A data driven nonlinear stochastic model for blood glucose dynamics.

PubMed

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. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Closed-loop suppression of chaos in nonlinear driven oscillators

NASA Astrophysics Data System (ADS)

Aguirre, L. A.; Billings, S. A.

1995-05-01

This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.

Strange nonchaotic attractors for computation

NASA Astrophysics Data System (ADS)

Sathish Aravindh, M.; Venkatesan, A.; Lakshmanan, M.

2018-05-01

We investigate the response of quasiperiodically driven nonlinear systems exhibiting strange nonchaotic attractors (SNAs) to deterministic input signals. We show that if one uses two square waves in an aperiodic manner as input to a quasiperiodically driven double-well Duffing oscillator system, the response of the system can produce logical output controlled by such a forcing. Changing the threshold or biasing of the system changes the output to another logic operation and memory latch. The interplay of nonlinearity and quasiperiodic forcing yields logical behavior, and the emergent outcome of such a system is a logic gate. It is further shown that the logical behaviors persist even for an experimental noise floor. Thus the SNA turns out to be an efficient tool for computation.

Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

PubMed

Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

2018-06-01

This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables

NASA Astrophysics Data System (ADS)

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-01

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables.

PubMed

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-07

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Design of fuzzy system by NNs and realization of adaptability

NASA Technical Reports Server (NTRS)

Takagi, Hideyuki

1993-01-01

The issue of designing and tuning fuzzy membership functions by neural networks (NN's) was started by NN-driven Fuzzy Reasoning in 1988. NN-driven fuzzy reasoning involves a NN embedded in the fuzzy system which generates membership values. In conventional fuzzy system design, the membership functions are hand-crafted by trial and error for each input variable. In contrast, NN-driven fuzzy reasoning considers several variables simultaneously and can design a multidimensional, nonlinear membership function for the entire subspace.

Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering

NASA Astrophysics Data System (ADS)

Dorier, V.; Gevorgyan, M.; Ishkhanyan, A.; Leroy, C.; Jauslin, H. R.; Guérin, S.

2017-12-01

We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.

Critical slowing down in driven-dissipative Bose-Hubbard lattices

NASA Astrophysics Data System (ADS)

Vicentini, Filippo; Minganti, Fabrizio; Rota, Riccardo; Orso, Giuliano; Ciuti, Cristiano

2018-01-01

We explore theoretically the dynamical properties of a first-order dissipative phase transition in coherently driven Bose-Hubbard systems, describing, e.g., lattices of coupled nonlinear optical cavities. Via stochastic trajectory calculations based on the truncated Wigner approximation, we investigate the dynamical behavior as a function of system size for one-dimensional (1D) and 2D square lattices in the regime where mean-field theory predicts nonlinear bistability. We show that a critical slowing down emerges for increasing number of sites in 2D square lattices, while it is absent in 1D arrays. We characterize the peculiar properties of the collective phases in the critical region.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

NASA Astrophysics Data System (ADS)

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-05-01

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m-3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

Nonlinear Tracking Control of a Conductive Supercoiled Polymer Actuator.

PubMed

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

2018-04-01

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

Localization of intense electromagnetic waves in a relativistically hot plasma.

PubMed

Shukla, P K; Eliasson, B

2005-02-18

We consider nonlinear interactions between intense short electromagnetic waves (EMWs) and a relativistically hot electron plasma that supports relativistic electron holes (REHs). It is shown that such EMW-REH interactions are governed by a coupled nonlinear system of equations composed of a nonlinear Schro dinger equation describing the dynamics of the EMWs and the Poisson-relativistic Vlasov system describing the dynamics of driven REHs. The present nonlinear system of equations admits both a linearly trapped discrete number of eigenmodes of the EMWs in a quasistationary REH and a modification of the REH by large-amplitude trapped EMWs. Computer simulations of the relativistic Vlasov and Maxwell-Poisson system of equations show complex interactions between REHs loaded with localized EMWs.

Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method.

PubMed

Zhang, Huaguang; Cui, Lili; Zhang, Xin; Luo, Yanhong

2011-12-01

In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.

Simulation and Visualization of Chaos in a Driven Nonlinear Pendulum -- An Aid to Introducing Chaotic Systems in Physics

NASA Astrophysics Data System (ADS)

Akpojotor, Godfrey; Ehwerhemuepha, Louis; Amromanoh, Ogheneriobororue

2013-03-01

The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The results obtained which highlight the hypersensitivity of the pendulum are used to discuss the effectiveness of teaching and learning the physics of chaotic system using Python. This study is one of the many studies under the African Computational Science and Engineering Tour Project (PASET) which is using Python to model, simulate and visualize concepts, laws and phenomena in Science and Engineering to compliment the teaching/learning of theory and experiment.

Constraint-Driven Software Design: An Escape from the Waterfall Model.

ERIC Educational Resources Information Center

de Hoog, Robert; And Others

1994-01-01

Presents the principles of a development methodology for software design based on a nonlinear, product-driven approach that integrates quality aspects. Two examples are given to show that the flexibility needed for building high quality systems leads to integrated development environments in which methodology, product, and tools are closely…

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

NASA Technical Reports Server (NTRS)

Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce

2003-01-01

Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.

Nonlinear Dynamics of a Magnetically Driven Duffing-Type Spring-Magnet Oscillator in the Static Magnetic Field of a Coil

ERIC Educational Resources Information Center

Donoso, Guillermo; Ladera, Celso L.

2012-01-01

We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…

Nonlinear decoding of a complex movie from the mammalian retina

PubMed Central

Deny, Stéphane; Martius, Georg

2018-01-01

Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed “pixel-by-pixel”. We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains. PMID:29746463

Data driven discrete-time parsimonious identification of a nonlinear state-space model for a weakly nonlinear system with short data record

NASA Astrophysics Data System (ADS)

Relan, Rishi; Tiels, Koen; Marconato, Anna; Dreesen, Philippe; Schoukens, Johan

2018-05-01

Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.

Nonlinear and Synchronous Dissolved Organic Matter Dynamics in Streams Across an Agriculture Land Use and Climate Setting

NASA Astrophysics Data System (ADS)

Xenopoulos, M. A.; Vogt, R. J.

2014-12-01

There is now increasing evidence that non-linearity is a common response in ecological systems to pressures caused by human activities. There is also increasing evidence that exogenous environmental drivers, such as climate, induce spatial and temporal synchrony in a wide range of ecological variables. Using Moran's I and Pearson's correlation, we quantified the synchrony of dissolved organic carbon concentration (DOC) and quality (DOM; e.g., specific UV absorbance, Fluorescence Index, PARAFAC), nutrients, discharge and temperature in 40 streams that span an agriculture gradient (0 to >70% cropland), over 10 years. We then used breakpoint regression, 2D-Kolmogorov-Smirnov test and significant zero crossings (SiZer) analyses to quantify the prevalence of nonlinearity and ecological thresholds (breakpoints) where applicable. There was a high degree of synchrony in DOM quality (r > 0.7) but not DOC (r < 0.4). The degree of synchrony was driven in part by the catchment's land use. With respect to the nonlinear analyses we found non-linearity in ~50% of bivariate datasets analyzed. Non-linearity was also driven in part by the catchment's land use. Breakpoints defined different DOM properties. Nonlinearity and synchronous behaviour in DOM are intimately linked to land use.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond.

