quadrupole triplet installed in SPEAR3.
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.
Method to Sense Changes in Network Parameters with High-Speed, Nonlinear Dynamical Nodes
NASA Astrophysics Data System (ADS)
Callan, Kristine E.
The study of dynamics on networks has been a major focus of nonlinear science over the past decade. Inferring network properties from the nodal dynamics is both a challenging task and of growing importance for applied network science. A subset of this broad question is: How can one determine changes to the coupling strength between elements in a small network of chaotic oscillators just by measuring the dynamics of one of the elements (nodes) in the network? In this dissertation, I propose and report on an implementation of a method to simultaneously determine: (1) which link is affected and (2) by how much it is attenuated when the coupling strength along one of the links in a small network of dynamical nodes is changed. After proper calibration, realizing this method involves only measurements of the dynamical features of a single node. Previous attempts to solve this problem focus mainly on synchronization-based approaches implemented in low-speed, homogeneous experimental systems. In contrast, the experimental apparatus I use to implement my method comprises two high-speed (ps-timescale), heterogeneous optoelectronic oscillators (OEOs). Each OEO constitutes a node, and a network is formed by mutually coupling two nodes. I find that the correlation properties of the chaotic dynamics generated by the nodes, which are heavily influenced by the propagation time delays in the network, change in a quantifiable way when the coupling strength along either the input or output link is attenuated. By monitoring multiple aspects of the correlation properties, which I call "time delay signatures'' (TDSs), I find that the affected link can be determined for changes in coupling strength greater than 20% +/- 10%. Due to the sensitivity with which the TDSs change, it is also feasible to determine approximately the time-varying coupling strength for large enough attenuations. I also verify that the TDSs' sensitivity to changes in coupling strength are captured by a simple
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
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.
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
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.
Nonlinear dynamics of the movement of the venus flytrap.
Li, Yongfeng; Lenaghan, Scott C; Zhang, Mingjun
2012-10-01
The Venus flytrap has long been regarded as one of the most amazing examples of movement in the plant kingdom. The trapping ability of the flytrap consists of three unique features. First, trap closure represents one of the fastest movements in the plant kingdom. Second, a decision-making stage allows the plant to "decide" whether to completely close or open the trap, based on stimuli provided from the trapped object. Finally, the Venus flytrap contains a "memory function" that requires two mechanical stimuli within about 30 seconds to initiate trap closure. The movement involved in trap closure consists of nonlinear dynamics that have not been well understood. By understanding the movement, through nonlinear dynamics analysis, it will be possible to better understand this biological process. A mathematical model describing the movement of the Venus flytrap was first proposed by the authors in Yang et al., Plant Signal. Behav. 5(8), 968-978 (2010). In the current work, the earlier research has been advanced and an in-depth nonlinear and control analysis of the dynamic process has been provided.
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.
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
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.
Contributions of plasma physics to chaos and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Escande, D. F.
2016-11-01
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016
Dynamics in a nonlinear Keynesian good market model
Naimzada, Ahmad; Pireddu, Marina
2014-03-15
In this paper, we show how a rich variety of dynamical behaviors can emerge in the standard Keynesian income-expenditure model when a nonlinearity is introduced, both in the cases with and without endogenous government spending. A specific sigmoidal functional form is used for the adjustment mechanism of income with respect to the excess demand, in order to bound the income variation. With the aid of analytical and numerical tools, we investigate the stability conditions, bifurcations, as well as periodic and chaotic dynamics. Globally, we study multistability phenomena, i.e., the coexistence of different kinds of attractors.
Dynamic Analysis of Flexible Slider-Crank Mechanisms with Non-Linear Finite Element Method
NASA Astrophysics Data System (ADS)
CHEN, J.-S.; HUANG, C.-L.
2001-09-01
Previous research in finite element formulation of flexible mechanisms usually neglected high order terms in the strain-energy function. In particular, the quartic term of the displacement gradient is always neglected due to the common belief that it is not important in the dynamic analysis. In this paper, we show that this physical intuition is not always valid. By retaining all the high order terms in the strain-energy function the equations of motion naturally become non-linear, which can then be solved by the Newmark method. In the low-speed range it is found that the dynamic responses predicted by non-linear and linear approaches indeed make no significant difference. However, when the rotation speed increases up to about one-fifth of the fundamental bending natural frequency of the connecting rod, simplified approaches begin to incur noticeable error. Specifically, for a connecting rod with a slenderness ratio of 0·01 the conventional simplified approaches overestimate the vibration amplitude almost 10-fold when the rotation speed is comparable to the fundamental natural frequency of the connecting rod. Therefore, non-linear finite element formulation taking into account the complete non-linear strain is needed in analyzing high-speed flexible mechnisms with slender links.
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 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 of dipoles in microtubules: Pseudospin model.
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. PMID:27415303
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.
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.
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.
Characterising dynamic non-linearity in floating wind turbines
NASA Astrophysics Data System (ADS)
Lupton, R. C.
2014-12-01
Fully coupled aero-hydro-control-elastic codes are being developed to cope with the new modelling challenges presented by floating wind turbines, but there is also a place for more efficient methods of analysis. One option is linearisation and analysis in the frequency domain. For this to be an effective method, the non-linearities in the system must be well understood. The present study focusses on understanding the dynamic response of the rotor to the overall platform motion, as would arise from wave loading, by using a simple model of a floating wind turbine with a rigid tower and flexible rotor (represented by hinged rigid blades). First, an equation of motion of the blade is derived and an approximate solution for the blade response is found using the perturbation method. Secondly, the full non-linear solution is found by time- domain simulation. The response is found to be linear at lower platform pitching frequencies, becoming non-linear at higher frequencies, with the approximate solution giving good results for weakly non-linear behaviour. Higher rotor speeds have a stabilising effect on the response. In the context of typical floating turbine parameters, it is concluded that the blade flapwise response is likely to be linear.
Investigation of nonlinear pupil dynamics by recurrence quantification analysis.
Mesin, L; Monaco, A; Cattaneo, R
2013-01-01
Pupil is controlled by the autonomous nervous system (ANS). It shows complex movements and changes of size even in conditions of constant stimulation. The possibility of extracting information on ANS by processing data recorded during a short experiment using a low cost system for pupil investigation is studied. Moreover, the significance of nonlinear information contained in the pupillogram is investigated. We examined 13 healthy subjects in different stationary conditions, considering habitual dental occlusion (HDO) as a weak stimulation of the ANS with respect to the maintenance of the rest position (RP) of the jaw. Images of pupil captured by infrared cameras were processed to estimate position and size on each frame. From such time series, we extracted linear indexes (e.g., average size, average displacement, and spectral parameters) and nonlinear information using recurrence quantification analysis (RQA). Data were classified using multilayer perceptrons and support vector machines trained using different sets of input indexes: the best performance in classification was obtained including nonlinear indexes in the input features. These results indicate that RQA nonlinear indexes provide additional information on pupil dynamics with respect to linear descriptors, allowing the discrimination of even a slight stimulation of the ANS. Their use in the investigation of pathology is suggested. PMID:24187665
Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity
NASA Astrophysics Data System (ADS)
Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.
2012-12-01
In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (< 10-6), the nonlinear classical theory issued from a Taylor decomposition can explain the harmonic content. For higher strain, harmonic content becomes richer and the material exhibits more hysteretic behaviors, i.e. strain rate dependencies. Such observations have been made in the past (e.g., Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.
Nonlinear 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.
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.
Impact of nonlinearity phenomenon FWM in DWDM optical link considering dispersive fiber
NASA Astrophysics Data System (ADS)
Puche, William S.; Amaya, Ferney O.; Sierra, Javier E.
2013-12-01
The increasing demand of network traffic requires new research centers; improve their communications networks, due to the excessive use of mobile and portable devices wanting to have greater access to the network by downloading interactive content quickly and effectively. For our case analyze optical network link through simulation results assuming a DWDM (Dense wavelength Division Multiplexing) optical link, considering the nonlinearity phenomenon FWM (Four Mixed Wavelength) in order to compare their performance, assuming transmission bit rates to 2.5 Gbps and 10 Gbps, using three primary wavelengths of 1450 nm, 1550 nm and 1650 nm for the transmission of information, whose separation is 100 GHz to generate 16 channels or user information. Tests were conducted to analyze optical amplifiers EDFAs link robustness at a maximum distance of 200 km and identify parameters OSNR, SNR and BER, for a robust and effective transmission
Exploring the control landscape for nonlinear quantum dynamics
NASA Astrophysics Data System (ADS)
Yan, Julia; Hocker, David; Long, Ruixing; Ho, Tak-San; Rabitz, Herschel
2014-06-01
Manipulation of a quantum system can be viewed in the framework of a control landscape defined as the physical objective as a functional of the control. Control landscape analyses have thus far considered linear quantum dynamics. This paper extends the analysis of control landscape topology to nonlinear quantum dynamics with the objective of steering a finite-level quantum system from an initial state to a final target state. The analysis rests on the assumptions that (i) the final state is reachable from the initial state, (ii) the differential mapping from the control to the state is surjective, and (iii) the control resources are unconstrained. Under these assumptions, landscape critical points (i.e., where the slope vanishes) for nonlinear quantum dynamics only appear as the global maximum and minimum; thus, the landscape is free of traps. Moreover, the landscape Hessian (i.e., the second derivative with respect to the control) at the global maximum has finite rank, indicating the presence of a large level set of optimal controls that preserve the value of the maximum. Extensive numerical simulations on finite-level models of the Gross-Pitaevskii equation confirm the trap-free nature of the landscape as well as the Hessian rank analysis, using either an applied electric field or a tunable condensate two-body interaction strength as the control. In addition, the control mechanisms arising in the numerical simulations are qualitatively assessed. These results are a generalization of previous findings for the linear Schrödinger equation, and show promise for successful control in a wide range of nonlinear quantum dynamics applications.
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-03-22
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.
Bifurcation techniques for nonlinear dynamic analysis of compressor stall phenomena
NASA Technical Reports Server (NTRS)
Razavi, H. C.; Mehra, R. K.
1985-01-01
Compressor stall phenomena is analyzed from nonlinear control theory viewpoint, based on bifurcation-catastrophe techniques. This new approach appears promising and offers insight into such well known compressor instability problems as surge and rotating stall; furthermore it suggests strategies for recovery from stall. Three interlocking dynamic nonlinear state space models are developed. It is shown that the problem of rotating stall can be viewed as an (induced) bifurcation of solution of the unstalled model. Hysteresis effect is shown to exist in the stall/recovery process. Surge cycles are observed to develop for some critical parameter values. It is shown that the oscillatory behavior is due to development of limit cycles, generated by Hopf bifurcation of solutions. Both stable and unstable limit cycles are observed. To further illustrate the usefulness of the methodology some partial computation of domains of attraction of equilibria is carried out, and parameter sensitivity analysis is performed.
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.
Optical nonlinearity and structural dynamics of VO2 films
NASA Astrophysics Data System (ADS)
Lysenko, S.; Rua, A.; Fernandez, F.; Liu, H.
2009-02-01
The degenerate-four-wave-mixing, ultrafast optical pump-probe reflection, and scattering techniques were applied to study the nonlinear optical properties of VO2 in insulating and metallic phases. The third-order nonlinear susceptibility was measured for thin films at different excitation regimes. The VO2 recovery dynamics after light-induced phase transition (PT) shows strong sensitivity to optical pump energy and could be governed by pure electronic relaxation excluding thermal contribution at sufficiently low excitation. Increased light scattering during thermally and light-induced PT demonstrates significant VO2 heterogeneity which appears as a coexistence of insulating and metallic phases accompanied by fluctuations of dielectric constants. Different desorption activity was monitored for insulating and metallic VO2 thin solid films under femtosecond optical excitation.
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 problems of complex natural systems: Sun and climate dynamics.
Bershadskii, A
2013-01-13
The universal role of the nonlinear one-third subharmonic resonance mechanism in generation of strong fluctuations in complex natural dynamical systems related to global climate is discussed using wavelet regression detrended data. The role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Niño phenomenon have been discussed in detail. The large fluctuations in the reconstructed temperature on millennial time scales (Antarctic ice core data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to the Earth's precession effect on the energy that the intertropical regions receive from the Sun. The effects of galactic turbulence on the temperature fluctuations are also discussed. PMID:23185052
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
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.
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.
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.
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.
On nonlinearly-induced noise in single-channel optical links with digital backpropagation.
Beygi, Lotfollah; Irukulapati, Naga V; Agrell, Erik; Johannisson, Pontus; Karlsson, Magnus; Wymeersch, Henk; Serena, Paolo; Bononi, Alberto
2013-11-01
In this paper, we investigate the performance limits of electronic chromatic dispersion compensation (EDC) and digital backpropagation (DBP) for a single-channel non-dispersion-managed fiber-optical link. A known analytical method to derive the performance of the system with EDC is extended to derive a first-order approximation for the performance of the system with DBP. In contrast to the cubic growth of the variance of the nonlinear noise-like interference, often called nonlinear noise, with input power for EDC, a quadratic growth is observed with DBP using this approximation. Finally, we provide numerical results to verify the accuracy of the proposed approach and compare it with existing analytical models. PMID:24216860
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
NASA Astrophysics Data System (ADS)
Aburjania, G. D.; Rogava, D. L.; Kharshiladze, O. A.
2011-06-01
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 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 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.
Sustained small oscillations in nonlinear control systems. [launch vehicle dynamics
NASA Technical Reports Server (NTRS)
George, J. H.; Gunderson, R. W.; Hahn, H.
1975-01-01
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
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.
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.
Concurrent and vectorized mixed time, explicit nonlinear structural dynamics algorithms
NASA Technical Reports Server (NTRS)
Belytschko, Ted; Gilbertsen, Noreen
1987-01-01
A nonlinear structural dynamics program with an element library that exploits parallel processing is described. The aim is to exploit scheduling-allocation so that parallel processing and vectorization can effectively be treated in a general purpose program with explicit time integration and different time steps in different parts of the mesh. The program uses an element group scheme, which, as a by-product, also provides an automatic scheme for assigning different time steps to different parts of the mesh. The program has been tested on the Alliant FX/8; it shows a fivefold improvement in speed over compiler optimization.
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
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.
Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods.
Calderhead, Ben; Girolami, Mark
2011-12-01
Mechanistic models based on systems of nonlinear differential equations can help provide a quantitative understanding of complex physical or biological phenomena. The use of such models to describe nonlinear interactions in molecular biology has a long history; however, it is only recently that advances in computing have allowed these models to be set within a statistical framework, further increasing their usefulness and binding modelling and experimental approaches more tightly together. A probabilistic approach to modelling allows us to quantify uncertainty in both the model parameters and the model predictions, as well as in the model hypotheses themselves. In this paper, the Bayesian approach to statistical inference is adopted and we examine the significant challenges that arise when performing inference over nonlinear ordinary differential equation models describing cell signalling pathways and enzymatic circadian control; in particular, we address the difficulties arising owing to strong nonlinear correlation structures, high dimensionality and non-identifiability of parameters. We demonstrate how recently introduced differential geometric Markov chain Monte Carlo methodology alleviates many of these issues by making proposals based on local sensitivity information, which ultimately allows us to perform effective statistical analysis. Along the way, we highlight the deep link between the sensitivity analysis of such dynamic system models and the underlying Riemannian geometry of the induced posterior probability distributions. PMID:23226584
NASA Astrophysics Data System (ADS)
Kurt, Mehmet; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2014-03-01
We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong
Induced dynamic nonlinear ground response at Gamer Valley, California
Lawrence, Z.; Bodin, P.; Langston, C.A.; Pearce, F.; Gomberg, J.; Johnson, P.A.; Menq, F.-Y.; Brackman, T.