PubMed

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-05-26

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 10(20) N m(-3). This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

PubMed Central

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-01-01

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m−3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics. PMID:27225287

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow.

PubMed

Heise, M; Hoffmann, Ch; Abshagen, J; Pinter, A; Pfister, G; Lücke, M

2008-02-15

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.

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

NASA Astrophysics Data System (ADS)

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

2008-04-01

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

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

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

Quantum statistics and squeezing for a microwave-driven interacting magnon system.

PubMed

Haghshenasfard, Zahra; Cottam, Michael G

2017-02-01

Theoretical studies are reported for the statistical properties of a microwave-driven interacting magnon system. Both the magnetic dipole-dipole and the exchange interactions are included and the theory is developed for the case of parallel pumping allowing for the inclusion of the nonlinear processes due to the four-magnon interactions. The method of second quantization is used to transform the total Hamiltonian from spin operators to boson creation and annihilation operators. By using the coherent magnon state representation we have studied the magnon occupation number and the statistical behavior of the system. In particular, it is shown that the nonlinearities introduced by the parallel pumping field and the four-magnon interactions lead to non-classical quantum statistical properties of the system, such as magnon squeezing. Also control of the collapse-and-revival phenomena for the time evolution of the average magnon number is demonstrated by varying the parallel pumping amplitude and the four-magnon coupling.

Efficient excitation of nonlinear phonons via chirped pulses: Induced structural phase transitions

NASA Astrophysics Data System (ADS)

Itin, A. P.; Katsnelson, M. I.

2018-05-01

Nonlinear phononics play important role in strong laser-solid interactions. We discuss a dynamical protocol for efficient phonon excitation, considering recent inspiring proposals: inducing ferroelectricity in paraelectric perovskites, and inducing structural deformations in cuprates [Subedi et al., Phys. Rev. B 89, 220301(R) (2014), 10.1103/PhysRevB.89.220301; Phys. Rev. B 95, 134113 (2017), 10.1103/PhysRevB.95.134113]. High-frequency phonon modes are driven by midinfrared pulses, and coupled to lower-frequency modes those indirect excitations cause structural deformations. We study in more detail the case of KTaO3 without strain, where it was not possible to excite the needed low-frequency phonon mode by resonant driving of the higher frequency one. Behavior of the system is explained using a reduced model of coupled driven nonlinear oscillators. We find a dynamical mechanism which prevents effective excitation at resonance driving. To induce ferroelectricity, we employ driving with sweeping frequency, realizing so-called capture into resonance. The method can be applied to many other related systems.

All-Phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in an Anharmonic Oscillator Ladder.

PubMed

Malishava, Merab; Khomeriki, Ramaz

2015-09-04

A conceptual mechanism of amplification of phonons by phonons on the basis of a nonlinear band-gap transmission (supratransmission) phenomenon is presented. As an example, a system of weakly coupled chains of anharmonic oscillators is considered. One (source) chain is driven harmonically by a boundary with a frequency located in the upper band close to the band edge of the ladder system. Amplification happens when a second (gate) chain is driven by a small signal in the counterphase and with the same frequency as the first chain. If the total driving of both chains overcomes the band-gap transmission threshold, the large amplitude band-gap soliton emerges and the amplification scenario is realized. The mechanism is interpreted as the nonlinear superposition of evanescent and propagating nonlinear modes manifesting in a single or double soliton generation working in band-gap or bandpass regimes, respectively. The results could be straightforwardly generalized for all-optical or all-magnonic contexts and have all the promise of logic gate operations.

All-Phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in an Anharmonic Oscillator Ladder

NASA Astrophysics Data System (ADS)

Malishava, Merab; Khomeriki, Ramaz

2015-09-01

A conceptual mechanism of amplification of phonons by phonons on the basis of a nonlinear band-gap transmission (supratransmission) phenomenon is presented. As an example, a system of weakly coupled chains of anharmonic oscillators is considered. One (source) chain is driven harmonically by a boundary with a frequency located in the upper band close to the band edge of the ladder system. Amplification happens when a second (gate) chain is driven by a small signal in the counterphase and with the same frequency as the first chain. If the total driving of both chains overcomes the band-gap transmission threshold, the large amplitude band-gap soliton emerges and the amplification scenario is realized. The mechanism is interpreted as the nonlinear superposition of evanescent and propagating nonlinear modes manifesting in a single or double soliton generation working in band-gap or bandpass regimes, respectively. The results could be straightforwardly generalized for all-optical or all-magnonic contexts and have all the promise of logic gate operations.

Nonlinear dynamics of a magnetically driven Duffing-type spring-magnet oscillator in the static magnetic field of a coil

NASA Astrophysics Data System (ADS)

Donoso, Guillermo; Ladera, Celso L.

2012-11-01

We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet-coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels.

A Nonlinear Gyrokinetic Vlasov-Maxwell System for High-frequency Simulation in Toroidal Geometry

NASA Astrophysics Data System (ADS)

Liu, Pengfei; Zhang, Wenlu; Lin, Jingbo; Li, Ding; Dong, Chao

2016-10-01

A nonlinear gyrokinetic Vlasov equation is derived through the Lie-perturbation method to the Lagrangian and Hamiltonian systems in extanded phase space. The gyrokinetic Maxwell equations are derived in terms of the moments of gyrocenter phase-space distribution through the push-forward and pull-back representations, where the polarization and magnetization effects of gyrocenter are retained. The goal of this work is to construct a global nonlinear gyrokinetic vlasov-maxwell system for high-frequency simulation in toroidal geometry relevent for ion cyclotron range of frequencies (ICRF) waves heating and lower hybrid wave current driven (LHCD). Supported by National Special Research Program of China For ITER and National Natural Science Foundation of China.

Baroclinic Adjustment of the Eddy-Driven Jet

NASA Astrophysics Data System (ADS)

Novak, Lenka; Ambaum, Maarten H. P.; Harvey, Ben J.

2017-04-01

The prediction of poleward shift in the midlatitude eddy-driven jets due to anthropogenic climate change is now a robust feature of climate models, but the magnitude of this shift or the processes responsible for it are less certain. This uncertainty comes from the complex response in storm tracks to large-scale forcing and their nonlinear modulation of the jet. This study uses global circulation models to reveal a relationship between eddy growth rate (referred to as baroclinicity) and eddy activity, whereby baroclinicity responds most rapidly to an eddy-dissipating forcing whereas eddy activity responds most rapidly to a baroclinicity-replenishing forcing. This nonlinearity can be generally explained using a two-dimensional dynamical system essentially describing the baroclinic adjustment as a predator-prey relationship. Despite this nonlinearity, the barotropic changes in the eddy-driven jet appear to be of a comparable magnitude for the ranges of both types of forcing tested in this study. It is implied that while changes in eddy activity or baroclinicity may indicate the sign of latitudinal jet shifting, the precise magnitude of this shifting is a result of a balance between these two quantities.

Experimental and Theoretical Investigations of a Mechanical Lever System Driven by a DC Motor

NASA Astrophysics Data System (ADS)

Nana, B.; Fautso Kuiate, G.; Yamgoué, S. B.

This paper presents theoretical and experimental results on the investigation of the dynamics of a nonlinear electromechanical system made of a lever arm actuated by a DC motor and controlled through a repulsive magnetic force. We use the method of harmonic balance to derive oscillatory solutions. Theoretical tools such as, bifurcation diagrams, Lyapunov exponents, phase portraits, are used to unveil the rich nonlinear behavior of the system including chaos and hysteresis. The experimental results are in close accordance with the theoretical predictions.