2008-01-01
We present results from a prototype experiment in which we actively induce, observe, and quantify in situ nonlinear sediment response in the near surface. This experiment was part of a suite of experiments conducted during August 2004 in Garner Valley, California, using a large mobile shaker truck from the Network for Earthquake Engineering Simulation (NEES) facility. We deployed a dense accelerometer array within meters of the mobile shaker truck to replicate a controlled, laboratory-style soil dynamics experiment in order to observe wave-amplitude-dependent sediment properties. Ground motion exceeding 1g acceleration was produced near the shaker truck. The wave field was dominated by Rayleigh surface waves and ground motions were strong enough to produce observable nonlinear changes in wave velocity. We found that as the force load of the shaker increased, the Rayleigh-wave phase velocity decreased by as much as ???30% at the highest frequencies used (up to 30 Hz). Phase velocity dispersion curves were inverted for S-wave velocity as a function of depth using a simple isotropic elastic model to estimate the depth dependence of changes to the velocity structure. The greatest change in velocity occurred nearest the surface, within the upper 4 m. These estimated S-wave velocity values were used with estimates of surface strain to compare with laboratory-based shear modulus reduction measurements from the same site. Our results suggest that it may be possible to characterize nonlinear soil properties in situ using a noninvasive field technique.
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.
Nonlinear dynamics of vortices in nano-structured superconductors
NASA Astrophysics Data System (ADS)
Peeters, Francois
2014-03-01
Nonlinear flux dynamics in superconductors is a prototype for many nonlinear phenomena occurring in different areas of physics. It is well-known that vortices in nano-structured superconductors with dimensions comparable to characteristic length scales behave very different from those in bulk materials, e.g. multi-quanta giant vortices and symmetry-induced vortex-antivortex pairs can nucleate which are impossible in bulk. I will give a few examples of the surprising behavior of vortex matter in different type of nano-structured superconducting films. Our analysis is based on the time-dependent Ginzburg-Landau theory. Where possible comparison with experiments.will be made. For example large resistance oscillations are found, different from the usual Little-Parks effect, that are due to current-excited moving vortices. Unusal field-induced increase in the critical current may be observed as a consequence of the nonlinear distribution of the current in a sample. In type-I superconductors even in the intermediate state the smallest building block turns out to be a flux quantum and the current driven nucleation of flux domains is discretized to a single fluxoid. Domains of opposite flux, when driven towards each other, annihilate through a discretized sequence of single vortex-antivortex pairs. Supported by the Flemish Science Foundation and the Methusalem programme of the Flemish Government. Work done in collaboration with G. Berdiyorov, M.V. Milosevic, Z.L. Xiao, W.K. Kwok and M.L. Latimer.
Phase and amplitude dynamics of nonlinearly coupled oscillators.
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.
The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
NASA Astrophysics Data System (ADS)
Pedlosky, J.; Flierl, G. R.
2006-12-01
The nonlinear dynamics of baroclinically unstable waves in a time dependent zonal shear flow is considered in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well below the critical value of the steady shear version of the model. Nevertheless, the time dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating shear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical, the resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear we have detected a symmetry breaking in which a second cross-stream mode is generated through an instability of the unstable wave although this second mode would by itself be stable on the basic time dependent current. For shear values that are substantially subcritical but of order of the critical shear, calculations with a full quasi-geostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded the inviscid, linear problem is formally stable. However, our calculations show that a small degree of nonlinearity is enough to destabilize the flow leading to large amplitude
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.
Design principle of a nonlinear robust dynamic vibration absorber
NASA Astrophysics Data System (ADS)
Koga, Yuki; Masuda, Arata
2016-04-01
This study aims to develop a design principle of a nonlinear dynamic vibration absorber focusing on its robustness against the alteration of the natural frequency of the primary system. To this end, a 2-DOF coupled system consisting of the primary and absorber systems is analytically solved to evaluate the maximally possible level of the displacement response of the primary system by means of averaging method. In this approach, the equation of motion of the vibration absorber is first solved in the steady-state by the averaging method for a given amplitude of the primary system assuming that the whole responses of the coupled system have the same frequency as the excitation force. Then, the equivalent dynamic stiffness of the dynamic absorber is derived which represents how the absorber acts on the primary system in reaction of the displacement of the primary system. Because the maximally possible displacement amplitude of the primary system is enveloped by the reciprocal of the imaginary part of the equivalent dynamic stiffness, the benefit of introducing a softening effect into the design of the dynamic absorber is theoretically suggested, and validated through numerical simulations.
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 flight dynamics and stability of hovering model insects.
Liang, Bin; Sun, Mao
2013-08-01
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.
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
Directing nonlinear dynamic systems to any desired orbit
Zonghua, L. |; Shigang, C.
1997-01-01
A method of controlling arbitrary nonlinear dynamic systems, dx/dt=F(x,t) (x{element_of}R{sup n}), is presented. It is proved that the system can be entrained to any arbitrary {open_quotes}goal{close_quotes} dynamics g(t) by use of the open-loop action and adjusting the control parameter at the same time. Examples of some entrainment {open_quotes}goals{close_quotes} are given for the Lorenz and the R{umlt o}ssler systems. The basins of entrainment are also established for the Lorenz, R{umlt o}ssler, and Duffing systems. Numerical studies show that this method works as well as the closed-loop control method [Physica D {bold 85}, 1 (1995); Phys. Lett. A {bold 213}, 148 (1996)]. {copyright} {ital 1997} {ital The American Physical Society}
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 analysis of anesthesia dynamics by Fractal Scaling Exponent.
Gifani, P; Rabiee, H R; Hashemi, M R; Taslimi, P; Ghanbari, M
2006-01-01
The depth of anesthesia estimation has been one of the most research interests in the field of EEG signal processing in recent decades. In this paper we present a new methodology to quantify the depth of anesthesia by quantifying the dynamic fluctuation of the EEG signal. Extraction of useful information about the nonlinear dynamic of the brain during anesthesia has been proposed with the optimum Fractal Scaling Exponent. This optimum solution is based on the best box sizes in the Detrended Fluctuation Analysis (DFA) algorithm which have meaningful changes at different depth of anesthesia. The Fractal Scaling Exponent (FSE) Index as a new criterion has been proposed. The experimental results confirm that our new Index can clearly discriminate between aware to moderate and deep anesthesia levels. Moreover, it significantly reduces the computational complexity and results in a faster reaction to the transients in patients' consciousness levels in relations with the other algorithms.
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
Exploiting link dynamics in LEO-to-ground communications
Palmer, Joseph Mcrae; Caffrey, Michael P
2009-01-01
The high dynamics of the LEO-to-ground radio channel are described. An analysis shows how current satellite radio systems largely underutilize the available radio link, and that a radio that can adaptively vary the bit rate can more fully exploit it, resulting in increased data throughput and improved power efficiency. We propose one method for implementing the adaptivity, and present simulation results.
The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links
NASA Astrophysics Data System (ADS)
Carillo, Sandra; Fuchssteiner, Benno
1989-07-01
Explicit computation for a Kawamoto-type equation shows that there is a rich associated symmetry structure for four separate hierarchies of nonlinear integrodifferential equations. Contrary to the general belief that symmetry groups for nonlinear evolution equations in 1+1 dimensions have to be Abelian, it is shown that, in this case, the symmetry group is noncommutative. Its semisimple part is isomorphic to the affine Lie algebra A(1)1 associated to sl(2,C). In two of the additional hierarchies that were found, an explicit dependence of the independent variable occurs. Surprisingly, the generic invariance for the Kawamoto-type equation obtained in Rogers and Carillo [Phys. Scr. 36, 865 (1987)] via a reciprocal link to the Möbius invariance of the singularity equation of the Kaup-Kupershmidt (KK) equation only holds for one of the additional hierarchies of symmetry groups. Thus the generic invariance is not a universal property for the complete symmetry group of equations obtained by reciprocal links. In addition to these results, the bi-Hamiltonian formulation of the hierarchy is given. A direct Bäcklund transformation between the (KK) hierarchy and the hierarchy of singularity equation for the Caudrey-Dodd-Gibbon-Sawada-Kotera equation is exhibited: This shows that the abundant symmetry structure found for the Kawamoto equation must exist for all fifth-order equations, which are known to be completely integrable since these equations are connected either by Bäcklund transformations or reciprocal links. It is shown that similar results must hold for all hierarchies emerging out of singularity hierarchies via reciprocal links. Furthermore, general aspects of the results are 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.
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.
Nonlinear identification of process dynamics using neural networks
Parlos, A.G.; Atiya, A.F.; Chong, K.T. . Dept. of Nuclear Engineering); Tsai, W.K. )
1992-01-01
In this paper the nonlinear identification of process dynamics encountered in nuclear power plant components is addressed, in an input-output sense, using artificial neural systems. A hybrid feedforward/feedback neural network, namely, a recurrent multilayer perceptron, is used as the model structure to be identified. The feedforward portion of the network architecture provides its well-known interpolation property, while through recurrency and cross-talk, the local information feedback enables representation of temporal variations in the system nonlinearities. The standard backpropagation learning algorithm is modified, and it is used for the supervised training of the proposed hybrid network. The performance of recurrent multilayer perceptron networks in identifying process dynamics is investigated via the case study of a U-tube steam generator. The response of representative steam generator is predicted using a neural network, and it is compared to the response obtained from a sophisticated computer model based on first principles. The transient responses compare well, although further research is warranted to determine the predictive capabilities of these networks during more severe operational transients and accident scenarios.
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.
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 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.
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.
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.
Sentjabrskaja, T.; Chaudhuri, P.; Hermes, M.; Poon, W. C. K.; Horbach, J.; Egelhaaf, S. U.; Laurati, M.
2015-01-01
Mechanical properties are of central importance to materials sciences, in particular if they depend on external stimuli. Here we investigate the rheological response of amorphous solids, namely colloidal glasses, to external forces. Using confocal microscopy and computer simulations, we establish a quantitative link between the macroscopic creep response and the microscopic single-particle dynamics. We observe dynamical heterogeneities, namely regions of enhanced mobility, which remain localized in the creep regime, but grow for applied stresses leading to steady flow. These different behaviors are also reflected in the average particle dynamics, quantified by the mean squared displacement of the individual particles, and the fraction of active regions. Both microscopic quantities are found to be proportional to the macroscopic strain, despite the non-equilibrium and non-linear conditions during creep and the transient regime prior to steady flow. PMID:26153523
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.
Effects of adaptive dynamical linking in networked games
NASA Astrophysics Data System (ADS)
Yang, Zhihu; Li, Zhi; Wu, Te; Wang, Long
2013-10-01
The role of dynamical topologies in the evolution of cooperation has received considerable attention, as some studies have demonstrated that dynamical networks are much better than static networks in terms of boosting cooperation. Here we study a dynamical model of evolution of cooperation on stochastic dynamical networks in which there are no permanent partners to each agent. Whenever a new link is created, its duration is randomly assigned without any bias or preference. We allow the agent to adaptively adjust the duration of each link during the evolution in accordance with the feedback from game interactions. By Monte Carlo simulations, we find that cooperation can be remarkably promoted by this adaptive dynamical linking mechanism both for the game of pairwise interactions, such as the Prisoner's Dilemma game (PDG), and for the game of group interactions, illustrated by the public goods game (PGG). And the faster the adjusting rate, the more successful the evolution of cooperation. We also show that in this context weak selection favors cooperation much more than strong selection does. What is particularly meaningful is that the prosperity of cooperation in this study indicates that the rationality and selfishness of a single agent in adjusting social ties can lead to the progress of altruism of the whole population.
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 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.
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.
Nonlinear dynamics in the perceptual grouping of connected surfaces.
Hock, Howard S; Schöner, Gregor
2016-09-01
Evidence obtained using the dynamic grouping method has shown that the grouping of an object's connected surfaces has properties characteristic of a nonlinear dynamical system. When a surface's luminance changes, one of its boundaries is perceived moving across the surface. The direction of this dynamic grouping (DG) motion indicates which of two flanking surfaces has been grouped with the changing surface. A quantitative measure of overall grouping strength (affinity) for adjacent surfaces is provided by the frequency of DG motion perception in directions promoted by the grouping variables. It was found that: (1) variables affecting surface grouping for three-surface objects evolve over time, settling at stable levels within a single fixation, (2) how often DG motion is perceived when a surface's luminance is perturbed (changed) depends on the pre-perturbation affinity state of the surface grouping, (3) grouping variables promoting the same surface grouping combine cooperatively and nonlinearly (super-additively) in determining the surface grouping's affinity, (4) different DG motion directions during different trials indicate that surface grouping can be bistable, which implies that inhibitory interactions have stabilized one of two alternative surface groupings, and (5) when alternative surface groupings have identical affinity, stochastic fluctuations can break the symmetry and inhibitory interactions can then stabilize one of the surface groupings, providing affinity levels are not too high (which results in bidirectional DG motion). A surface-grouping network is proposed within which boundaries vary in salience. Low salience or suppressed boundaries instantiate surface grouping, and DG motion results from changes in boundary salience. PMID:26235970
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.
2012-01-01
Summary 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 (D2) 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 D2 = 2.14), jazz (median D2 = 2.24), pop (median D2 = 2.60), MT (median D2 = 2.73), and soul (mean D2 = 3.26). Correlation dimension was significantly higher in opera (P < 0.001) with median D2 = 6.19. In this study, acoustic analysis in opera singing gave significantly high values for shimmer and D2, 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
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.
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.
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
Complex Population Dynamics in Mussels Arising from Density-Linked Stochasticity
Wootton, J. Timothy; Forester, James D.
2013-01-01
Population fluctuations are generally attributed to the deterministic consequences of strong non-linear interactions among organisms, or the effects of random stochastic environmental variation superimposed upon the deterministic skeleton describing population change. Analysis of the population dynamics of the mussel Mytilus californianus taken in 16 plots over 18-years found no evidence that these processes explained observed strong fluctuations. Instead, population fluctuations arose because environmental stochasticity varied with abundance, which we term density-linked stochasticity. This phenomenon arises from biologically relevant mechanisms: recruitment variation and transmission of disturbance among neighboring individuals. Density-linked stochasticity is probably present frequently in populations, as it arises naturally from several general ecological processes, including stage structure variation with density, ontogenetic niche shifts, and local transmission of stochastic perturbations. More thoroughly characterizing and interpreting deviations from the mean behavior of a system will lead to better ecological prediction and improved insight into the important processes affecting populations and ecosystems. PMID:24086617
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.
Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems.
Wang, Chi-Hsu; Lin, Tsung-Chih; Lee, Tsu-Tian; Liu, Han-Leih
2002-01-01
A new hybrid direct/indirect adaptive fuzzy neural network (FNN) controller with a state observer and supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which can be adjusted by the tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive FNN controller and direct adaptive FNN controller. Furthermore, a supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be deactivated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Two nonlinear systems, namely, inverted pendulum system and Chua's (1989) chaotic circuit, are fully illustrated to track sinusoidal signals. The resulting hybrid direct/indirect FNN control systems show better performances, i.e., tracking error and control effort can be made smaller and it is more flexible during the design process.
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.
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.
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.