Coexistence of Multiple Nonlinear States in a Tristable Passive Kerr Resonator

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Review on the Modeling of Electrostatic MEMS

PubMed Central

Chuang, Wan-Chun; Lee, Hsin-Li; Chang, Pei-Zen; Hu, Yuh-Chung

2010-01-01

Electrostatic-driven microelectromechanical systems devices, in most cases, consist of couplings of such energy domains as electromechanics, optical electricity, thermoelectricity, and electromagnetism. Their nonlinear working state makes their analysis complex and complicated. This article introduces the physical model of pull-in voltage, dynamic characteristic analysis, air damping effect, reliability, numerical modeling method, and application of electrostatic-driven MEMS devices. PMID:22219707

Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Moon, H. T.; Goldman, M. V.

1984-01-01

The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

PubMed

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-08-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

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

Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn

2016-08-15

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Nonlinear imaging (NIM) of barely visible impact damage (BVID) in composite panels using a semi and full air-coupled linear and nonlinear ultrasound technique

NASA Astrophysics Data System (ADS)

Malfense Fierro, Gian Piero; Meo, Michele

2018-03-01

Two non-contact methods were evaluated to address the reliability and reproducibility concerns affecting industry adoption of nonlinear ultrasound techniques for non-destructive testing and evaluation (NDT/E) purposes. A semi and a fully air-coupled linear and nonlinear ultrasound method was evaluated by testing for barely visible impact damage (BVID) in composite materials. Air coupled systems provide various advantages over contact driven systems; such as: ease of inspection, no contact and lubrication issues and a great potential for non-uniform geometry evaluation. The semi air-coupled setup used a suction attached piezoelectric transducer to excite the sample and an array of low-cost microphones to capture the signal over the inspection area, while the second method focused on a purely air-coupled setup, using an air-coupled transducer to excite the structure and capture the signal. One of the issues facing nonlinear and any air-coupled systems is transferring enough energy to stimulate wave propagation and in the case of nonlinear ultrasound; damage regions. Results for both methods provided nonlinear imaging (NIM) of damage regions using a sweep excitation methodology, with the semi aircoupled system providing clearer results.

Nonlinear response and bistability of driven ion acoustic waves

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-08-01

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

Research on ponderomotive driven Vlasov–Poisson system in electron acoustic wave parametric region

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

Xiao, C. Z.; Huang, T. W.; Liu, Z. J.

2014-03-15

Theoretical analysis and corresponding 1D Particle-in-Cell (PIC) simulations of ponderomotive driven Vlasov–Poisson system in electron acoustic wave (EAW) parametric region are demonstrated. Theoretical analysis identifies that under the resonant condition, a monochromatic EAW can be excited when the wave number of the drive ponderomotive force satisfies 0.26≲k{sub d}λ{sub D}≲0.53. If k{sub d}λ{sub D}≲0.26, nonlinear superposition of harmonic waves can be resonantly excited, called kinetic electrostatic electron nonlinear waves. Numerical simulations have demonstrated these wave excitation and evolution dynamics, in consistence with the theoretical predictions. The physical nature of these two waves is supposed to be interaction of harmonic waves, andmore » their similar phase space properties are also discussed.« less

The spike trains of inhibited pacemaker neurons seen through the magnifying glass of nonlinear analyses.

PubMed

Segundo, J P; Sugihara, G; Dixon, P; Stiber, M; Bersier, L F

1998-12-01

This communication describes the new information that may be obtained by applying nonlinear analytical techniques to neurobiological time-series. Specifically, we consider the sequence of interspike intervals Ti (the "timing") of trains recorded from synaptically inhibited crayfish pacemaker neurons. As reported earlier, different postsynaptic spike train forms (sets of timings with shared properties) are generated by varying the average rate and/or pattern (implying interval dispersions and sequences) of presynaptic spike trains. When the presynaptic train is Poisson (independent exponentially distributed intervals), the form is "Poisson-driven" (unperturbed and lengthened intervals succeed each other irregularly). When presynaptic trains are pacemaker (intervals practically equal), forms are either "p:q locked" (intervals repeat periodically), "intermittent" (mostly almost locked but disrupted irregularly), "phase walk throughs" (intermittencies with briefer regular portions), or "messy" (difficult to predict or describe succinctly). Messy trains are either "erratic" (some intervals natural and others lengthened irregularly) or "stammerings" (intervals are integral multiples of presynaptic intervals). The individual spike train forms were analysed using attractor reconstruction methods based on the lagged coordinates provided by successive intervals from the time-series Ti. Numerous models were evaluated in terms of their predictive performance by a trial-and-error procedure: the most successful model was taken as best reflecting the true nature of the system's attractor. Each form was characterized in terms of its dimensionality, nonlinearity and predictability. (1) The dimensionality of the underlying dynamical attractor was estimated by the minimum number of variables (coordinates Ti) required to model acceptably the system's dynamics, i.e. by the system's degrees of freedom. Each model tested was based on a different number of Ti; the smallest number whose predictions were judged successful provided the best integer approximation of the attractor's true dimension (not necessarily an integer). Dimensionalities from three to five provided acceptable fits. (2) The degree of nonlinearity was estimated by: (i) comparing the correlations between experimental results and data from linear and nonlinear models, and (ii) tuning model nonlinearity via a distance-weighting function and identifying the either local or global neighborhood size. Lockings were compatible with linear models and stammerings were marginal; nonlinear models were best for Poisson-driven, intermittent and erratic forms. (3) Finally, prediction accuracy was plotted against increasingly long sequences of intervals forecast: the accuracies for Poisson-driven, locked and stammering forms were invariant, revealing irregularities due to uncorrelated noise, but those of intermittent and messy erratic forms decayed rapidly, indicating an underlying deterministic process. The excellent reconstructions possible for messy erratic and for some intermittent forms are especially significant because of their relatively low dimensionality (around 4), high degree of nonlinearity and prediction decay with time. This is characteristic of chaotic systems, and provides evidence that nonlinear couplings between relatively few variables are the major source of the apparent complexity seen in these cases. This demonstration of different dimensions, degrees of nonlinearity and predictabilities provides rigorous support for the categorization of different synaptically driven discharge forms proposed earlier on the basis of more heuristic criteria. This has significant implications. (1) It demonstrates that heterogeneous postsynaptic forms can indeed be induced by manipulating a few presynaptic variables. (2) Each presynaptic timing induces a form with characteristic dimensionality, thus breaking up the preparation into subsystems such that the physical variables in each operate as one

Nonadiabatic effects in periodically driven dissipative open quantum systems

NASA Astrophysics Data System (ADS)

Reimer, Viktor; Pedersen, Kim G. L.; Tanger, Niklas; Pletyukhov, Mikhail; Gritsev, Vladimir

2018-04-01

We present a general method to calculate the periodic steady state of a driven-dissipative system coupled to a transmission line (and more generally, to a reservoir) under periodic modulation of its parameters. Using Floquet's theorem, we formulate the differential equation for the system's density operator which has to be solved for a single period of modulation. On this basis we also provide systematic expansions in both the adiabatic and high-frequency regime. Applying our method to three different systems—two- and three-level models as well as the driven nonlinear cavity—we propose periodic modulation protocols of parameters leading to a temporary suppression of effective dissipation rates, and study the arising nonadiabatic features in the response of these systems.

Shear-Flow Instability Saturation by Stable Modes: Hydrodynamics and Gyrokinetics

NASA Astrophysics Data System (ADS)

Fraser, Adrian; Pueschel, M. J.; Terry, P. W.; Zweibel, E. G.

2017-10-01

We present simulations of shear-driven instabilities, focusing on the impact of nonlinearly excited, large-scale, linearly stable modes on the nonlinear cascade, momentum transport, and secondary instabilities. Stable modes, which have previously been shown to significantly affect instability saturation [Fraser et al. PoP 2017], are investigated in a collisionless, gyrokinetic, periodic zonal flow using the Gene code by projecting the results of nonlinear simulations onto a basis of linear eigenmodes that includes both stable and unstable modes. Benchmarking growth rates against previous gyrokinetic studies and an equivalent fluid system demonstrates comparable linear dynamics in the fluid and gyrokinetic systems. Cases of driven and decaying shear-flow turbulence are compared in Gene by using a Krook operator as an effective forcing. For comparison with existing hydrodynamic and MHD shear-flow instability studies, we present results for the shear layer obtained by similar means with the code Dedalus. Supported by U.S. DOE Grant No. DE-FG02-89ER53291, the NSF, and UW-Madison.

FAST TRACK COMMUNICATION: Quantum anomalies and linear response theory

NASA Astrophysics Data System (ADS)

Sela, Itamar; Aisenberg, James; Kottos, Tsampikos; Cohen, Doron

2010-08-01

The analysis of diffusive energy spreading in quantized chaotic driven systems leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation, a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient D that is proportional to the intensity ɛ2 of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time tɛ, and a self-generated (intrinsic) dephasing process leads to nonlinear dependence of D on ɛ2.

Nonlinear cavity optomechanics with nanomechanical thermal fluctuations

PubMed Central

Leijssen, Rick; La Gala, Giada R.; Freisem, Lars; Muhonen, Juha T.; Verhagen, Ewold

2017-01-01

Although the interaction between light and motion in cavity optomechanical systems is inherently nonlinear, experimental demonstrations to date have allowed a linearized description in all except highly driven cases. Here, we demonstrate a nanoscale optomechanical system in which the interaction between light and motion is so large (single-photon cooperativity C0≈103) that thermal motion induces optical frequency fluctuations larger than the intrinsic optical linewidth. The system thereby operates in a fully nonlinear regime, which pronouncedly impacts the optical response, displacement measurement and radiation pressure backaction. Specifically, we measure an apparent optical linewidth that is dominated by thermo-mechanically induced frequency fluctuations over a wide temperature range, and show that in this regime thermal displacement measurements cannot be described by conventional analytical models. We perform a proof-of-concept demonstration of exploiting the nonlinearity to conduct sensitive quadratic readout of nanomechanical displacement. Finally, we explore how backaction in this regime affects the mechanical fluctuation spectra. PMID:28685755

Evaluating data-driven causal inference techniques in noisy physical and ecological systems

NASA Astrophysics Data System (ADS)

Tennant, C.; Larsen, L.

2016-12-01

Causal inference from observational time series challenges traditional approaches for understanding processes and offers exciting opportunities to gain new understanding of complex systems where nonlinearity, delayed forcing, and emergent behavior are common. We present a formal evaluation of the performance of convergent cross-mapping (CCM) and transfer entropy (TE) for data-driven causal inference under real-world conditions. CCM is based on nonlinear state-space reconstruction, and causality is determined by the convergence of prediction skill with an increasing number of observations of the system. TE is the uncertainty reduction based on transition probabilities of a pair of time-lagged variables. With TE, causal inference is based on asymmetry in information flow between the variables. Observational data and numerical simulations from a number of classical physical and ecological systems: atmospheric convection (the Lorenz system), species competition (patch-tournaments), and long-term climate change (Vostok ice core) were used to evaluate the ability of CCM and TE to infer causal-relationships as data series become increasingly corrupted by observational (instrument-driven) or process (model-or -stochastic-driven) noise. While both techniques show promise for causal inference, TE appears to be applicable to a wider range of systems, especially when the data series are of sufficient length to reliably estimate transition probabilities of system components. Both techniques also show a clear effect of observational noise on causal inference. For example, CCM exhibits a negative logarithmic decline in prediction skill as the noise level of the system increases. Changes in TE strongly depend on noise type and which variable the noise was added to. The ability of CCM and TE to detect driving influences suggest that their application to physical and ecological systems could be transformative for understanding driving mechanisms as Earth systems undergo change.

Coordination of heterogeneous nonlinear multi-agent systems with prescribed behaviours

NASA Astrophysics Data System (ADS)

Tang, Yutao

2017-10-01

In this paper, we consider a coordination problem for a class of heterogeneous nonlinear multi-agent systems with a prescribed input-output behaviour which was represented by another input-driven system. In contrast to most existing multi-agent coordination results with an autonomous (virtual) leader, this formulation takes possible control inputs of the leader into consideration. First, the coordination was achieved by utilising a group of distributed observers based on conventional assumptions of model matching problem. Then, a fully distributed adaptive extension was proposed without using the input of this input-output behaviour. An example was given to verify their effectiveness.

Nonlinear cross-field coupling on the route to broadband turbulence

NASA Astrophysics Data System (ADS)

Brandt, Christian; Thakur, Saikat C.; Cui, Lang; Gosselin, Jordan J.; Negrete, Jose, Jr.; Holland, Chris; Tynan, George R.

2013-10-01

In the linear magnetized plasma device CSDX (Controlled Shear De-correlation eXperiment) drift interchange modes are studied coexisting on top of a weak turbulence driven azimuthally symmetric, radially sheared plasma flow. In helicon discharges (helicon antenna diameter 15 cm) with increasing magnetic field (B <= 0 . 24 T) the system can be driven to fully developed broadband turbulence. Fast imaging using a refractive telescope setup is applied to study the dynamics in the azimuthal-radial cross-section. The image data is supported by Langmuir probe measurements. In the present study we examine the development of nonlinear transfer as the fully developed turbulence emerges. Nonlinear cross-field coupling between eigenmodes at different radial positions is investigated using Fourier decomposition of azimuthal eigenmodes. The coupling strength between waves at different radial positions is inferred to radial profiles and cross-field transport between adjacent magnetic flux surfaces. Nonlinear effects like synchronization, phase slippages, phase pulling and periodic pulling are observed. The effects of mode coupling and the stability of modes is compared to the dynamics of a coupled chain of Kuramoto oscillators.

Feedforward hysteresis compensation in trajectory control of piezoelectrically-driven nanostagers

NASA Astrophysics Data System (ADS)

Bashash, Saeid; Jalili, Nader

2006-03-01

Complex structural nonlinearities of piezoelectric materials drastically degrade their performance in variety of micro- and nano-positioning applications. From the precision positioning and control perspective, the multi-path time-history dependent hysteresis phenomenon is the most concerned nonlinearity in piezoelectric actuators to be analyzed. To realize the underlying physics of this phenomenon and to develop an efficient compensation strategy, the intelligent properties of hysteresis with the effects of non-local memories are discussed. Through performing a set of experiments on a piezoelectrically-driven nanostager with high resolution capacitive position sensor, it is shown that for the precise prediction of hysteresis path, certain memory units are required to store the previous hysteresis trajectory data. Based on the experimental observations, a constitutive memory-based mathematical modeling framework is developed and trained for the precise prediction of hysteresis path for arbitrarily assigned input profiles. Using the inverse hysteresis model, a feedforward control strategy is then developed and implemented on the nanostager to compensate for the system everpresent nonlinearity. Experimental results demonstrate that the controller remarkably eliminates the nonlinear effect if memory units are sufficiently chosen for the inverse model.