Simple models for quorum sensing: Nonlinear dynamical analysis
NASA Astrophysics Data System (ADS)
Chiang, Wei-Yin; Li, Yue-Xian; Lai, Pik-Yin
2011-10-01
Quorum sensing refers to the change in the cooperative behavior of a collection of elements in response to the change in their population size or density. This behavior can be observed in chemical and biological systems. These elements or cells are coupled via chemicals in the surrounding environment. Here we focus on the change of dynamical behavior, in particular from quiescent to oscillatory, as the cell population changes. For instance, the silent behavior of the elements can become oscillatory as the system concentration or population increases. In this work, two simple models are constructed that can produce the essential representative properties in quorum sensing. The first is an excitable or oscillatory phase model, which is probably the simplest model one can construct to describe quorum sensing. Using the mean-field approximation, the parameter regime for quorum sensing behavior can be identified, and analytical results for the detailed dynamical properties, including the phase diagrams, are obtained and verified numerically. The second model consists of FitzHugh-Nagumo elements coupled to the signaling chemicals in the environment. Nonlinear dynamical analysis of this mean-field model exhibits rich dynamical behaviors, such as infinite period bifurcation, supercritical Hopf, fold bifurcation, and subcritical Hopf bifurcations as the population parameter changes for different coupling strengths. Analytical result is obtained for the Hopf bifurcation phase boundary. Furthermore, two elements coupled via the environment and their synchronization behavior for these two models are also investigated. For both models, it is found that the onset of oscillations is accompanied by the synchronized dynamics of the two elements. Possible applications and extension of these models are also discussed.
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.
Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics
NASA Astrophysics Data System (ADS)
Bun Tse, Bosco Chun
This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.
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 adaptive trajectory tracking using dynamic neural networks.
Poznyak, A S; Yu, W; Sanchez, E N; Perez, J P
1999-01-01
In this paper the adaptive nonlinear identification and trajectory tracking are discussed via dynamic neural networks. By means of a Lyapunov-like analysis we determine stability conditions for the identification error. Then we analyze the trajectory tracking error by a local optimal controller. An algebraic Riccati equation and a differential one are used for the identification and the tracking error analysis. As our main original contributions, we establish two theorems: the first one gives a bound for the identification error and the second one establishes a bound for the tracking error. We illustrate the effectiveness of these results by two examples: the second-order relay system with multiple isolated equilibrium points and the chaotic system given by Duffing equation. PMID:18252641
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.
Nonlinear Radiation Pressure Dynamics in an Optomechanical Crystal.
Krause, Alex G; Hill, Jeff T; Ludwig, Max; Safavi-Naeini, Amir H; Chan, Jasper; Marquardt, Florian; Painter, Oskar
2015-12-01
Utilizing a silicon nanobeam optomechanical crystal, we investigate the attractor diagram arising from the radiation pressure interaction between a localized optical cavity at λ_{c}=1542 nm and a mechanical resonance at ω_{m}/2π=3.72 GHz. At a temperature of T_{b}≈10 K, highly nonlinear driving of mechanical motion is observed via continuous wave optical pumping. Introduction of a time-dependent (modulated) optical pump is used to steer the system towards an otherwise inaccessible dynamically stable attractor in which mechanical self-oscillation occurs for an optical pump red detuned from the cavity resonance. An analytical model incorporating thermo-optic effects due to optical absorption heating is developed and found to accurately predict the measured device behavior.
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.
A nonlinear model of the phasic dynamics of muscle activation
NASA Technical Reports Server (NTRS)
Hannaford, Blake
1990-01-01
A phasic excitation-activation (PEXA) model is presented of the process of motoneuron excitation and the resultant activation and force development of a motor unit. The model input is an amount of depolarizing current (as when injected with an intracellular electrode), and the model output is muscle force. The model includes dynamics and nonlinearities similar to phenomena discovered experimentally by others: the firing rate response of motoneurons to steps of depolarizing current and the catch-like enhancement of force produced by overlapping motor neuron action potentials. The parameter values used in this model are derived from experimentally measured data and are expressed in physical units. Model predictions extend to published data beyond those used in generating the model parameter values.
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 behavior of an impact damaged composite skin-stiffener structure
NASA Astrophysics Data System (ADS)
Ooijevaar, T. H.; Rogge, M. D.; Loendersloot, R.; Warnet, L. L.; Akkerman, R.; Tinga, T.
2015-09-01
One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage. A wide range of technologies, comprising global vibration and local wave propagation methods, can be employed for health monitoring purposes. Traditional modal analysis based methods are linear methods. The effectiveness of these methods is sometimes limited since they rely on a stationary and linear description of the system. The nonlinear interaction between a low frequency wave field and a local impact induced damage in a composite skin-stiffener structure is experimentally demonstrated in this work. The different mechanisms linked to the distorted waveforms are separated with the help of phase portraits. The harmonic waveform distortions are concentrated at the damaged region and increased for higher excitation amplitudes. It is shown that linear damage identification methods are feasible for low excitation amplitudes, but that the presence of nonlinear dynamic effects cannot remain silent for higher amplitudes. Analyzing the damage induced nonlinear effects can provide useful information about the current state of the structure.
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
Social-support moderated stress: a nonlinear dynamical model and the stress-buffering hypothesis.
Field, Richard J; Schuldberg, David
2011-01-01
Health psychology has studied the cross-sectional, stationary relationships linking stress, social support, and health. Levels of stress-related illness are generally modeled by including a nonlinear multiplicative or 'buffering' effect, corresponding to the interaction of stressor levels with social support from family and friends. The motivation of the present research is to extend an iterative, dynamic model of this well-investigated psychological process using a dynamical systems model expressed as a set of continuous, nonlinear differential equations similar to those of the 'Oregonator,' a model of a nonlinear dynamic chemical system. This model of the behavior of an individual is amenable to numerical investigation of its stationary-state stability properties, temporal evolution, and cause-effect relationships. The continuous variables in this new approach refer to varying states of an individual; they are Perceived stress (X), Symptoms (Y), and Social support (Z). It is expected that poor health in this model, represented by Symptoms (Y), is directly related to Perceived stress, as well as being tied in more complicated ways to Social support. A number of such models may be envisioned, some including a multiplicative, 'buffering' (- X x Z) effect of social support dependent on stress levels. We explore the behavior of this model over ranges of parameter values and initial conditions and relate these results to how an individual reacts to environmental challenges at various levels of stressors and social-support recruitment. Data generated by the model are in turn analyzed with a traditional cross-sectional statistical technique. Similarities and differences between chemical and psychological systems are discussed.
NASA Astrophysics Data System (ADS)
Zhu, F. H.; Fu, Y. M.
2008-12-01
By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.
Does the Cerebral Cortex Exploit High-Dimensional, Non-linear Dynamics for Information Processing?
Singer, Wolf; Lazar, Andreea
2016-01-01
The discovery of stimulus induced synchronization in the visual cortex suggested the possibility that the relations among low-level stimulus features are encoded by the temporal relationship between neuronal discharges. In this framework, temporal coherence is considered a signature of perceptual grouping. This insight triggered a large number of experimental studies which sought to investigate the relationship between temporal coordination and cognitive functions. While some core predictions derived from the initial hypothesis were confirmed, these studies, also revealed a rich dynamical landscape beyond simple coherence whose role in signal processing is still poorly understood. In this paper, a framework is presented which establishes links between the various manifestations of cortical dynamics by assigning specific coding functions to low-dimensional dynamic features such as synchronized oscillations and phase shifts on the one hand and high-dimensional non-linear, non-stationary dynamics on the other. The data serving as basis for this synthetic approach have been obtained with chronic multisite recordings from the visual cortex of anesthetized cats and from monkeys trained to solve cognitive tasks. It is proposed that the low-dimensional dynamics characterized by synchronized oscillations and large-scale correlations are substates that represent the results of computations performed in the high-dimensional state-space provided by recurrently coupled networks. PMID:27713697
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.
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…
Curri, Vittorio; Carena, Andrea; Poggiolini, Pierluigi; Bosco, Gabriella; Forghieri, Fabrizio
2013-02-11
We show the extension of the Gaussian Noise model, which describes non-linear propagation in uncompensated links of multilevel modulation formats, to systems using Raman amplification. We successfully validate the analytical results by comparison with numerical simulations of Nyquist-WDM PM-16QAM channels transmission over multi-span uncompensated links made of a single fiber type and using hybrid EDFA/Raman amplification with counter-propagating pumps. We analyze two typical high- and low-dispersion fiber types. We show that Raman amplification always induces a limited non-linear interference enhancement compared to the dominant ASE noise reduction.
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.
Linear-Nonlinear-Poisson models of primate choice dynamics.
Corrado, Greg S; Sugrue, Leo P; Seung, H Sebastian; Newsome, William T
2005-11-01
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 eye movements to one of two colored icons presented on a computer monitor, each rewarded on dynamic variable-interval schedules. Using a generalization of Wiener kernel analysis, we recover a compact mechanistic description of the impact of past reward on future choice in the form of a Linear-Nonlinear-Poisson model. We validate this model through rigorous predictive and generative testing. Compared to our earlier work with this same data set, this model proves to be a better description of choice behavior and is more tightly correlated with putative neural value signals. Refinements over previous models include hyperbolic (as opposed to exponential) temporal discounting of past rewards, and differential (as opposed to fractional) comparisons of option value. Through numerical simulation we find that within this class of strategies, the model parameters employed by animals are very close to those that maximize reward harvesting efficiency.
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.
Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Marston, J. B.; Hastings, M. B.
2005-03-01
The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.
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.
A closed-loop identification protocol for nonlinear dynamical systems.
Feng, Xiao-jiang; Rabitz, Herschel; Turinici, Gabriel; Le Bris, Claude
2006-06-29
A previous work introduced an optimal identification (OI) technique for reliably extracting model parameters of biochemical reaction systems from tailored laboratory experiments. The notion of optimality enters through seeking an external control in the laboratory producing data that leads to minimum uncertainties in the identified parameter distributions. A number of algorithmic and operational improvements are introduced in this paper to OI, aiming to build a more practical and efficient closed-loop identification protocol/procedure (CLIP) for nonlinear dynamical systems. The improvements in CLIP include (a) inversion cost function modification to preferably search for the upper and lower boundaries of the parameter distributions consistent with the observed data, (b) dynamic search range updating of the unknown parameters to better exploit the information from the prior iterative experiments, (c) replacing the control genetic algorithm by the simplex method to enable better balance between operational cost and inversion quality, and (d) utilizing virtual sensitivity optimization techniques to further reduce the laboratory costs. The workings of CLIP utilizing these new algorithms are illustrated in indentifying a simulated tRNA proofreading model, and the results demonstrate enhanced performance of CLIP in terms of algorithmic reliability and efficiency. PMID:16789759
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.
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}.
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.
Double nonlinear resonance in ferromagnets and other dynamic systems
NASA Astrophysics Data System (ADS)
Bakai, A. S.
2010-08-01
The phenomenon of double nonlinear resonances in nonlinear oscillators of general type is described. The results are used to describe a double nonlinear ferromagnetic resonance in a uniaxial ferromagnet. The possibility of a similar resonance in the system of brain biocurrents is considered.
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
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
Identification of nonlinear dynamic processes based on dynamic radial basis function networks
NASA Astrophysics Data System (ADS)
Ayoubi, Mihiar; Isermann, Rolf
1996-03-01
An attempts has been made to establish a discrete-time neuron model with a radial basis function. The neuron is utilized to build RBF-networks with locally distributed dynamics to identify input/output models of dynamic nonlinear processes. The adaptation algorithm which ascertains the optimal network parameters is provided. Further, an enhanced parameter estimation algorithm is derived, the so-called compound estimation procedure, which combines elaborated least squares techniques to highly decrease the training times. The proposed neural model is applied to identify black-box models of a turbocharging process within a Diesel engine. Benefits and drawbacks of the proposed neural structure are worked out.
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.
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
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.
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
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
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
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
Population dynamics of Microtus pennsylvanicus in corridor-linked patches
Coffman, C.J.; Nichols, J.D.; Pollock, K.H.
2001-01-01
Corridors have become a key issue in the discussion of conservation planning: however, few empirical data exist on the use of corridors and their effects on population dynamics. The objective of this replicated, population level, capture-re-capture experiment on meadow voles was to estimate and compare population characteristics of voles between (1) corridor-linked fragments, (2) isolated or non-linked fragments, and (3) unfragmented areas. We conducted two field experiments involving 22600 captures of 5700 individuals. In the first, the maintained corridor study, corridors were maintained at the time of fragmentation, and in the second, the constructed corridor study, we constructed corridors between patches that had been fragmented for some period of time. We applied multistate capture-recapture models with the robust design to estimate adult movement and survival rates, population size, temporal variation in population size, recruitment, and juvenile survival rates. Movement rates increased to a greater extent on constructed corridor-linked grids than on the unfragmented or non-linked fragmented grids between the pre- and post-treatment periods. We found significant differences in local survival on the treated (corridor-linked) grids compared to survival on the fragmented and unfragmented grids between the pre- and post-treatment periods. We found no clear pattern of treatment effects on population size or recruitment in either study. However, in both studies, we found that unfragmented grids were more stable than the fragmented grids based on lower temporal variability in population size. To our knowledge, this is the first experimental study demonstrating that corridors constructed between existing fragmented populations can indeed cause increases in movement and associated changes in demography, supporting the use of constructed corridors for this purpose in conservation biology.
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 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.
Observation of chaotic dynamics of coupled nonlinear oscillators
Van Buskirk, R.; Jeffries, C.
1985-05-01
The nonlinear charge storage property of driven Si p-n junction passive resonators gives rise to chaotic dynamics: period doubling, chaos, periodic windows, and an extended period-adding sequence corresponding to entrainment of the resonator by successive subharmonics of the driving frequency. The physical system is described; equations of motion and iterative maps are reviewed. Computed behavior is compared to data, with reasonable agreement for Poincare sections, bifurcation diagrams, and phase diagrams in parameter space (drive voltage, drive frequency). N = 2 symmetrically coupled resonators are found to display period doubling, Hopf bifurcations, entrainment horns (''Arnol'd tongues''), breakup of the torus, and chaos. This behavior is in reasonable agreement with theoretical models based on the characteristics of single-junction resonators. The breakup of the torus is studied in detail, by Poincare sections and by power spectra. Also studied are oscillations of the torus and cyclic crises. A phase diagram of the coupled resonators can be understood from the model. Poincare sections show self-similarity and fractal structure, with measured values of fractal dimension d = 2.03 and d = 2.23 for N = 1 and N = 2 resonators, respectively. Two line-coupled resonators display first a Hopf bifurcation as the drive parameter is increased, in agreement with the model. For N = 4 and N = 12 line-coupled resonators complex quasiperiodic behavior is observed with up to 3 and 4 incommensurate frequencies, respectively.
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
Population dynamics and climate change: what are the links?
Stephenson, Judith; Newman, Karen; Mayhew, Susannah
2010-06-01
Climate change has been described as the biggest global health threat of the 21(st) century. World population is projected to reach 9.1 billion by 2050, with most of this growth in developing countries. While the principal cause of climate change is high consumption in the developed countries, its impact will be greatest on people in the developing world. Climate change and population can be linked through adaptation (reducing vulnerability to the adverse effects of climate change) and, more controversially, through mitigation (reducing the greenhouse gases that cause climate change). The contribution of low-income, high-fertility countries to global carbon emissions has been negligible to date, but is increasing with the economic development that they need to reduce poverty. Rapid population growth endangers human development, provision of basic services and poverty eradication and weakens the capacity of poor communities to adapt to climate change. Significant mass migration is likely to occur in response to climate change and should be regarded as a legitimate response to the effects of climate change. Linking population dynamics with climate change is a sensitive issue, but family planning programmes that respect and protect human rights can bring a remarkable range of benefits. Population dynamics have not been integrated systematically into climate change science. The contribution of population growth, migration, urbanization, ageing and household composition to mitigation and adaptation programmes needs urgent investigation.