A bifurcation giving birth to order in an impulsively driven complex system

NASA Astrophysics Data System (ADS)

Seshadri, Akshay; Sujith, R. I.

2016-08-01

Nonlinear oscillations lie at the heart of numerous complex systems. Impulsive forcing arises naturally in many scenarios, and we endeavour to study nonlinear oscillators subject to such forcing. We model these kicked oscillatory systems as a piecewise smooth dynamical system, whereby their dynamics can be investigated. We investigate the problem of pattern formation in a turbulent combustion system and apply this formalism with the aim of explaining the observed dynamics. We identify that the transition of this system from low amplitude chaotic oscillations to large amplitude periodic oscillations is the result of a discontinuity induced bifurcation. Further, we provide an explanation for the occurrence of intermittent oscillations in the system.

A bifurcation giving birth to order in an impulsively driven complex system

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

Seshadri, Akshay, E-mail: akshayseshadri@gmail.com; Sujith, R. I., E-mail: sujith@iitm.ac.in

Nonlinear oscillations lie at the heart of numerous complex systems. Impulsive forcing arises naturally in many scenarios, and we endeavour to study nonlinear oscillators subject to such forcing. We model these kicked oscillatory systems as a piecewise smooth dynamical system, whereby their dynamics can be investigated. We investigate the problem of pattern formation in a turbulent combustion system and apply this formalism with the aim of explaining the observed dynamics. We identify that the transition of this system from low amplitude chaotic oscillations to large amplitude periodic oscillations is the result of a discontinuity induced bifurcation. Further, we provide anmore » explanation for the occurrence of intermittent oscillations in the system.« less

Sliding Mode Tracking Control of a Wire-Driven Upper-Limb Rehabilitation Robot with Nonlinear Disturbance Observer.

PubMed

Niu, Jie; Yang, Qianqian; Wang, Xiaoyun; Song, Rong

2017-01-01

Robot-aided rehabilitation has become an important technology to restore and reinforce motor functions of patients with extremity impairment, whereas it can be extremely challenging to achieve satisfactory tracking performance due to uncertainties and disturbances during rehabilitation training. In this paper, a wire-driven rehabilitation robot that can work over a three-dimensional space is designed for upper-limb rehabilitation, and sliding mode control with nonlinear disturbance observer is designed for the robot to deal with the problem of unpredictable disturbances during robot-assisted training. Then, simulation and experiments of trajectory tracking are carried out to evaluate the performance of the system, the position errors, and the output forces of the designed control scheme are compared with those of the traditional sliding mode control (SMC) scheme. The results show that the designed control scheme can effectively reduce the tracking errors and chattering of the output forces as compared with the traditional SMC scheme, which indicates that the nonlinear disturbance observer can reduce the effect of unpredictable disturbances. The designed control scheme for the wire-driven rehabilitation robot has potential to assist patients with stroke in performing repetitive rehabilitation training.

Linear dynamical modes as new variables for data-driven ENSO forecast

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Seleznev, Aleksei; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander; Kurths, Juergen

2018-05-01

A new data-driven model for analysis and prediction of spatially distributed time series is proposed. The model is based on a linear dynamical mode (LDM) decomposition of the observed data which is derived from a recently developed nonlinear dimensionality reduction approach. The key point of this approach is its ability to take into account simple dynamical properties of the observed system by means of revealing the system's dominant time scales. The LDMs are used as new variables for empirical construction of a nonlinear stochastic evolution operator. The method is applied to the sea surface temperature anomaly field in the tropical belt where the El Nino Southern Oscillation (ENSO) is the main mode of variability. The advantage of LDMs versus traditionally used empirical orthogonal function decomposition is demonstrated for this data. Specifically, it is shown that the new model has a competitive ENSO forecast skill in comparison with the other existing ENSO models.

Nonlinear forecasting analysis of inflation-deflation patterns of an active caldera (Campi Flegrei, Italy)

USGS Publications Warehouse

Cortini, M.; Barton, C.C.

1993-01-01

The ground level in Pozzuoli, Italy, at the center of the Campi Flegrei caldera, has been monitored by tide gauges. Previous work suggests that the dynamics of the Campi Flegrei system, as reconstructed from the tide gauge record, is chaotic and low dimensional. According to this suggestion, in spite of the complexity of the system, at a time scale of days the ground motion is driven by a deterministic mechanism with few degrees of freedom; however, the interactions of the system may never be describable in full detail. New analysis of the tide gauge record using Nonlinear Forecasting, confirms low-dimensional chaos in the ground elevation record at Campi Flegrei and suggests that Nonlinear Forecasting could be a useful tool in volcanic surveillance. -from Authors

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

PubMed

Song, Qi; Song, Yong-Duan

2011-12-01

This paper investigates the position and velocity tracking control problem of high-speed trains with multiple vehicles connected through couplers. A dynamic model reflecting nonlinear and elastic impacts between adjacent vehicles as well as traction/braking nonlinearities and actuation faults is derived. Neuroadaptive fault-tolerant control algorithms are developed to account for various factors such as input nonlinearities, actuator failures, and uncertain impacts of in-train forces in the system simultaneously. The resultant control scheme is essentially independent of system model and is primarily data-driven because with the appropriate input-output data, the proposed control algorithms are capable of automatically generating the intermediate control parameters, neuro-weights, and the compensation signals, literally producing the traction/braking force based upon input and response data only--the whole process does not require precise information on system model or system parameter, nor human intervention. The effectiveness of the proposed approach is also confirmed through numerical simulations.

Period doubling in period-one steady states

NASA Astrophysics Data System (ADS)

Wang, Reuben R. W.; Xing, Bo; Carlo, Gabriel G.; Poletti, Dario

2018-02-01

Nonlinear classical dissipative systems present a rich phenomenology in their "route to chaos," including period doubling, i.e., the system evolves with a period which is twice that of the driving. However, typically the attractor of a periodically driven quantum open system evolves with a period which exactly matches that of the driving. Here, we analyze a periodically driven many-body open quantum system whose classical correspondent presents period doubling. We show that by studying the dynamical correlations, it is possible to show the occurrence of period doubling in the quantum (period-one) steady state. We also discuss that such systems are natural candidates for clean and intrinsically robust Floquet time crystals.

Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Boskovic, Jovan D.

2008-01-01

This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.

Multi-Constraint Multi-Variable Optimization of Source-Driven Nuclear Systems

NASA Astrophysics Data System (ADS)

Watkins, Edward Francis

1995-01-01

A novel approach to the search for optimal designs of source-driven nuclear systems is investigated. Such systems include radiation shields, fusion reactor blankets and various neutron spectrum-shaping assemblies. The novel approach involves the replacement of the steepest-descents optimization algorithm incorporated in the code SWAN by a significantly more general and efficient sequential quadratic programming optimization algorithm provided by the code NPSOL. The resulting SWAN/NPSOL code system can be applied to more general, multi-variable, multi-constraint shield optimization problems. The constraints it accounts for may include simple bounds on variables, linear constraints, and smooth nonlinear constraints. It may also be applied to unconstrained, bound-constrained and linearly constrained optimization. The shield optimization capabilities of the SWAN/NPSOL code system is tested and verified in a variety of optimization problems: dose minimization at constant cost, cost minimization at constant dose, and multiple-nonlinear constraint optimization. The replacement of the optimization part of SWAN with NPSOL is found feasible and leads to a very substantial improvement in the complexity of optimization problems which can be efficiently handled.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Modeling nonlinearities in MEMS oscillators.

PubMed

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Rayleigh-type parametric chemical oscillation.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2015-09-28

We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.

Homoclinic orbits in three-dimensional Shilnikov-type chaotic systems

NASA Astrophysics Data System (ADS)

Feng, Jing-Jing; Zhang, Qi-Chang; Wang, Wei; Hao, Shu-Ying

2013-09-01

In this paper, the Padé approximant and analytic solution in the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic trajectories in three-dimensional nonlinear dynamical systems. The PID controller system with quadratic and cubic nonlinearities, the simplified solar-wind-driven-magnetosphere-ionosphere system, and the human DNA sequence system are considered. With the aid of presenting a new condition, the solutions of solving the boundary-value problems which are formulated for the trajectory and evaluating the initial amplitude values become available. At the same time, the value of the bifurcation parameter is obtained directly, which is almost consistent with the numerical result.

A data-driven approach for modeling post-fire debris-flow volumes and their uncertainty

USGS Publications Warehouse

Friedel, Michael J.

2011-01-01

This study demonstrates the novel application of genetic programming to evolve nonlinear post-fire debris-flow volume equations from variables associated with a data-driven conceptual model of the western United States. The search space is constrained using a multi-component objective function that simultaneously minimizes root-mean squared and unit errors for the evolution of fittest equations. An optimization technique is then used to estimate the limits of nonlinear prediction uncertainty associated with the debris-flow equations. In contrast to a published multiple linear regression three-variable equation, linking basin area with slopes greater or equal to 30 percent, burn severity characterized as area burned moderate plus high, and total storm rainfall, the data-driven approach discovers many nonlinear and several dimensionally consistent equations that are unbiased and have less prediction uncertainty. Of the nonlinear equations, the best performance (lowest prediction uncertainty) is achieved when using three variables: average basin slope, total burned area, and total storm rainfall. Further reduction in uncertainty is possible for the nonlinear equations when dimensional consistency is not a priority and by subsequently applying a gradient solver to the fittest solutions. The data-driven modeling approach can be applied to nonlinear multivariate problems in all fields of study.

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

NASA Technical Reports Server (NTRS)

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

2009-01-01

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

Flexible cue combination in the guidance of attention in visual search

PubMed Central

Brand, John; Oriet, Chris; Johnson, Aaron P.; Wolfe, Jeremy M.

2014-01-01

Hodsoll and Humphreys (2001) have assessed the relative contributions of stimulus-driven and user-driven knowledge on linearly- and nonlinearly separable search. However, the target feature used to determine linear separability in their task (i.e., target size) was required to locate the target. In the present work, we investigated the contributions of stimulus-driven and user-driven knowledge when a linearly- or nonlinearly-separable feature is available but not required for target identification. We asked observers to complete a series of standard color X orientation conjunction searches in which target size was either linearly- or nonlinearly separable from the size of the distractors. When guidance by color X orientation and by size information are both available, observers rely on whichever information results in the best search efficiency. This is the case irrespective of whether we provide target foreknowledge by blocking stimulus conditions, suggesting that feature information is used in both a stimulus-driven and user-driven fashion. PMID:25463553

Chaos without nonlinear dynamics.

PubMed

Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N

2006-07-14

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system.

A comprehensive study of the delay vector variance method for quantification of nonlinearity in dynamical systems

PubMed Central

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

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

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-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.

Event-driven simulations of nonlinear integrate-and-fire neurons.

PubMed

Tonnelier, Arnaud; Belmabrouk, Hana; Martinez, Dominique

2007-12-01

Event-driven strategies have been used to simulate spiking neural networks exactly. Previous work is limited to linear integrate-and-fire neurons. In this note, we extend event-driven schemes to a class of nonlinear integrate-and-fire models. Results are presented for the quadratic integrate-and-fire model with instantaneous or exponential synaptic currents. Extensions to conductance-based currents and exponential integrate-and-fire neurons are discussed.

Genetic algorithm driven spectral shaping of supercontinuum radiation in a photonic crystal fiber

NASA Astrophysics Data System (ADS)

Michaeli, Linor; Bahabad, Alon

2018-05-01

We employ a genetic algorithm to control a pulse-shaping system pumping a nonlinear photonic crystal with ultrashort pulses. With this system, we are able to modify the spectrum of the generated supercontinuum (SC) radiation to yield narrow Gaussian-like features around pre-selected wavelengths over the whole SC spectrum.

Temporal cross-correlation asymmetry and departure from equilibrium in a bistable chemical system.

PubMed

Bianca, C; Lemarchand, A

2014-06-14

This paper aims at determining sustained reaction fluxes in a nonlinear chemical system driven in a nonequilibrium steady state. The method relies on the computation of cross-correlation functions for the internal fluctuations of chemical species concentrations. By employing Langevin-type equations, we derive approximate analytical formulas for the cross-correlation functions associated with nonlinear dynamics. Kinetic Monte Carlo simulations of the chemical master equation are performed in order to check the validity of the Langevin equations for a bistable chemical system. The two approaches are found in excellent agreement, except for critical parameter values where the bifurcation between monostability and bistability occurs. From the theoretical point of view, the results imply that the behavior of cross-correlation functions cannot be exploited to measure sustained reaction fluxes in a specific nonlinear system without the prior knowledge of the associated chemical mechanism and the rate constants.

Robust ion current oscillations under a steady electric field: An ion channel analog.

PubMed

Yan, Yu; Wang, Yunshan; Senapati, Satyajyoti; Schiffbauer, Jarrod; Yossifon, Gilad; Chang, Hsueh-Chia

2016-08-01

We demonstrate a nonlinear, nonequilibrium field-driven ion flux phenomenon, which unlike Teorell's nonlinear multiple field theory, requires only the application of one field: robust autonomous current-mass flux oscillations across a porous monolith coupled to a capillary with a long air bubble, which mimics a hydrophobic protein in an ion channel. The oscillations are driven by the hysteretic wetting dynamics of the meniscus when electro-osmotic flow and pressure driven backflow, due to bubble expansion, compete to approach zero mass flux within the monolith. Delayed rupture of the film around the advancing bubble cuts off the electric field and switches the monolith mass flow from the former to the latter. The meniscus then recedes and repairs the rupture to sustain an oscillation for a range of applied fields. This generic mechanism shares many analogs with current oscillations in cell membrane ion channel. At sufficiently high voltage, the system undergoes a state transition characterized by appearance of the ubiquitous 1/f power spectrum.

Spike-like solitary waves in incompressible boundary layers driven by a travelling wave.