Dynamic graphics in a GIS: More examples using linked software
NASA Astrophysics Data System (ADS)
Cook, Dianne; Symanzik, Jürgen; Majure, James J.; Cressie, Noel
1997-05-01
This document describes the linking of two software packages to provide exploratory dynamic graphical tools directly from within a geographic information system (GIS). The GIS we have used is ArcView 2.1, which is a widely used package for examining maps and images. XGobi is the dynamic graphics package that is publicly available and also widely used for exploring multivariate data. The link involves cross-referencing each location in the map view provided by ArcView with a multitude of plot types in XGobi. This cross-referencing allows a user to interact with either the map view or the XGobi plots by painting (that is, brushing) groups of points with different colors or glyph (shape) types, identifying points, or erasing them, and have the similar changes made automatically in the other view. Examples of the different types of plots and interactions are given in the paper in both image and video format. ArcView is a registered trademark of Environmental Systems Research Institute, Inc., Redlands, CA, U.S.A.
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.
Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations
Zhang, Yu; Jiang, Jack J.
2009-01-01
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. PMID:22505778
NASA Astrophysics Data System (ADS)
Hyun, Kyu; Kim, Wonho
2011-12-01
Large Amplitude Oscillatory Shear (LAOS) is a test method for the characterization of complex fluids. Varying independently both strain amplitude (γ0) and frequency (ω) allows covering a broad spectrum of rheological responses with respect to time scales and involved non-linearity. Moreover, it is experimentally relatively simple to generate LAOS flow, because dynamic oscillatory shear does not involve any sudden jump in either strain or strain rate. There are several methods to analyze the resulting torque data received from the LAOS test protocol: (1) the G' and G″ as a function of strain amplitude (2) Stress shape (stress vs. time) or Lissajous pattern (stress vs. strain or stress vs. strain rate) (3) Fourier transform (4) generalized "storage" and "loss" modulus when decomposing the nonlinear stress data (5) Chebyschev polynomials using decomposing stress data and further development of Chebyschev polynomials. The Fourier Transform (FT)-Rheology is perhaps the most sensitive method of those discussed above. A new nonlinear parameter Q established from FT-Rheolgy under LAOS flow, i.e. Q( ω,γ 0) ≡ I 3/1/ γ {0/2}, as well as the zero-strain nonlinearity or intrinsic nonlinearity Q_0 ( ω ) equiv lim _{γ _0 to 0} Q( {ω ,γ _0 } ) by Hyun and Wilhelm (2009). In this study, therefore recent experiment and simulation results of nonlinear parameter Q from FT-Rheology for polymer melt and polymer composite systemsare reviewed.
NASA Astrophysics Data System (ADS)
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
NASA Astrophysics Data System (ADS)
Yang, J. H.; Yang, J.; Kitipornchai, S.
2012-12-01
This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán-Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response.
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
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
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…
Entangled polymer dynamics in equilibrium and flow modeled through slip links.
Schieber, Jay D; Andreev, Marat
2014-01-01
The idea that the dynamics of concentrated, high-molecular weight polymers are largely governed by entanglements is now widely accepted and typically understood through the tube model. Here we review alternative approaches, slip-link models, that share some similarities to and offer some advantages over tube models. Although slip links were proposed at the same time as tubes, only recently have detailed, quantitative mathematical models arisen based on this picture. In this review, we focus on these models, with most discussion limited to mathematically well-defined objects that conform to state-of-the-art beyond-equilibrium thermodynamics. These models are connected to each other through successive coarse graining, using nonequilibrium thermodynamics along the way, and with a minimal parameter set. In particular, the most detailed level of description has four parameters, three of which can be determined directly from atomistic simulations. Once the remaining parameter is determined for any system, all parameters for all members of the hierarchy are determined. We show how, using this hierarchy of slip-link models combined with atomistic simulations, we can make predictions about the nonlinear rheology of monodisperse homopolymer melts, polydisperse melts, or blends of different architectures. Mathematical details are given elsewhere, so these are limited here, and physical ideas are emphasized. We conclude with an outlook on remaining challenges that might be tackled successfully using this approach, including complex flow fields and polymer blends. PMID:24655135
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.
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.
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.
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?'
Novoa, David; Michinel, Humberto; Tommasini, Daniele; Carpentier, Alicia V.
2010-04-15
We analyze both theoretically and by means of numerical simulations the phenomena of filamentation and dynamical formation of self-guided nonlinear waves in media featuring competing cubic and quintic nonlinearities. We provide a theoretical description of recent experiments in terms of a linear stability analysis supported with simulations, showing the possibility of the observation of modulational instability suppression of intense light pulses traveling across such nonlinear media. We also show a mechanism of indirect excitation of light condensates by means of coalescence processes of nonlinear coherent structures produced by managed filamentation of high-power laser beams.
Stokesian dynamics optimization of three linked spheres microswimmers
NASA Astrophysics Data System (ADS)
Marconi, V. I.; Berdakin, I.; Banchio, A. J.
2014-03-01
Self-propulsion of swimmers is only possible due to motility strategies able to overcome the absence of inertia. Only the swimming strategies that are time-irreversible are successful. One of the simplest swimmers fulfilling this requirement is the three-linked-spheres swimmer, TLS, a toy model swimmer built upon three spheres linked by two arms that contracts asynchronously. This TLS has received significant attention because it can be studied both, analytically and numerically. Using stokesian dynamics we investigate in detail the net displacement, velocities, forces and power consumption. We compare two swimming strategies: square and circular phase-space cycles. If the efficiency is defined as the ratio between power dissipation and the work needed to produce the same motion by an external force, we show that the most efficient swimmer is the one with almost maximum (maximum) arms contraction for square (circular) cycles. Interestingly, under these optimum conditions, the analytical predictions based on point force approximations of the hydrodynamic mobility tensor differ significantly from those found in our more accurate simulations. This fact highlights the importance of a proper treatment of the hydrodynamic interactions. Supported by CONICET and SeCyt-UNC, Cordoba, Argentina, and NSF(USA)-CONICET(Argentina).
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 Control of Dynamical Systems from Time Series
NASA Astrophysics Data System (ADS)
Petrov, Valery; Showalter, Kenneth
1996-04-01
Feedback control of multidimensional, nonlinear single-input single-output systems is formulated in terms of an invariant hypersurface in the delayed state space of a system observable and a control parameter. The surface is created directly from the response of the system to random perturbations, providing a model-independent nonlinear control algorithm. The algorithm can be used to stabilize unstable states or to drive a system to any particular objective state in a minimum number of steps.
QCL-based nonlinear sensing of independent targets dynamics.
Mezzapesa, F P; Columbo, L L; Dabbicco, M; Brambilla, M; Scamarcio, G
2014-03-10
We demonstrate a common-path interferometer to measure the independent displacement of multiple targets through nonlinear frequency mixing in a quantum-cascade laser (QCL). The sensing system exploits the unique stability of QCLs under strong optical feedback to access the intrinsic nonlinearity of the active medium. The experimental results using an external dual cavity are in excellent agreement with the numerical simulations based on the Lang-Kobayashi equations.
Highly nonlinear Bragg quasisolitons in the dynamics of water waves.
Ruban, V P
2008-05-01
Finite-amplitude gravity water waves in Bragg resonance with a periodic one-dimensional topography are studied numerically using exact equations of motion for ideal potential free-surface flows. Spontaneous formation of highly nonlinear localized structures is observed in the numerical experiments. These coherent structures consisting of several nearly standing extreme waves are similar in many aspects to the Bragg solitons previously known in nonlinear optics. PMID:18643128
Quantitative Assessment of UVA-Riboflavin Corneal Cross-Linking Using Nonlinear Optical Microscopy
Chai, Dongyul; Gaster, Ronald N.; Roizenblatt, Roberto; Juhasz, Tibor; Brown, Donald J.
2011-01-01
Purpose. Corneal collagen cross-linking (CXL) by the use of riboflavin and ultraviolet-A light (UVA) is a promising and novel treatment for keratoconus and other ectatic disorders. Since CXL results in enhanced corneal stiffness, this study tested the hypothesis that CXL-induced stiffening would be proportional to the collagen autofluorescence intensity measured with nonlinear optical (NLO) microscopy. Methods. Rabbit eyes (n = 50) were separated into five groups including: (1) epithelium intact; (2) epithelium removed; (3) epithelium removed and soaked in riboflavin, (4) epithelium removed and soaked in riboflavin, with 15 minutes of UVA exposure; and (5) epithelium removed and soaked in riboflavin, with 30 minutes of UVA exposure. Corneal stiffness was quantified by measuring the force required to displace the cornea 500 μm. Corneas were then fixed in paraformaldehyde and sectioned, and the collagen autofluorescence over the 400- to 450-nm spectrum was recorded. Results. There was no significant difference in corneal stiffness among the three control groups. Corneal stiffness was significantly and dose dependently increased after UVA (P < 0.0005). Autofluorescence was detected only within the anterior stroma of the UVA-treated groups, with no significant difference in the depth of autofluorescence between different UVA exposure levels. The signal intensity was also significantly increased with longer UVA exposure (P < 0.001). Comparing corneal stiffness with autofluorescence intensity revealed a significant correlation between these values (R2 = 0.654; P < 0.0001). Conclusions. The results of this study indicate a significant correlation between corneal stiffening and the intensity of collagen autofluorescence after CXL. This finding suggests that the efficacy of CXL in patients could be monitored by assessing collagen autofluorescence. PMID:21508101
Nonlinear dynamic behavior of simply supported laminated composite plates subjected to blast load
NASA Astrophysics Data System (ADS)
Kazancı, Zafer; Mecitoğlu, Zahit
2008-11-01
This paper deals with the analysis and discussion of nonlinear dynamic response of a laminated composite plate subjected to blast load. Dynamic equations of the plate are derived by the use of the virtual work principle. The geometric nonlinearity effects are taken into account with the von Kármán large deflection theory of thin plates. Approximate solutions for a simply supported plate are assumed for the space domain. The single term approximation functions are selected by considering the nonlinear static deformations of plate, which is obtained using finite element method. The Galerkin Method is used to obtain the nonlinear differential equations in the time domain. The finite difference method is applied to solve the system of coupled nonlinear equations. The results of approximate-numerical analysis are obtained and compared with the literature and finite element results. Good agreement is found for the character and frequencies of vibrations.
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.
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.
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.
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.
Nonlinear systems identification and control via dynamic multitime scales neural networks.
Fu, Zhi-Jun; Xie, Wen-Fang; Han, Xuan; Luo, Wei-Dong
2013-11-01
This paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network (NN) with different timescales. Two NN identifiers are proposed for nonlinear systems identification via dynamic NNs with different timescales including both fast and slow phenomenon. The first NN identifier uses the output signals from the actual system for the system identification. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the NNs. The online identification algorithms for both NN identifier parameters are proposed using Lyapunov function and singularly perturbed techniques. With the identified NN models, two indirect adaptive NN controllers for the nonlinear systems containing slow and fast dynamic processes are developed. For both developed adaptive NN controllers, the trajectory errors are analyzed and the stability of the systems is proved. Simulation results show that the controller based on the second identifier has better performance than that of the first identifier.
Non-linear substructure approach for dynamic analysis of rigid-flexible multibody systems
NASA Astrophysics Data System (ADS)
Liu, A. Q.; Liew, K. M.
1994-04-01
This paper presents a substructure synthesis method (SSM) for nonlinear analysis of multibody systems. The detailed derivation of the equation of motion which takes into account the geometric nonlinear effects of large rotation undergoing small strain elastic deformation is presented. Using the substructure synthesis approach, the equation of motion is condensed through the boundary conditions at the interface between the flexible and rigid substructures. As a result, equations of motion for multi-flexible-body systems including the geometric non-linear effects of large rotation are derived. To demonstrate the applicability and accuracy of the proposed approach, an example of a two-link manipulator was chosen for this presentation. The results using the linear and nonlinear models are presented to highlight the effects of geometric nonlinearities.
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.
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.
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.
Nonlinear kink mode dynamics in circular and noncircular pinches
Wahlberg, C. )
1992-06-01
It is shown that the global (free-boundary) {ital m}=1 kink instability of the ideal, magnetohydrodynamic (MHD) sharp boundary (surface current) pinch is stabilized by nonlinear effects, provided {ital B}{sub {ital e}}{approx lt}1 and {beta}{sub {ital p}}{lt}1, where {beta}{sub {ital p}}=1+{ital B}{sup 2}{sub {ital e}}{minus}{ital B}{sup 2}{sub {ital i}} and {ital B}{sub {ital i}} and {ital B}{sub {ital e}} denote, respectively, the internal and external axial magnetic fields of the pinch, normalized to the poloidal magnetic field. The stabilization has to do with the bending of the interior, frozen'' field lines and associated volume currents induced in the pinch, and does not occur in a pure surface current model, which neglects these currents and only conserves the total magnetic flux through the pinch. It is suggested that the global, helical {ital m}=1 structures observed in various pinch experiments may have to do with the stabilizing mechanism above. The nonlinear stability has been calculated by means of a new approach to the bifurcated equilibria of the helical {ital m}=1 mode, and the method should also be useful in connection with other nonlinear, ideal MHD phenomena. The regime of nonlinear stability above corresponds to intermediate or short wavelengths of the marginal mode ({ital ka}{approx gt}1). In the opposite, long-wavelength regime, the ideal MHD model and the pure surface current model give similar results, predicting nonlinear instability for, e.g., the nearly marginal Kruskal--Shafranov mode in tokamaks, in agreement with previous theories. Effects of mode rotation as well as of a noncircular cross section of the pinch, modeling the Extrap (Fusion Technol. {bold 16}, 7 (1989)) configuration, have also been considered, extending the results of a previous, linear investigation (Phys. Fluids B {bold 2}, 1601 (1990)) to the nonlinear regime.
NASA Technical Reports Server (NTRS)
Changizi, Koorosh
1989-01-01
A nonlinear Lagrangian formulation for the spatial kinematic and dynamic analysis of open chain deformable links consisting of cylindrical joints that connect pairs of flexible links is developed. The special cases of revolute or prismatic joint can also be obtained from the kinematic equations. The kinematic equations are described using a 4x4 matrix method. The configuration of each deformable link in the open loop kinematic chain is identified using a coupled set of relative joint variables, constant geometric parameters, and elastic coordinates. The elastic coordinates define the link deformation with respect to a selected joint coordinate system that is consistent with the kinematic constraints on the boundary of the deformable link. These coordinates can be introduced using approximation techniques such as Rayleigh-Ritz method, finite element technique or any other desired approach. The large relative motion between two neighboring links are defined by a set of joint coordinates which describes the large relative translational and rotational motion between two neighboring joint coordinate systems. The origin of these coordinate systems are rigidly attached to the neighboring links at the joint definition points along the axis of motion.
A Quantitative Adverse Outcome Pathway Linking Aromatase Inhibition in Fathead Minnows with Population DynamicsAn adverse outcome pathway (AOP) is a qualitative description linking a molecular initiating event (MIE) with measureable key events leading to an adverse outcome (AO). ...
Dynamical Casimir effect in microwave cavities containing nonlinear crystals
NASA Astrophysics Data System (ADS)
Dodonov, V. V.