PubMed

Feng, Peihua; Zhang, Jiazhong; Wang, Wei

2016-06-01

Nonlinear waves produced in an incompressible boundary layer driven by a travelling wave are investigated, with damping considered as well. As one of the typical nonlinear waves, the spike-like wave is governed by the driven-damped Benjamin-Ono equation. The wave field enters a completely irregular state beyond a critical time, increasing the amplitude of the driving wave continuously. On the other hand, the number of spikes of solitary waves increases through multiplication of the wave pattern. The wave energy grows in a sequence of sharp steps, and hysteresis loops are found in the system. The wave energy jumps to different levels with multiplication of the wave, which is described by winding number bifurcation of phase trajectories. Also, the phenomenon of multiplication and hysteresis steps is found when varying the speed of driving wave as well. Moreover, the nature of the change of wave pattern and its energy is the stability loss of the wave caused by saddle-node bifurcation.

Millimeter-wave interconnects for microwave-frequency quantum machines

NASA Astrophysics Data System (ADS)

Pechal, Marek; Safavi-Naeini, Amir H.

2017-10-01

Superconducting microwave circuits form a versatile platform for storing and manipulating quantum information. A major challenge to further scalability is to find approaches for connecting these systems over long distances and at high rates. One approach is to convert the quantum state of a microwave circuit to optical photons that can be transmitted over kilometers at room temperature with little loss. Many proposals for electro-optic conversion between microwave and optics use optical driving of a weak three-wave mixing nonlinearity to convert the frequency of an excitation. Residual absorption of this optical pump leads to heating, which is problematic at cryogenic temperatures. Here we propose an alternative approach where a nonlinear superconducting circuit is driven to interconvert between microwave-frequency (7 ×109 Hz) and millimeter-wave-frequency photons (3 ×1011 Hz). To understand the potential for quantum state conversion between microwave and millimeter-wave photons, we consider the driven four-wave mixing quantum dynamics of nonlinear circuits. In contrast to the linear dynamics of the driven three-wave mixing converters, the proposed four-wave mixing converter has nonlinear decoherence channels that lead to a more complex parameter space of couplings and pump powers that we map out. We consider physical realizations of such converter circuits by deriving theoretically the upper bound on the maximum obtainable nonlinear coupling between any two modes in a lossless circuit, and synthesizing an optimal circuit based on realistic materials that saturates this bound. Our proposed circuit dissipates less than 10-9 times the energy of current electro-optic converters per qubit. Finally, we outline the quantum link budget for optical, microwave, and millimeter-wave connections, showing that our approach is viable for realizing interconnected quantum processors for intracity or quantum data center environments.

Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion.

PubMed

Leszczynski, Henryk; Wrzosek, Monika

2017-02-01

We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

Spin Seebeck effect in a metal-single-molecule-magnet-metal junction

NASA Astrophysics Data System (ADS)

Niu, Pengbin; Liu, Lixiang; Su, Xiaoqiang; Dong, Lijuan; Luo, Hong-Gang

2018-01-01

We investigate the nonlinear regime of temperature-driven spin-related currents through a single molecular magnet (SMM), which is connected with two metal electrodes. Under a large spin approximation, the SMM is simplified to a natural two-channel model possessing spin-opposite configuration and Coulomb interaction. We find that in temperature-driven case the system can generate spin-polarized currents. More interestingly, at electron-hole symmetry point, the competition of the two channels induces a temperature-driven pure spin current. This device demonstrates that temperature-driven SMM junction shows some results different from the usual quantum dot model, which may be useful in the future design of thermal-based molecular spintronic devices.

A Physics-driven Neural Networks-based Simulation System (PhyNNeSS) for multimodal interactive virtual environments involving nonlinear deformable objects

PubMed Central

De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S.

2012-01-01

Background While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. Methods In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. Results We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. Conclusions A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal Interactive Simulation) for general use. PMID:22629108

Thermally Driven Inhibition of Superconducting Vortex Avalanches

NASA Astrophysics Data System (ADS)

Lara, Antonio; Aliev, Farkhad G.; Moshchalkov, Victor V.; Galperin, Yuri M.

2017-09-01

Complex systems close to their critical state can exhibit abrupt transitions—avalanches—between their metastable states. It is a challenging task to understand the mechanism of the avalanches and control their behavior. Here, we investigate microwave stimulation of avalanches in the so-called vortex matter of type-II superconductors—a system of interacting Abrikosov vortices close to the critical (Bean) state. Our main finding is that the avalanche incubation strongly depends on the excitation frequency, a completely unexpected behavior observed close to the so-called depinning frequencies. Namely, the triggered vortex avalanches in Pb superconducting films become effectively inhibited approaching the critical temperature or critical magnetic field when the microwave stimulus is close to the vortex depinning frequency. We suggest a simple model explaining the observed counterintuitive behaviors as a manifestation of the strongly nonlinear dependence of the driven vortex core size on the microwave excitation intensity. This paves the way to controlling avalanches in superconductor-based devices through their nonlinear response.

Quantum-optical nonlinearities induced by Rydberg-Rydberg interactions: A perturbative approach

NASA Astrophysics Data System (ADS)

Grankin, A.; Brion, E.; Bimbard, E.; Boddeda, R.; Usmani, I.; Ourjoumtsev, A.; Grangier, P.

2015-10-01

In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical nonlinearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant thus generalizing our previous results. We can thus investigate quantitatively new features associated with the resonant behavior of the system. We also propose an effective nonlinear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system.

Many-body dynamics of driven-dissipative Rydberg cavity polaritons

NASA Astrophysics Data System (ADS)

Pistorius, Tim; Fan, Jingtao; Weimer, Hendrik

2017-04-01

The usage of photons as long-range information carriers has greatly increased the interest in systems with nonlinear optical properties in recent years. The nonlinearity is easily achievable in Rydberg mediums through the strong van der Waals interaction which makes them one of the best candidates for such a system. Here, we propose a way to analyze the steady state solutions of a Rydberg medium in a cavity through the combination of the variational principle for open quantum systems and the P-distribution of the density matrix. To get a better understanding of the many-body-dynamics a transformation into the polariton picture is performed and investigated. Volkswagen Foundation, Deutsche Forschungsgemeinschaft.

Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks.

PubMed

Vlachas, Pantelis R; Byeon, Wonmin; Wan, Zhong Y; Sapsis, Themistoklis P; Koumoutsakos, Petros

2018-05-01

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.

Steady-State Solutions Originating from an Enhanced Nonlinear Feedback in a Hybrid Opto-mechanical System

NASA Astrophysics Data System (ADS)

Fan, Qiu-Bo; Wang, Yi-Ru; Chen, Jin; Pan, Yue-Wu; Han, Bai-Ping; Fu, Chang-Bao; Sun, Yan

2017-06-01

The steady-state properties of a hybrid system are investigated in this paper. Many cold atoms in the four-level tripod configuration are confined in an optical cavity with a movable end mirror. The confined cold atoms are driven with two external classical fields and an internal cavity field. The internal cavity field is excited by an external driving field and shows a radiation pressure upon the movable end mirror. The coupling of atom-light and opto-mechanical interactions is enhanced by embedding a four-level atomic system in a typical opto-mechanical cavity. And an enhanced nonlinear feedback mechanism is offered by the enhanced coupling, which permits the observation of five and three steady-state solutions for relevant variables near two-photon resonance. The enhanced nonlinear feedback mechanism also allows us to observe the obvious difference in the double-EIT phenomenon between the atom-assisted opto-mechanical system and usual atom-field system.