2015-06-01
I consider a possibility of parametric amplification of the microwave vacuum field in a reentrant cavity enclosing a nonlinear crystal whose refractive index is modulated by periodic high-intensity short laser pulses. The main result is that the total number of created ‘Casimir quanta’ depends neither on the laser beam shape, nor on the duration or power of individual pulses, but it depends on the total energy of all the pulses, provided the duration of each pulse is much shorter than the period of field oscillations in the selected resonant mode. The scheme can be feasible if reliable materials with high nonlinear coefficients can be found.
Ion and Electron Dynamics in Nonlinear PIC Simulations
Jolliet, S.; Angelino, P.; Tran, T. M.; McMillan, B. F.; Sauter, O.; Villard, L.; Bottino, A.; Peeters, A. G.; Poli, E.; Hatzky, R.
2006-11-30
ITG and ETG turbulence is investigated with the nonlinear global PIC code ORB5. The large variety of numerical schemes and simulations domains used has sometimes lead to important discrepancies in the transport predictions. In order to discuss these disagreements, emphasis must be put on ways to check the numerical accuracy, such as energy conservation and numerical noise measurement. This paper therefore presents benchmarks, new algorithms and a noise diagnostic. After having demonstrated the numerical quality of our simulations, 2 topics are visited: the unclear role of the parallel nonlinearity and the transport level in ETG turbulence, for which predictions differing by one order of magnitude had been made elsewhere.
Mastering nonlinear flow dynamics for laminar flow control
NASA Astrophysics Data System (ADS)
Sattarzadeh, Sohrab S.; Fransson, Jens H. M.
2016-08-01
A laminar flow control technique based on spanwise mean velocity gradients (SVGs) has recently proven successful in delaying transition in boundary layers. Here we take advantage of a well-known nonlinear effect, namely, the interaction of two oblique waves at high amplitude, to produce spanwise mean velocity variations. Against common belief we are able to fully master the first stage of this nonlinear interaction to generate steady and stable streamwise streaks, which in turn trigger the SVG method. Our experimental results show that the region of laminar flow can be extended by up to 230%.
Mastering nonlinear flow dynamics for laminar flow control.
Sattarzadeh, Sohrab S; Fransson, Jens H M
2016-08-01
A laminar flow control technique based on spanwise mean velocity gradients (SVGs) has recently proven successful in delaying transition in boundary layers. Here we take advantage of a well-known nonlinear effect, namely, the interaction of two oblique waves at high amplitude, to produce spanwise mean velocity variations. Against common belief we are able to fully master the first stage of this nonlinear interaction to generate steady and stable streamwise streaks, which in turn trigger the SVG method. Our experimental results show that the region of laminar flow can be extended by up to 230%. PMID:27627235
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.
Short-pulse dynamics in strongly nonlinear dissipative granular chains.
Rosas, Alexandre; Romero, Aldo H; Nesterenko, Vitali F; Lindenberg, Katja
2008-11-01
We study the energy decay properties of a pulse propagating in a strongly nonlinear granular chain with damping proportional to the relative velocity of the grains. We observe a wave disturbance that at low viscosities consists of two parts exhibiting two entirely different time scales of dissipation. One part is an attenuating solitary wave, dominated by discreteness and nonlinearity effects as in a dissipationless chain, and has the shorter lifetime. The other is a purely dissipative shocklike structure with a much longer lifetime and exists only in the presence of dissipation. The range of viscosities and initial configurations that lead to this complex wave disturbance are explored.
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.
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.
Dynamic nonlinear analysis of shells of revolution (DYNASOR II)
NASA Technical Reports Server (NTRS)
Tillerson, J. R.; Haisler, W. E.
1974-01-01
Equations of motion of shell are solved using Houbolt's numerical procedure with nonlinear terms being moved to right-hand side of equilibrium equations and treated as generalized loads. Program was written in FORTRAN IV for IBM 360 or CDC 6000 series computers.
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.
Nonlinear effects in the dynamics of clouds of bubbles.
Kumar, S; Brennen, C E
1991-02-01
This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.
Self-Consistent Nonlinear Dynamics of Fishbone Oscillations
NASA Astrophysics Data System (ADS)
Candy, J.; Berk, H.; Breizman, B.; Porcelli, F.
1997-11-01
The excitation of the internal kink mode by fast-ions (produced by neutral beam injection or ion-cyclotron resonance heating) has been identified as the mechanism for plasma oscillations known as fishbones. To describe the nonlinear evolution of the fishbone instability, we present a numerical model which includes the detailed linear physics of the bulk plasma (multiple poloidal harmonics of the n=1 mode, q=1 layer physics including plasma resistivity, ion FLR, and ion viscosity) together with the energetic particle current. This current is computed numerically in realistic tokamak geometry, including orbit nonlinearities (i.e., particle trapping), by the δf particle-code FAC. The resulting model is valid over a wide frequency range, and thus unifies the treatment of low-frequency diamagnetic (ω ~ wdia) and high-frequency precessional drift (ω ~ wdhot) fishbones. We compute saturation levels for diamagnetic modes, and also reproduce the nonlinear frequency downshift characteristic of the precessional drift branch during the nonlinear pulse. Orbit loss characteristics for fishbone activity in both JET and PDX discharges are discussed.
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.
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.
Influence of adaptation on the nonlinear dynamics of a system of competing populations
NASA Astrophysics Data System (ADS)
Dimitrova, Zlatinka I.; Vitanov, Nikolay K.
2000-08-01
We investigate the nonlinear dynamics of a system of populations competing for the same limited resource assuming that they can adapt their growth rates and competition coefficients with respect to the number of individuals of each population. The adaptation leads to an enrichment of the nonlinear dynamics of the system which is demonstrated by a discussion of new orbits in the phase space of the system, completely dependent on the adaptation parameters, as well as by an investigation of the influence of the adaptation parameters on the dynamics of a strange attractor of the model system of ODEs.
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.
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.
Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics.
Kashima, Kenji
2016-06-06
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
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
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
Unexpected Course of Nonlinear Cardiac Interbeat Interval Dynamics during Childhood and Adolescence
Cysarz, Dirk; Linhard, Maijana; Edelhäuser, Friedrich; Längler, Alfred; Van Leeuwen, Peter; Henze, Günter; Seifert, Georg
2011-01-01
The fluctuations of the cardiac interbeat series contain rich information because they reflect variations of other functions on different time scales (e.g., respiration or blood pressure control). Nonlinear measures such as complexity and fractal scaling properties derived from 24 h heart rate dynamics of healthy subjects vary from childhood to old age. In this study, the age-related variations during childhood and adolescence were addressed. In particular, the cardiac interbeat interval series was quantified with respect to complexity and fractal scaling properties. The R-R interval series of 409 healthy children and adolescents (age range: 1 to 22 years, 220 females) was analyzed with respect to complexity (Approximate Entropy, ApEn) and fractal scaling properties on three time scales: long-term (slope β of the power spectrum, log power vs. log frequency, in the frequency range 10−4 to 10−2 Hz) intermediate-term (DFA, detrended fluctuation analysis, α2) and short-term (DFA α1). Unexpectedly, during age 7 to 13 years β and ApEn were higher compared to the age <7 years and age >13 years (β: −1.06 vs. −1.21; ApEn: 0.88 vs. 0.74). Hence, the heart rate dynamics were closer to a 1/f power law and most complex between 7 and 13 years. However, DFA α1 and α2 increased with progressing age similar to measures reflecting linear properties. In conclusion, the course of long-term fractal scaling properties and complexity of heart rate dynamics during childhood and adolescence indicates that these measures reflect complex changes possibly linked to hormonal changes during pre-puberty and puberty. PMID:21625487
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.
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
Almaraz, Pablo; Green, Andy J; Aguilera, Eduardo; Rendón, Miguel A; Bustamante, Javier
2012-09-01
1. Understanding the impact of environmental variability on migrating species requires the estimation of sequential abiotic effects in different geographic areas across the life cycle. For instance, waterfowl (ducks, geese and swans) usually breed widely dispersed throughout their breeding range and gather in large numbers in their wintering headquarters, but there is a lack of knowledge on the effects of the sequential environmental conditions experienced by migrating birds on the long-term community dynamics at their wintering sites. 2. Here, we analyse multidecadal time-series data of 10 waterfowl species wintering in the Guadalquivir Marshes (SW Spain), the single most important wintering site for waterfowl breeding in Europe. We use a multivariate state-space approach to estimate the effects of biotic interactions, local environmental forcing during winter and large-scale climate during breeding and migration on wintering multispecies abundance fluctuations, while accounting for partial observability (observation error and missing data) in both population and environmental data. 3. The joint effect of local weather and large-scale climate explained 31·6% of variance at the community level, while the variability explained by interspecific interactions was negligible (<5%). In general, abiotic conditions during winter prevailed over conditions experienced during breeding and migration. Across species, a pervasive and coherent nonlinear signal of environmental variability on population dynamics suggests weaker forcing at extreme values of abiotic variables. 4. Modelling missing observations through data augmentation increased the estimated magnitude of environmental forcing by an average 30·1% and reduced the impact of stochasticity by 39·3% when accounting for observation error. Interestingly however, the impact of environmental forcing on community dynamics was underestimated by an average 15·3% and environmental stochasticity overestimated by 14·1% when
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.
Nonlinear dynamics near the stability margin in rotating pipe flow
NASA Technical Reports Server (NTRS)
Yang, Z.; Leibovich, S.
1991-01-01
The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.
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.
Two-dimensional nonlinear dynamics of four driven vortices
Guzdar, P.N.; Finn, J.M.; Rogalsky, A.V.; Drake, J.F. )
1994-03-01
The interaction of four alternately driven counterrotating vortices in a two-dimensional box, with inpenetrable free-slip boundary conditions in the [ital x] direction and periodic boundary conditions in the [ital y] direction, has been studied numerically. For viscosity above a critical value the nonlinear state consists of four alternately counterrotating vortices. For a lower value of the viscosity the system evolves to a nonlinear steady state consisting of four vortices and shear flow generated by the peeling instability'' [Drake [ital et] [ital al]., Phys. Fluids B 4, 447 (1992)]. For a still lower viscosity the steady-state nonlinear state undergoes a Hopf bifurcation. The periodic state is caused by a secondary instability associated with vortex pairing. However, the vorticity of the shear flow, though periodic, has a definite sign. With a further decrease in the viscosity, a global bifurcation gives rise to a periodic state during which the vorticity of the shear flow changes sign. At even lower viscosity, there is a transition to a steady state, involving dominantly shear flow and a two-vortex state. Finally, this state undergoes a bifurcation to a temporally chaotic state, with the further decrease of viscosity. The results are compared to some recent experiments in fluids with driven vortices [P. Tabeling [ital et] [ital al]., J. Fluid Mech. 215, 511 (1990)].
Strongly nonlinear dynamics of electrolytes in large ac voltages.
Højgaard Olesen, Laurits; Bazant, Martin Z; Bruus, Henrik
2010-07-01
We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features--significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination" since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.
Nonlinear Bubble Dynamics And The Effects On Propagation Through Near-Surface Bubble Layers
NASA Astrophysics Data System (ADS)
Leighton, Timothy G.
2004-11-01
Nonlinear bubble dynamics are often viewed as the unfortunate consequence of having to use high acoustic pressure amplitudes when the void fraction in the near-surface oceanic bubble layer is great enough to cause severe attenuation (e.g. >50 dB/m). This is seen as unfortunate since existing models for acoustic propagation in bubbly liquids are based on linear bubble dynamics. However, the development of nonlinear models does more than just allow quantification of the errors associated with the use of linear models. It also offers the possibility of propagation modeling and acoustic inversions which appropriately incorporate the bubble nonlinearity. Furthermore, it allows exploration and quantification of possible nonlinear effects which may be exploited. As a result, high acoustic pressure amplitudes may be desirable even in low void fractions, because they offer opportunities to gain information about the bubble cloud from the nonlinearities, and options to exploit the nonlinearities to enhance communication and sonar in bubbly waters. This paper presents a method for calculating the nonlinear acoustic cross-sections, scatter, attenuations and sound speeds from bubble clouds which may be inhomogeneous. The method allows prediction of the time dependency of these quantities, both because the cloud may vary and because the incident acoustic pulse may have finite and arbitrary time history. The method can be readily adapted for bubbles in other environments (e.g. clouds of interacting bubbles, sediments, structures, in vivo, reverberant conditions etc.). The possible exploitation of bubble acoustics by marine mammals, and for sonar enhancement, is explored.
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.
Conditioned reinforcement dynamics in three-link chained schedules.
Williams, B A
1997-01-01
In two experiments rats were trained on three-link concurrent-chains schedules of reinforcement. In Experiment 1, additional entries to one terminal link were added during one of the middle links to a baseline schedule that was otherwise equal for the two chains, and, depending on the condition, these additional terminal-link presentations ended either in food or in no food. When food occurred, preference was always in favor of the chain with the additional terminal-link presentations (which also entailed a higher rate of reinforcement). When no food occurred at the end of the additional terminal links, the outcome depended on the nature of the stimuli associated with these additional terminal links. When stimuli different from the reinforced baseline terminal links were used for the no-food terminal links, preference was against the choice alternative that led to the extra periods of extinction. When the same stimulus was used for the two kinds of terminal links, preference was near indifference, that is, significantly greater than when different stimuli were used. In Experiment 2, rats learned repeated reversals of a simultaneous discrimination under a three-link concurrent-chains schedule, in which the food or no-food choice outcomes were delayed until the end of the chain. Different conditions were defined by the point in the chain at which differential stimuli occurred. When the middle and terminal links provided no differential stimuli, discrimination was acquired more slowly than when differential stimuli occurred in both links. When differential stimuli occurred in the middle but not the terminal links, acquisition rates were intermediate. Both experiments together show that the effects of stimuli in a chain schedule are due partly to the time to food correlated with the stimuli and partly to the time to the next conditioned reinforcer in the sequence.
Nonlinear dynamics and control of flexible structures. Annual report, September 1988-August 1989
Bennett, W.H.; Kwatny, H.G.; Blakenship, G.L.; Akhrif, O.
1989-12-12
Basic performance requirements for space-based directed energy weapons involve unprecedented requirements for integrated control of rapid retargeting and precision pointing of space structures. Multibody interactions excite nonlinear couplings which complicate the dynamic response. Attempts to reduce flexure response for such weapon platforms by passive techniques alone may be inadequate due to stringent pointing requirements. The principal objective of the research program is the validation and testing of high precision, nonlinear control of multibody systems with significant structural flexure where interactions arise due to rapid slewing. Dominant nonlinear couplings effecting LOS response have been identified based on a comprehensive model of the nonlinear multibody dynamics of a generic space weapon. The innovative approach to LOS slewing/pointing developed in this study is based on implementation of decoupling (by feedback control) of the principal nonlinear dynamics and structural flexure response. In this study we have focused on the implementation of partial feedback linearization and decoupling and have identified practical conditions for its implementation. A principal contribution of the study is the reconciliation of design of discontinuous control via sliding mode control with partial feedback linearization for rapid slewing of system effective LOS. The report includes extensive simulation and tradeoff studies of nonlinear control implementation of rapid slewing and precision pointing of a generic model of a space-based laser beam expander.
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.
Newton's method: A link between continuous and discrete solutions of nonlinear problems
NASA Technical Reports Server (NTRS)
Thurston, G. A.
1980-01-01
Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.
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
Effects of ADC Nonlinearity on the Spurious Dynamic Range Performance of Compressed Sensing
Tian, Pengwu; Yu, Hongyi
2014-01-01
Analog-to-information converter (AIC) plays an important role in the compressed sensing system; it has the potential to significantly extend the capabilities of conventional analog-to-digital converter. This paper evaluates the impact of AIC nonlinearity on the dynamic performance in practical compressed sensing system, which included the nonlinearity introduced by quantization as well as the circuit non-ideality. It presents intuitive yet quantitative insights into the harmonics of quantization output of AIC, and the effect of other AIC nonlinearity on the spurious dynamic range (SFDR) performance is also analyzed. The analysis and simulation results demonstrated that, compared with conventional ADC-based system, the measurement process decorrelates the input signal and the quantization error and alleviate the effect of other decorrelates of AIC, which results in a dramatic increase in spurious free dynamic range (SFDR). PMID:24895645
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.
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.
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
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
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
Non-linear controls influence functions in an aircraft dynamics simulator
NASA Astrophysics Data System (ADS)
Guerreiro, Nelson M.; Hubbard, James E., Jr.; Motter, Mark A.
2006-03-01
In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft's control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland's continuing study of active wing load control.
Measurement of heart rate variability by methods based on nonlinear dynamics.
Huikuri, Heikki V; Mäkikallio, Timo H; Perkiömäki, Juha
2003-01-01
Heart rate (HR) variability has been conventionally analyzed with time and frequency domain methods, which measure the overall magnitude of R-R interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of HR dynamics by methods based on chaos theory and nonlinear system theory has gained recent interest. This interest is based on observations suggesting that the mechanisms involved in cardiovascular regulation likely interact with each other in a nonlinear way. Furthermore, recent observational studies suggest that some indexes describing nonlinear HR dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional HR variability indexes. In particular, short-term fractal scaling exponent measured by detrended fluctuation analysis method has been shown to predict fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of HR dynamics, which describes the complexity of R-R interval behavior, has provided information on the vulnerability to atrial fibrillation. There are many other nonlinear indexes, eg, Lyapunov exponent and correlation dimensions, which also give information on the characteristics of HR dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of HR behavior in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for future research to expand our knowledge concerning the behavior of cardiovascular oscillations in normal healthy conditions as well as in disease states.
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
Global and local dynamics of an aeroelastic system with a control surface freeplay nonlinearity
NASA Astrophysics Data System (ADS)
Trickey, Stephen T.
2000-11-01
The effects of a freeplay structural nonlinearity on an aeroelastic system comprised of a 2D typical section with an approximation of Theodorsen theory aerodynamics is presented. Particular attention is paid to the stability of a nonlinear aeroelastic response or limit cycle oscillation (LCO). The principal contribution of this work to the field of aeroelasticity lies in the migration of experimental testing and analysis methods from the fields of system identification and nonlinear dynamics to the arena of a nonlinear aeroelastic stability problem. Innovations from the field of nonlinear dynamics include the use of time delay embedded coordinates to reconstruct system dynamics, the use of a Poincare section to prescribe an operating point about which a linear description of the dynamics can be approximated, and the use of a basin of attraction measure to assess initial condition dependence. Two different system identification approaches are taken to generate a linear approximation of the experimental system dynamics about the limit cycle oscillation. A large scale perturbation method using a rotating slotted cylinder gust generator and using a least squares fit of the resulting transient dynamics was shown to be a viable method to ascertain stability information to within the limitations of the experimental setup. A small scale stochastic stability measurement technique using the natural turbulence in a low speed wind tunnel as the stochastic input and a subspace system identification method to estimate the dynamics of the system provided more repeatable and consistent results. Also in this work is a derivation of the analytical model and a description of the experimental model. Typical global dynamic features of the aeroelastic system are presented from both numerical simulation and experiments including periodic limit cycle oscillations (LCO), quasi-periodic responses and chaotic responses.
Strongly nonlinear dynamics of electrolytes in large ac voltages
NASA Astrophysics Data System (ADS)
Højgaard Olesen, Laurits; Bazant, Martin Z.; Bruus, Henrik
2010-07-01
We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features—significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of “ac capacitive desalination” since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan
2016-01-01
In this wIn 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.ork, we explore finite
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.
Non-linear dynamics of a spur gear pair
NASA Technical Reports Server (NTRS)
Kahraman, A.; Singh, R.
1990-01-01
The backlash nonlinearity excited primarily by transmission error between spur gear pairs is studied for both external and internal excitations. The digital simulation technique and the method of harmonic balance are used to develop steady state solutions for the internal sinuosidal excitations. The analytic predictions agreed well with available experimental data. Digital simulation is used to observe that at the chaotic and subharmonic resonances may exist in a gear pair depending on the mean or design load, mean to alternating force ratio, damping, and backlash.
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.
Dynamics of parabolic problems with memory. Subcritical and critical nonlinearities
NASA Astrophysics Data System (ADS)
Li, Xiaojun
2016-08-01
In this paper, we study the long-time behavior of the solutions of non-autonomous parabolic equations with memory in cases when the nonlinear term satisfies subcritical and critical growth conditions. In order to do this, we show that the family of processes associated to original systems with heat source f(x, t) being translation bounded in Lloc 2 ( R ; L 2 ( Ω ) ) is dissipative in higher energy space M α , 0 < α ≤ 1, and possesses a compact uniform attractor in M 0 .
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.
[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.
ERIC Educational Resources Information Center
Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng
2010-01-01
Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…
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
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)
Zausner, Tobi
Chaos theory may provide models for creativity and for the personality of the artist. A collection of speculative hypotheses examines the connection between art and such fundamentals of non-linear dynamics as iteration, dissipative processes, open systems, entropy, sensitivity to stimuli, autocatalysis, subsystems, bifurcations, randomness, unpredictability, irreversibility, increasing levels of organization, far-from-equilibrium conditions, strange attractors, period doubling, intermittency and self-similar fractal organization. Non-linear dynamics may also explain why certain individuals suffer mental disorders while others remain intact during a lifetime of sustained creative output.
Li, Zhaoying; Zhou, Wenjie; Liu, Hao
2016-09-01
This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach.
Li, Zhaoying; Zhou, Wenjie; Liu, Hao
2016-09-01
This paper addresses the nonlinear robust tracking controller design problem for hypersonic vehicles. This problem is challenging due to strong coupling between the aerodynamics and the propulsion system, and the uncertainties involved in the vehicle dynamics including parametric uncertainties, unmodeled model uncertainties, and external disturbances. By utilizing the feedback linearization technique, a linear tracking error system is established with prescribed references. For the linear model, a robust controller is proposed based on the signal compensation theory to guarantee that the tracking error dynamics is robustly stable. Numerical simulation results are given to show the advantages of the proposed nonlinear robust control method, compared to the robust loop-shaping control approach. PMID:27132149
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
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 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.
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 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.
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.
Nonlinear dynamics of domain walls with cross-ties
NASA Astrophysics Data System (ADS)
Dubovik, M. N.; Zverev, V. V.; Filippov, B. N.
2016-07-01
The dynamic behavior of a domain wall with cross-ties is analyzed on the basis of micromagnetic simulation with exact allowance for all main (exchange, magnetoanisotropic, and magnetostatic) interactions in thin magnetically uniaxial ferromagnetic films with planar anisotropy. It is found that the peculiarities of motion of such domain walls are closely related to the behavior of topological defects in the magnetization distribution (generation, motion, and annihilation of vortex-antivortex pairs on the film surface and Bloch points). We observe three different regimes of motion (stationary, periodic, and turbulent regimes), each of which is realized in a certain range of fields oriented along the easy magnetization axis. It is shown that the experimentally observed dynamic bends of the walls with cross-ties are determined by the type of motion of vortices and antivortices. The velocities of domain walls in different regimes are calculated, and the dynamic configurations of the magnetization and existing dynamic transitions between them are investigated.
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.
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
Coupled nonlinear flight dynamics, aeroelasticity, and control of very flexible aircraft
NASA Astrophysics Data System (ADS)
Shearer, Christopher M.
Flight dynamics and control of rigid aircraft motion coupled with linearized structural dynamics has been studied for several decades. However, new requirements for very flexible aircraft are challenging the validity of most rigid body coupled linearized structural motion formulations, due to the presence of large elastic motions. This dissertation presents, the flight dynamics, integration, and control of the six degree-of-freedom equations of motion of a reference point on a very flexible aircraft coupled with the aeroelastic equations which govern the geometrically nonlinear structural response of the vehicle. A low-order strain-based nonlinear structural analysis coupled with unsteady finite-state potential flow aerodynamics form the basis for the aeroelastic formulation. The nonlinear beam structural model is based upon the finite strain approach. Kinematic differential equations are used to provide orientation and position of the fixed reference point. The resulting governing differential equations are non-linear, first- and second-order differential algebraic equations and provide a low-order complete nonlinear aircraft formulation. The resulting equations are integrated using an implicit Modified Newmark Method. The method incorporates both first- and second-order nonlinear equations without the necessity of transforming second-order equations to first-order form. The method also incorporates a Newton-Raphson sub-iteration scheme to reduce residual error. Due to the inherent flexibility of these aircraft, the low order structural modes couple directly with the rigid body modes. This creates a system which cannot be separated as in traditional control schemes. Trajectory control techniques are developed based upon a combination of linear and nonlinear inner-loop tracking and an outer-loop nonlinear transformation from desired trajectories to reference frame velocities. Numerical simulations are presented validating the proposed integration scheme and the
Adaptive robust stabilisation for a class of uncertain nonlinear time-delay dynamical systems
NASA Astrophysics Data System (ADS)
Wu, Hansheng
2013-02-01
The problem of adaptive robust stabilisation is considered for a class of uncertain nonlinear dynamical systems with multiple time-varying delays. It is assumed that the upper bounds of the nonlinear delayed state perturbations are unknown and that the time-varying delays are any non-negative continuous and bounded functions which do not require that their derivatives have to be less than one. In particular, it is only required that the nonlinear uncertainties, which can also include time-varying delays, are bounded in any non-negative nonlinear functions which are not required to be known for the system designer. For such a class of uncertain nonlinear time-delay systems, a new method is presented whereby a class of continuous memoryless adaptive robust state feedback controllers with a rather simpler structure is proposed. It is also shown that the solutions of uncertain nonlinear time-delay systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. Finally, as an application, an uncertain nonlinear time-delay ecosystem with two competing species is given to demonstrate the validity of the results.
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.
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.
Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics.
Bhattacharyya, Indrajit; Priyadarshi, Shekhar; Goswami, Debabrata
2009-02-01
We apply ultrafast single beam Z-scan technique to measure saturation absorption coefficients and nonlinear-refraction coefficients of primary alcohols at 1560 nm. The nonlinear effects result from vibronic transitions and cubic nonlinear-refraction. To measure the pure total third-order nonlinear susceptibility, we removed thermal effects with a frequency optimized optical-chopper. Our measurements of thermal-relaxation dynamics of alcohols, from 1560 nm thermal lens pump and 780 nm probe experiments revealed faster and slower thermal-relaxation timescales, respectively, from conduction and convection. The faster timescale accurately predicts thermal-diffusivity, which decreases linearly with alcohol chain-lengths since thermal-relaxation is slower in heavier molecules. The relation between thermal-diffusivity and alcohol chain-length confirms structure-property relationship.
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.
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.
Assessment of gait nonlinear dynamics by inhomogeneous point-process models.
Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo
2014-01-01
Point-process linear models of stride intervals have been recently proven to provide a unique characterization of human gait dynamics through instantaneous time domain features. In this study we propose novel instantaneous measures characterizing nonlinear gait dynamics using a quadratic autoregressive inhomogeneous point-process model recently devised for the instantaneous assessment of physiological, natural, and physical discrete dynamical systems. Our mathematical framework accounts for long-term information given by the past events of non-stationary non-Gaussian time series, expressed by a Laguerre expansion of the Wiener-Volterra terms. Here, we present a study of gait variability from data gathered from physionet.org, including 15 recordings from young and elderly healthy volunteers, and patients with Parkinson's disease. Results show that our instantaneous polyspectral characterization provides an informative tracking of the inherent nonlinear dynamics of human gait, which is significantly affected by aging and locomotor disabilities.
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
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.
Stošovic, Miona V Andrejevic; Litovski, Vanco B
2013-11-01
Simulation is indispensable during the design of many biomedical prostheses that are based on fundamental electrical and electronic actions. However, simulation necessitates the use of adequate models. The main difficulties related to the modeling of such devices are their nonlinearity and dynamic behavior. Here we report the application of recurrent artificial neural networks for modeling of a nonlinear, two-terminal circuit equivalent to a specific implantable hearing device. The method is general in the sense that any nonlinear dynamic two-terminal device or circuit may be modeled in the same way. The model generated was successfully used for simulation and optimization of a driver (operational amplifier)-transducer ensemble. This confirms our claim that in addition to the proper design and optimization of the hearing actuator, optimization in the electronic domain, at the electronic driver circuit-to-actuator interface, should take place in order to achieve best performance of the complete hearing aid.
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.
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.
Interpretation of nonlinear effects on the dynamic response of a TLP
Palk, I.; Mekha, B.B.; Powers, E.J.; Roesset, J.M.
1995-12-31
To determine the nature and importance of various nonlinear effects on the dynamic response of a TLP, a number of parametric studies have been conducted determining the dynamic response of a simplified model to wave and current action. The results of these analyses were then used to compute linear, quadratic and cubic transfer functions, based on Volterra series, to assess the type of nonlinearity which controls the response over the different frequency ranges. The nonlinearities result in the existence of response amplitudes and energy at frequencies which are outside of the range of the excitation frequencies but which correspond to the natural frequencies of the TLP in surge, heave and pitch. They are of different order (quadratic or cubic) over the different frequency ranges (below or above the wave frequency range).
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.
Nonlinear dynamics of flexible rotor supported on the gas foil journal bearings
NASA Astrophysics Data System (ADS)
Bhore, Skylab P.; Darpe, Ashish K.
2013-09-01
Investigation on nonlinear dynamics of a flexible rotor supported on the gas foil journal bearings is attempted. A time domain orbit simulation is carried out that couples the equations of rotor motion, unsteady Reynolds equation and foil deformation. The unsteady Reynolds equation is solved using control volume formulation with power law hybrid scheme and Gauss-Seidel method. The nonlinear dynamic response is analyzed using disc center and journal center trajectories, Poincaré maps, Fast Fourier transforms and bifurcation plots. The analysis is carried out for different system parameters, namely, rotating speed, unbalance eccentricity, compliance and loss factor of gas foil bearing. The analysis reveals highly nonlinear behavior with periodic, multi-periodic and quasiperiodic motion of the disc and the journal center. The present analysis can be useful in designing and selection of suitable operating parameters of rotor bearing system.
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
NASA Astrophysics Data System (ADS)
Tewatia, D. K.; Tolakanahalli, R. P.; Paliwal, B. R.; Tomé, W. A.
2011-04-01
The underlying requirements for successful implementation of any efficient tumour motion management strategy are regularity and reproducibility of a patient's breathing pattern. The physiological act of breathing is controlled by multiple nonlinear feedback and feed-forward couplings. It would therefore be appropriate to analyse the breathing pattern of lung cancer patients in the light of nonlinear dynamical system theory. The purpose of this paper is to analyse the one-dimensional respiratory time series of lung cancer patients based on nonlinear dynamics and delay coordinate state space embedding. It is very important to select a suitable pair of embedding dimension 'm' and time delay 'τ' when performing a state space reconstruction. Appropriate time delay and embedding dimension were obtained using well-established methods, namely mutual information and the false nearest neighbour method, respectively. Establishing stationarity and determinism in a given scalar time series is a prerequisite to demonstrating that the nonlinear dynamical system that gave rise to the scalar time series exhibits a sensitive dependence on initial conditions, i.e. is chaotic. Hence, once an appropriate state space embedding of the dynamical system has been reconstructed, we show that the time series of the nonlinear dynamical systems under study are both stationary and deterministic in nature. Once both criteria are established, we proceed to calculate the largest Lyapunov exponent (LLE), which is an invariant quantity under time delay embedding. The LLE for all 16 patients is positive, which along with stationarity and determinism establishes the fact that the time series of a lung cancer patient's breathing pattern is not random or irregular, but rather it is deterministic in nature albeit chaotic. These results indicate that chaotic characteristics exist in the respiratory waveform and techniques based on state space dynamics should be employed for tumour motion management.
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
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.
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.
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
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)…
A Nonlinear Discrete Dynamical Model for Transcriptional Regulation: Construction and Properties
Goutsias, John; Kim, Seungchan
2004-01-01
Transcriptional regulation is a fundamental mechanism of living cells, which allows them to determine their actions and properties, by selectively choosing which proteins to express and by dynamically controlling the amounts of those proteins. In this article, we revisit the problem of mathematically modeling transcriptional regulation. First, we adopt a biologically motivated continuous model for gene transcription and mRNA translation, based on first-order rate equations, coupled with a set of nonlinear equations that model cis-regulation. Then, we view the processes of transcription and translation as being discrete, which, together with the need to use computational techniques for large-scale analysis and simulation, motivates us to model transcriptional regulation by means of a nonlinear discrete dynamical system. Classical arguments from chemical kinetics allow us to specify the nonlinearities underlying cis-regulation and to include both activators and repressors as well as the notion of regulatory modules in our formulation. We show that the steady-state behavior of the proposed discrete dynamical system is identical to that of the continuous model. We discuss several aspects of our model, related to homeostatic and epigenetic regulation as well as to Boolean networks, and elaborate on their significance. Simulations of transcriptional regulation of a hypothetical metabolic pathway illustrate several properties of our model, and demonstrate that a nonlinear discrete dynamical system may be effectively used to model transcriptional regulation in a biologically relevant way. PMID:15041638
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...
Larger, Laurent; Goedgebuer, Jean-Pierre; Erneux, Thomas
2004-03-01
A subcritical Hopf bifurcation in a dynamical system modeled by a scalar nonlinear delay differential equation is studied theoretically and experimentally. The subcritical Hopf bifurcation leads to a significant domain of bistability where stable steady and time-periodic states coexist.
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.
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.
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).
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…
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.
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.
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 Actuation Dynamics of Driven Casimir Oscillators with Rough Surfaces
NASA Astrophysics Data System (ADS)
Broer, Wijnand; Waalkens, Holger; Svetovoy, Vitaly B.; Knoester, Jasper; Palasantzas, George
2015-11-01
At separations below 100 nm, Casimir-Lifshitz forces strongly influence the actuation dynamics of microelectromechanical systems (MEMS) in dry vacuum conditions. For a micron-size plate oscillating near a surface, which mimics a frequently used setup in experiments with MEMS, we show that the roughness of the surfaces significantly influences the qualitative dynamics of the oscillator. Via a combination of analytical and numerical methods, it is shown that surface roughness leads to a clear increase of initial conditions associated with chaotic motion, that eventually lead to stiction between the surfaces. Since stiction leads to a malfunction of MEMS oscillators, our results are of central interest for the design of microdevices. Moreover, stiction is of significance for fundamentally motivated experiments performed with MEMS.
Nonlinear problems in flight dynamics involving aerodynamic bifurcations
NASA Technical Reports Server (NTRS)
Tobak, M.; Chapman, G. T.
1985-01-01
Aerodynamic bifurcation is defined as the replacement of an unstable equilibrium flow by a new stable equilibrium flow at a critical value of a parameter. A mathematical model of the aerodynamic contribution to the aircraft's equations of motion is amended to accommodate aerodynamic bifurcations. Important bifurcations such as, the onset of large-scale vortex-shedding are defined. The amended mathematical model is capable of incorporating various forms of aerodynamic responses, including those associated with dynamic stall of airfoils.
NASA Astrophysics Data System (ADS)
Wang, X.; Zheng, G. T.
2016-02-01
A simple and general Equivalent Dynamic Stiffness Mapping technique is proposed for identifying the parameters or the mathematical model of a nonlinear structural element with steady-state primary harmonic frequency response functions (FRFs). The Equivalent Dynamic Stiffness is defined as the complex ratio between the internal force and the displacement response of unknown element. Obtained with the test data of responses' frequencies and amplitudes, the real and imaginary part of Equivalent Dynamic Stiffness are plotted as discrete points in a three dimensional space over the displacement amplitude and the frequency, which are called the real and the imaginary Equivalent Dynamic Stiffness map, respectively. These points will form a repeatable surface as the Equivalent Dynamic stiffness is only a function of the corresponding data as derived in the paper. The mathematical model of the unknown element can then be obtained by surface-fitting these points with special functions selected by priori knowledge of the nonlinear type or with ordinary polynomials if the type of nonlinearity is not pre-known. An important merit of this technique is its capability of dealing with strong nonlinearities owning complicated frequency response behaviors such as jumps and breaks in resonance curves. In addition, this technique could also greatly simplify the test procedure. Besides there is no need to pre-identify the underlying linear parameters, the method uses the measured data of excitation forces and responses without requiring a strict control of the excitation force during the test. The proposed technique is demonstrated and validated with four classical single-degree-of-freedom (SDOF) numerical examples and one experimental example. An application of this technique for identification of nonlinearity from multiple-degree-of-freedom (MDOF) systems is also illustrated.
Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology
NASA Technical Reports Server (NTRS)
Strganac, Thomas W.; Payne, Debbie Flowers; Biskup, Bruce A.; Letton, Alan
1995-01-01
Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.
Dynamically Tuned Blade Pitch Links for Vibration Reduction
NASA Technical Reports Server (NTRS)
Milgram, Judah; Chopra, Inderjit; Kottapalli, Sesi
1994-01-01
A passive vibration reduction device in which the conventional main rotor blade pitch link is replaced by a spring/damper element is investigated using a comprehensive rotorcraft analysis code. A case study is conducted for a modern articulated helicopter main rotor. Correlation of vibratory pitch link loads with wind tunnel test data is satisfactory for lower harmonics. Inclusion of unsteady aerodynamics had little effect on the correlation. In the absence of pushrod damping, reduction in pushrod stiffness from the baseline value had an adverse effect on vibratory hub loads in forward flight. However, pushrod damping in combination with reduced pushrod stiffness resulted in modest improvements in fixed and rotating system hub loads.
NASA Astrophysics Data System (ADS)
Schuch, Dieter
2014-04-01
Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.
Comparison of dynamical approximation schemes for nonlinear gravitaional clustering
NASA Technical Reports Server (NTRS)
Melott, Adrian L.
1994-01-01
We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.
Nonlinear Dynamics and Nucleation Kinetics in Near-Critical Liquids
NASA Technical Reports Server (NTRS)
Patashinski, Alexander Z.; Ratner, Mark A.; Pines, Vladimir
1996-01-01
The objective of our study is to model the nonlinear behavior of a near-critical liquid following a rapid change of the temperature and/or other thermodynamic parameters (pressure, external electric or gravitational field). The thermodynamic critical point is manifested by large, strongly correlated fluctuations of the order parameter (particle density in liquid-gas systems, concentration in binary solutions) in the critical range of scales. The largest critical length scale is the correlation radius r(sub c). According to the scaling theory, r(sub c) increases as r(sub c) = r(sub 0)epsilon(exp -alpha) when the nondimensional distance epsilon = (T - T(sub c))/T(sub c) to the critical point decreases. The normal gravity alters the nature of correlated long-range fluctuations when one reaches epsilon approximately equal to 10(exp -5), and correspondingly the relaxation time, tau(r(sub c)), is approximately equal to 10(exp -3) seconds; this time is short when compared to the typical experimental time. Close to the critical point, a rapid, relatively small temperature change may perturb the thermodynamic equilibrium on many scales. The critical fluctuations have a hierarchical structure, and the relaxation involves many length and time scales. Above the critical point, in the one-phase region, we consider the relaxation of the liquid following a sudden temperature change that simultaneously violates the equilibrium on many scales. Below T(sub c), a non-equilibrium state may include a distribution of small scale phase droplets; we consider the relaxation of such a droplet following a temperature change that has made the phase of the matrix stable.
Nonlinearity in the rotational dynamics of Haidinger's brushes
NASA Astrophysics Data System (ADS)
Rothmayer, Mark; Dultz, Wolfgang; Frins, Erna; Zhan, Qiwen; Tierney, Dennis; Schmitzer, Heidrun
2007-10-01
Haidinger's brushes are an entoptic effect of the human visual system that enables us to detect polarized light. However, individual perceptions of Haidinger's brushes can vary significantly. We find that the birefringence of the cornea influences the rotational motion and the contrast of Haidinger's brushes and may offer an explanation for individual differences. We have devised an experimental setup to simulate various phase shifts of the cornea and found a switching effect in the rotational dynamics of Haidinger's brushes. In addition, age related macular degeneration reduces the polarization effect of the macula and thus also leads to changes in the brush pattern.
NASA Astrophysics Data System (ADS)
Kunert, James Michael
Networks of many nonlinearly-coupled dynamical components are ubiquitous in the physical sciences, but often difficult to characterize. However, their dynamics are often low-dimensional, being dominated by a few functional, coherent patterns. We wish to understand: (1) How do nonlinear networks generate functional responses? (2) What role does the network's structure play in generating such responses? (3) To what extent are the network dynamics robust to network damage? Towards these ends we model the C. elegans neuronal network, the connectivity of which is known. Chapter 2 constructs a full-Connectome dynamical model which can generate proxies for known behaviors (specifically demonstrating a proxy for forward motion). Chapter 3 explores the input space via interpretable bifurcation diagrams. The highly multistable dynamics give rise to long transient timescales (orders of magnitude longer than intrinsic nodal timescales). Chapter 4 models network injuries, which significantly distort dynamics. We develop a metric to quantify the injury level and help predict an injury's functional outcome. Chapter 5 uses Dynamic Mode Decomposition to relate connectivity to low-dimensional dynamical structure. In the process, we demonstrate consistency with proprioception-driven locomotion which is facilitated by network structure.
Nonlinear dynamics of three-magnon process driven by ferromagnetic resonance in yttrium iron garnet
Cunha, R. O.; Holanda, J.; Azevedo, A.; Rezende, S. M.; Vilela-Leão, L. H.; Rodríguez-Suárez, R. L.
2015-05-11
We report an investigation of the dynamics of the three-magnon splitting process associated with the ferromagnetic resonance (FMR) in films of the insulating ferrimagnet yttrium iron garnet (YIG). The experiments are performed with a 6 μm thick YIG film close to a microstrip line fed by a microwave generator operating in the 2–6 GHz range. The magnetization precession is driven by the microwave rf magnetic field perpendicular to the static magnetic field, and its dynamics is observed by monitoring the amplitude of the FMR absorption peak. The time evolution of the amplitude reveals that if the frequency is lowered below a critical value of 3.3 GHz, the FMR mode pumps two magnons with opposite wave vectors that react back on the FMR, resulting in a nonlinear dynamics of the magnetization. The results are explained by a model with coupled nonlinear equations describing the time evolution of the magnon modes.
Changes in cytoskeletal dynamics and nonlinear rheology with metastatic ability in cancer cell lines
NASA Astrophysics Data System (ADS)
Coughlin, Mark F.; Fredberg, Jeffrey J.
2013-12-01
Metastatic outcome is impacted by the biophysical state of the primary tumor cell. To determine if changes in cancer cell biophysical properties facilitate metastasis, we quantified cytoskeletal biophysics in well-characterized human skin, bladder, prostate and kidney cell line pairs that differ in metastatic ability. Using magnetic twisting cytometry with optical detection, cytoskeletal dynamics was observed through spontaneous motion of surface bound marker beads and nonlinear rheology was characterized through large amplitude forced oscillations of probe beads. Measurements of cytoskeletal dynamics and nonlinear rheology differed between strongly and weakly metastatic cells. However, no set of biophysical parameters changed systematically with metastatic ability across all cell lines. Compared to their weakly metastatic counterparts, the strongly metastatic kidney cancer cells exhibited both increased cytoskeletal dynamics and stiffness at large deformation which are thought to facilitate the process of vascular invasion.
Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation.
Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun
2016-08-01
In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system. PMID:27586626
Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation
NASA Astrophysics Data System (ADS)
Wen, Shao-Fang; Shen, Yong-Jun; Wang, Xiao-Na; Yang, Shao-Pu; Xing, Hai-Jun
2016-08-01
In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system.
Small parametric model for nonlinear dynamics of large scale cyclogenesis with wind speed variations
NASA Astrophysics Data System (ADS)
Erokhin, Nikolay; Shkevov, Rumen; Zolnikova, Nadezhda; Mikhailovskaya, Ludmila
2016-07-01
It is performed a numerical investigation of a self consistent small parametric model (SPM) for large scale cyclogenesis (RLSC) by usage of connected nonlinear equations for mean wind speed and ocean surface temperature in the tropical cyclone (TC). These equations may describe the different scenario of temporal dynamics of a powerful atmospheric vortex during its full life cycle. The numerical calculations have shown that relevant choice of SPMTs incoming parameters allows to describe the seasonal behavior of regional large scale cyclogenesis dynamics for a given number of TC during the active season. It is shown that SPM allows describe also the variable wind speed variations inside the TC. Thus by usage of the nonlinear small parametric model it is possible to study the features of RLSCTs temporal dynamics during the active season in the region given and to analyze the relationship between regional cyclogenesis parameters and different external factors like the space weather including the solar activity level and cosmic rays variations.
Nonlinear dynamics of three-magnon process driven by ferromagnetic resonance in yttrium iron garnet
NASA Astrophysics Data System (ADS)
Cunha, R. O.; Holanda, J.; Vilela-Leão, L. H.; Azevedo, A.; Rodríguez-Suárez, R. L.; Rezende, S. M.
2015-05-01
We report an investigation of the dynamics of the three-magnon splitting process associated with the ferromagnetic resonance (FMR) in films of the insulating ferrimagnet yttrium iron garnet (YIG). The experiments are performed with a 6 μm thick YIG film close to a microstrip line fed by a microwave generator operating in the 2-6 GHz range. The magnetization precession is driven by the microwave rf magnetic field perpendicular to the static magnetic field, and its dynamics is observed by monitoring the amplitude of the FMR absorption peak. The time evolution of the amplitude reveals that if the frequency is lowered below a critical value of 3.3 GHz, the FMR mode pumps two magnons with opposite wave vectors that react back on the FMR, resulting in a nonlinear dynamics of the magnetization. The results are explained by a model with coupled nonlinear equations describing the time evolution of the magnon modes.
Nonlinear dynamics of homeothermic temperature control in skunk cabbage, Symplocarpus foetidus
NASA Astrophysics Data System (ADS)
Ito, Takanori; Ito, Kikukatsu
2005-11-01
Certain primitive plants undergo orchestrated temperature control during flowering. Skunk cabbage, Symplocarpus foetidus, has been demonstrated to maintain an internal temperature of around 20 °C even when the ambient temperature drops below freezing. However, it is not clear whether a unique algorithm controls the homeothermic behavior of S. foetidus, or whether such an algorithm might exhibit linear or nonlinear thermoregulatory dynamics. Here we report the underlying dynamics of temperature control in S. foetidus using nonlinear forecasting, attractor and correlation dimension analyses. It was shown that thermoregulation in S. foetidus was governed by low-dimensional chaotic dynamics, the geometry of which showed a strange attractor named the “Zazen attractor.” Our data suggest that the chaotic thermoregulation in S. foetidus is inherent and that it is an adaptive response to the natural environment.
NASA Astrophysics Data System (ADS)
Kalmykov, Yuri P.; Titov, Serguey V.; Coffey, William T.
2015-11-01
The nonlinear ac stationary response of uniaxial paramagnets and superparamagnets—nanoscale solids or clusters with spin number S ˜100-104 —in superimposed uniform ac and dc bias magnetic fields of arbitrary strength, each applied along the easy axis of magnetization, is determined by solving the evolution equation for the reduced density matrix represented as a finite set of three-term differential-recurrence relations for its diagonal matrix elements. The various harmonic components arising from the nonlinear response of the magnetization, dynamic magnetic hysteresis loops, etc., are then evaluated via matrix continued fractions indicating a pronounced dependence of the response on S arising from the quantum spin dynamics, which differ markedly from the magnetization dynamics of classical nanomagnets. In the linear response approximation, the results concur with existing solutions.
High-Dynamic Range Fiberoptic Links for Antenna Remoting Applications
NASA Technical Reports Server (NTRS)
Gee, C. M.; Chen, T. R.; Chen, P. C.; Paslaski, J.; Lau, K. Y.; Logan, R. T.; Calhoun, M. D.; Lutes, G.
1993-01-01
In recent years, the performance and cost effectiveness of analog fiberoptic communication systems have improved so that many applications including antenna remoting which requires high dynamic range can now benefit from the many advantages of fiber optics.
Nonlinear dynamics of the heartbeat I. The AV junction: Passive conduit or active oscillator?
NASA Astrophysics Data System (ADS)
West, Bruce J.; Goldberger, Ary L.; Rovner, Galina; Bhargava, Valmik
1985-10-01
Under physiologic conditions, the AV junction is traditionally regarded as a passive conduit for the conduction of impulses from the atria to the ventricles. An alternative view, namely that subsidiary pacemakers play an active role in normal electrophysiologic dynamics during sinus rhythm, has been suggested based on nonlinear models of cardiac oscillators. A central problem has been the development of a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics. We use equations describing an analog electrical circuit with an external d.c. voltage source ( V0) and two nonlinear oscillators with intrinsic frequencies in the ratio of 3:2, comparable to the SA node and AV junction rates. The oscillators are coupled by means of a resistor. 1:1 (SA:AV) phase-locking of the oscillators occurs over a critical range of V0. Externally driving the SA oscillator at increasing rates results in 3:2 AV Wenckebach periodicity and a 2:1 AV block. These findings appear with no assumptions about conduction time or refractoriness. This dynamical model is consistent with the new interpretation that normal sinus rhythm may represent 1:1 coupling of two or more active nonlinear oscillators and also accounts for the appearance of an AV block with critical changes in a single parameter such as the pacing rate.
Influence of boron concentration on nonlinear absorption and ultrafast dynamics in GaSe crystals
NASA Astrophysics Data System (ADS)
Karatay, Ahmet; Yuksek, Mustafa; Ertap, Hüseyin; Mak, Ali Kemal; Karabulut, Mevlüt; Elmali, Ayhan
2016-10-01
The nonlinear absorption properties and ultrafast dynamics of pure and boron doped GaSe crystals have been studied by open aperture Z-scan and ultrafast pump probe spectroscopy techniques. All of the studied crystals showed nonlinear absorption under 100 fs pulse duration and 1200 nm wavelength excitations. Nonlinear absorption coefficients increase with increasing the doping ratio of boron atoms in crystals. These findings indicate that free carrier density increase with boron doping and this behavior leads to excited state absorption. Second harmonic generation signals of crystals were detected with the help of fiber optic spectrometer. The blue shift in the energy of the second harmonic generation signals was observed in boron doped crystals. Ultrafast pump probe experiments indicate that the excited state absorption signal with long lifetime observed for undoped GaSe crystal switches to bleach signal for boron doped GaSe crystals at 625 nm probe wavelength. The effects of increasing doping ratio were observed on ultrafast dynamics as a switching time changes. Our experimental results indicate that it is possible to control nonlinear absorption properties, frequency conversion and ultrafast dynamics of GaSe crystal by changing boron doping ratio.
Nonlinear dynamics and control of flexible structures. Annual report, September 1987-August 1988
Bennett, W.H.; Kwatny, H.G.; Blakenship, G.L.; Akhrif, O.
1988-11-15
The unprecedented requirements for rapid retargeting and precision pointing for spaced-based directed energy weapon platforms is the prime driver behind the reported modeling and control study. The combination of such requirements demand a comprehensive dynamic model of the nonlinear multibody dynamics of typical space platforms for such weapon including the interaction platform structural flexure effecting principal weapon system effective Line-Of-Sight. This report describes the first year effort of a three year project which focuses on: (1) the development of comprehensive; generic nonlinear dynamical models for typical space-based plat forms, (2) the development of high performance, nonlinear control laws for rapid slewing and precesion pointing of primary weapon system payload apertures, and (3) the design of a series of laboratory experiments to verify and test the control laws developed. The validation of the analytical models and the required control theory for the resulting class of nonlinear system is described in this report. Simulation results are given for a simplified benchmark model of a space-based laser slewing control and consideration for compensation for structural flexure effecting optical LOS using optical steering mirrors is discussed.
Non-linear dynamic modeling of an automobile hydraulic active suspension system
NASA Astrophysics Data System (ADS)
Mrad, R. Ben; Levitt, J. A.; Fassois, S. D.
1994-09-01
Motived by the strong need for realistically describing the dynamical behaviour of automotive systems through adequate mathematical models, a computer-stimulation-suitable non-linear quarter-car model of a hydraulic active suspension system is developed. Unlike previously available linear models characterised by idealised actuator and component behaviour, the developed model accounts for the dynamics of the main system components, including the suspension bushing, pump, accumulator, power and bypass valves, and hydraulic actuator, while also incorporating preliminary versions of the system controllers. Significant system characteristics, such as non-linear pressure-flow relationships, fluid compressibility, pump and valve non-linearities, leakages, as well as Coulomb friction, are also explicitly accounted for, and the underpinning assumptions are discussed. Simulation results obtained by exercising the model provide insight into the system behavior, illustrate the importance of the actuator/component dynamics and their associated non-linearities and reveal the inadequacy of the idealised linear models in capturing the system behaviour, demonstrate specific effects of valve leakage and fluid bulk modulus, are in qualitative agreement with experimental measurements, and stress the need for proper control law design and tuning. The developed model is particularly suitable for analysis, design, control law optimisation, and diagnostic strategies development.
Nonlinear dynamics of C-terminal tails in cellular microtubules
NASA Astrophysics Data System (ADS)
Sekulic, Dalibor L.; Sataric, Bogdan M.; Zdravkovic, Slobodan; Bugay, Aleksandr N.; Sataric, Miljko V.
2016-07-01
The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico, as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano-electrical waves elicited in the rows of very flexible C-terminal tails which decorate the outer surface of each microtubule. The fact that C-terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule-associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink-waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process.
Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection
RINZEL, JOHN; HUGUET, GEMMA
2014-01-01
We review some widely studied models and firing dynamics for neuronal systems, both at the single cell and network level, and dynamical systems techniques to study them. In particular, we focus on two topics in mathematical neuroscience that have attracted the attention of mathematicians for decades: single-cell excitability and bursting. We review the mathematical framework for three types of excitability and onset of repetitive firing behavior in single-neuron models and their relation with Hodgkin’s classification in 1948 of repetitive firing properties. We discuss the mathematical dissection of bursting oscillations using fast/slow analysis and demonstrate the approach using single-cell and mean-field network models. Finally, we illustrate the properties of Type III excitability in which case repetitive firing for constant or slow inputs is absent. Rather, firing is in response only to rapid enough changes in the stimulus. Our case study involves neuronal computations for sound localization for which neurons in the auditory brain stem perform extraordinarily precise coincidence detection with submillisecond temporal resolution. PMID:25392560
Non-linear dynamics of the complement system activation.
Korotaevskiy, Andrey A; Hanin, Leonid G; Khanin, Mikhail A
2009-12-01
The complement system (CS) plays a prominent role in the immune defense. The goal of this work is to study the dynamics of activation of the classic and alternative CS pathways based on the method of mathematical modeling. The principal difficulty that hinders modeling effort is the absence of the measured values of kinetic constants of many biochemical reactions forming the CS. To surmount this difficulty, an optimization procedure consisting of constrained minimization of the total protein consumption by the CS was designed. The constraints made use of published data on the in vitro kinetics of elimination of the Borrelia burgdorferi bacteria by the CS. Special features of the problem at hand called for a significant modification of the general constrained optimization procedure to include a mathematical model of the bactericidal effect of the CS in the iterative setting. Determination of the unknown kinetic constants of biochemical reactions forming the CS led to a fully specified mathematical model of the dynamics of cell killing induced by the CS. On the basis of the model, effects of the initial concentrations of complements and their inhibitors on the bactericidal action of the CS were studied. Proteins playing a critical role in the regulation of the bactericidal action of the CS were identified. Results obtained in this work serve as an important stepping stone for the study of functioning of the CS as a whole as well as for developing methods for control of pathogenic processes. PMID:19854207
NASA Technical Reports Server (NTRS)
Bacon, Barton J.; Ostroff, Aaron J.
2000-01-01
This paper presents an approach to on-line control design for aircraft that have suffered either actuator failure, missing effector surfaces, surface damage, or any combination. The approach is based on a modified version of nonlinear dynamic inversion. The approach does not require a model of the baseline vehicle (effectors at zero deflection), but does require feedback of accelerations and effector positions. Implementation issues are addressed and the method is demonstrated on an advanced tailless aircraft. An experimental simulation analysis tool is used to directly evaluate the nonlinear system's stability robustness.
Structure-unknown non-linear dynamic systems: identification through neural networks
NASA Astrophysics Data System (ADS)
Masri, S. F.; Chassiakos, A. G.; Caughey, T. K.
1992-03-01
Explores the potential of using parallel distributed processing (neural network) approaches to identify the internal forces of structure-unknown non-linear dynamic systems typically encountered in the field of applied mechanics. The relevant characteristics of neural networks, such as the processing elements, network topology, and learning algorithms, are discussed in the context of system identification. The analogy of the neural network procedure to a qualitatively similar non-parametric identification approach, which was previously developed by the authors for handling arbitrary non-linear systems, is discussed. The utility of the neural network approach is demonstrated by application to several illustrative problems.
Nonlinear characteristics of joints as elements of multi-body dynamic systems
NASA Technical Reports Server (NTRS)
Crawley, Edward F.
1989-01-01
As the connecting elements in multi-body structures, joints play a pivotal role in the overall dynamic response of these systems. Obviously, the linear stiffness of the joint strongly influences the system frequencies, but the joints are also likely to be the dominant sources of damping and nonlinearities, especially in aircraft and space structures. The general characteristics of such joints will be discussed. Then the state of the art in nonlinear joint characterization techniques will be surveyed. Finally, the impact that joints have on the overall response of structures will be evaluated.
Nonlinear waves in mechanics and gas dynamics. Final report, 1 Jun 87-30 Sep 90
Liu, T.P.
1990-12-21
The proposer has studied nonlinear hyperbolic-parabolic partial differential equations related to gas dynamics and mechanics. Hyperbolic conservation laws with relaxation are studied with applications to kinetic theory, elasticity with memory and gas flow with thermo-non-equilibrium in mind. Nonlinear waves for the compressible Navier-Stokes equations are studied for their stability and time-asymptotic behavior. The singular behavior of the magnetohydrodynamic shock waves in the small dissipation limits is clarified, and in particular, it is shown that intermediate shocks are stable uniformly with regards to the strength of dissipations only for 2-dimensional model, and not for 3-dimensional model.
Stretch flow of confined non-Newtonian fluids: nonlinear fingering dynamics.
Brandão, Rodolfo; Fontana, João V; Miranda, José A
2013-12-01
We employ a weakly nonlinear perturbative scheme to investigate the stretch flow of a non-Newtonian fluid confined in Hele-Shaw cell for which the upper plate is lifted. A generalized Darcy's law is utilized to model interfacial fingering formation in both the weak shear-thinning and weak shear-thickening limits. Within this context, we analyze how the interfacial finger shapes and the nonlinear competition dynamics among fingers are affected by the non-Newtonian nature of the stretched fluid. PMID:24483553
Nonlinear dynamic response of laminated composite plates subjected to pulse loading
NASA Astrophysics Data System (ADS)
Upadhyay, A. K.; Pandey, Ramesh; Shukla, K. K.
2011-11-01
An analytical solution methodology for the non-linear dynamic displacement response of laminated composite plates subjected to different types of pulse loading is presented. The mathematical formulation is based on third-order shear deformation plate theory and von-Karman non-linear kinematics. Fast-converging finite double Chebyshev series is employed for evaluating the displacement response. Houbolt time marching scheme is used for temporal discretization and quadratic extrapolation technique is used for linearization. The effects of magnitude and duration of the pulse load, boundary conditions and plate parameters on the central displacement and bending moment responses are studied.
NASA Technical Reports Server (NTRS)
Campbell, Stefan F.; Kaneshige, John T.
2010-01-01
Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).
Van Kirk, J.S.; Bogard, W.T.; Wood, L.R.
1982-01-01
Techniques are described for the transient dynamic analysis of nonlinear periodic structures subjected to time history excitations. These techniques consider the special characteristics of periodic structures in conjunction with the psuedo-force approach in numerical integration to reduce computerized solution costs. A special purpose computer code, based on these techniques, is applied to a specific nonlinear periodic structure: the response of a pressurized water reactor core to a postulated main coolant pipe rupture. Comparisons with a general purpose finite element code, using consistent integration methods, demonstrate the savings in solution cost.
Nonlinear Dynamics of a Foil Bearing Supported Rotor System: Simulation and Analysis
NASA Technical Reports Server (NTRS)
Li, Feng; Flowers, George T.
1996-01-01
Foil bearings provide noncontacting rotor support through a number of thin metal strips attached around the circumference of a stator and separated from the rotor by a fluid film. The resulting support stiffness is dominated by the characteristics of the foils and is a nonlinear function of the rotor deflection. The present study is concerned with characterizing this nonlinear effect and investigating its influence on rotordynamical behavior. A finite element model is developed for an existing bearing, the force versus deflection relation characterized, and the dynamics of a sample rotor system are studied. Some conclusions are discussed with regard to appropriate ranges of operation for such a system.
On psychoanalysis and non-linear dynamics: the paradigm of bifurcation.
Priel, B; Schreiber, G
1994-09-01
Some of Freud's main theoretical conceptualizations drew on metaphors from 19th century physics. However, though the physics of Freud's era was based on deterministic Newtonian mechanics and equilibrium thermodynamics, his descriptions of the dynamics of instincts, therapeutic change, and even transference, were far beyond this model. Freud's dynamic description of psychic development evokes contemporary theories of irreversible, far-from-equilibrium thermodynamics and non-linear dynamics. The present paper focuses on bifurcation theory, which offers a paradigm for the investigation of unpredictable but deterministic phenomena; this paradigm sheds a retroactive light on the classical psychoanalytical conceptualizations of complemental series, repetition compulsion, transference and cure.
Egorov, E. N. Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E.
2013-11-15
Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.