Investigating multiphoton phenomena using nonlinear dynamics

NASA Astrophysics Data System (ADS)

Huang, Shu

Many seemingly simple systems can display extraordinarily complex dynamics which has been studied and uncovered through nonlinear dynamical theory. The leitmotif of this thesis is changing phase-space structures and their (linear or non-linear) stabilities by adding control functions (which act on the system as external perturbations) to the relevant Hamiltonians. These phase-space structures may be periodic orbits, invariant tori or their stable and unstable manifolds. One-electron systems and diatomic molecules are fundamental and important staging ground for new discoveries in nonlinear dynamics. In past years, increasing emphasis and effort has been put on the control or manipulation of these systems. Recent developments of nonlinear dynamical tools can provide efficient ways of doing so. In the first subtopic of the thesis, we are adding a control function to restore tori at prescribed locations in phase space. In the remainder of the thesis, a control function with parameters is used to change the linear stability of the periodic orbits which govern the processes in question. In this thesis, we report our theoretical analyses on multiphoton ionization of Rydberg atoms exposed to strong microwave fields and the dissociation of diatomic molecules exposed to bichromatic lasers using nonlinear dynamical tools. This thesis is composed of three subtopics. In the first subtopic, we employ local control theory to reduce the stochastic ionization of hydrogen atom in a strong microwave field by adding a relatively small control term to the original Hamiltonian. In the second subtopic, we perform periodic orbit analysis to investigate multiphoton ionization driven by a bichromatic microwave field. Our results show quantitative and qualitative agreement with previous studies, and hence identify the mechanism through which short periodic orbits organize the dynamics in multiphoton ionization. In addition, we achieve substantial time savings with this approach. In the third subtopic we extend our periodic orbit analysis to the dissociation of diatomic molecules driven by a bichromatic laser. In this problem, our results based on periodic orbit analysis again show good agreement with previous work, and hence promise more potential applications of this approach in molecular physics.

Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra

DOE PAGES

Hatch, D. R.; Jenko, F.; Navarro, A. Banon; ...

2016-07-26

A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state—a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses—linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest inmore » the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a non-modal treatment is necessary to understand key features of the turbulence.« less

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Weakly Nonlinear Model with Exact Coefficients for the Fluttering and Spiraling Motion of Buoyancy-Driven Bodies

NASA Astrophysics Data System (ADS)

Tchoufag, Joël; Fabre, David; Magnaudet, Jacques

2015-09-01

Gravity- or buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Here, using a weakly nonlinear expansion of the full set of governing equations, we present a new generic reduced-order model based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (e.g., fluttering or spiraling) and characteristics (e.g., frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

A weakly nonlinear model with exact coefficients for the fluttering and spiraling motions of buoyancy-driven bodies

NASA Astrophysics Data System (ADS)

Magnaudet, Jacques; Tchoufag, Joel; Fabre, David

2015-11-01

Gravity/buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Using a weakly nonlinear expansion of the full set of governing equations, we derive a new generic reduced-order model of this class of phenomena based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (eg. fluttering or spiraling) and characteristics (eg. frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

Quantitative theory of driven nonlinear brain dynamics.

PubMed

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Nonlinear Electrostatic Steepening of Whistler Waves: The Guiding Factors and Dynamics in Inhomogeneous Systems

NASA Astrophysics Data System (ADS)

Agapitov, O.; Drake, J. F.; Vasko, I.; Mozer, F. S.; Artemyev, A.; Krasnoselskikh, V.; Angelopoulos, V.; Wygant, J.; Reeves, G. D.

2018-03-01

Whistler mode chorus waves are particularly important in outer radiation belt dynamics due to their key role in controlling the acceleration and scattering of electrons over a very wide energy range. The efficiency of wave-particle resonant interactions is defined by whistler wave properties which have been described by the approximation of plane linear waves propagating through the cold plasma of the inner magnetosphere. However, recent observations of extremely high-amplitude whistlers suggest the importance of nonlinear wave-particle interactions for the dynamics of the outer radiation belt. Oblique chorus waves observed in the inner magnetosphere often exhibit drastically nonsinusoidal (with significant power in the higher harmonics) waveforms of the parallel electric field, presumably due to the feedback from hot resonant electrons. We have considered the nature and properties of such nonlinear whistler waves observed by the Van Allen Probes and Time History of Events and Macroscale Interactions define during Substorms in the inner magnetosphere, and we show that the significant enhancement of the wave electrostatic component can result from whistler wave coupling with the beam-driven electrostatic mode through the resonant interaction with hot electron beams. Being modulated by a whistler wave, the electron beam generates a driven electrostatic mode significantly enhancing the parallel electric field of the initial whistler wave. We confirm this mechanism using a self-consistent particle-in-cell simulation. The nonlinear electrostatic component manifests properties of the beam-driven electron acoustic mode and can be responsible for effective electron acceleration in the inhomogeneous magnetic field.

Quantum annealing with parametrically driven nonlinear oscillators

NASA Astrophysics Data System (ADS)

Puri, Shruti

While progress has been made towards building Ising machines to solve hard combinatorial optimization problems, quantum speedups have so far been elusive. Furthermore, protecting annealers against decoherence and achieving long-range connectivity remain important outstanding challenges. With the hope of overcoming these challenges, I introduce a new paradigm for quantum annealing that relies on continuous variable states. Unlike the more conventional approach based on two-level systems, in this approach, quantum information is encoded in two coherent states that are stabilized by parametrically driving a nonlinear resonator. I will show that a fully connected Ising problem can be mapped onto a network of such resonators, and outline an annealing protocol based on adiabatic quantum computing. During the protocol, the resonators in the network evolve from vacuum to coherent states representing the ground state configuration of the encoded problem. In short, the system evolves between two classical states following non-classical dynamics. As will be supported by numerical results, this new annealing paradigm leads to superior noise resilience. Finally, I will discuss a realistic circuit QED realization of an all-to-all connected network of parametrically driven nonlinear resonators. The continuous variable nature of the states in the large Hilbert space of the resonator provides new opportunities for exploring quantum phase transitions and non-stoquastic dynamics during the annealing schedule.

Experimental study of linear and nonlinear regimes of density-driven instabilities induced by CO{sub 2} dissolution in water

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

Outeda, R.; D'Onofrio, A.; El Hasi, C.

Density driven instabilities produced by CO{sub 2} (gas) dissolution in water containing a color indicator were studied in a Hele Shaw cell. The images were analyzed and instability patterns were characterized by mixing zone temporal evolution, dispersion curves, and the growth rate for different CO{sub 2} pressures and different color indicator concentrations. The results obtained from an exhaustive analysis of experimental data show that this system has a different behaviour in the linear regime of the instabilities (when the growth rate has a linear dependence with time), from the nonlinear regime at longer times. At short times using a colormore » indicator to see the evolution of the pattern, the images show that the effects of both the color indicator and CO{sub 2} pressure are of the same order of magnitude: The growth rates are similar and the wave numbers are in the same range (0–30 cm{sup −1}) when the system is unstable. Although in the linear regime the dynamics is affected similarly by the presence of the indicator and CO{sub 2} pressure, in the nonlinear regime, the influence of the latter is clearly more pronounced than the effects of the color indicator.« less

Time-periodic solutions of driven-damped trimer granular crystals

DOE PAGES

Charalampidis, E. G.; Li, F.; Chong, C.; ...

2015-01-01

In this work, we consider time-periodic structures of granular crystals consisting of alternate chrome steel (S) and tungsten carbide (W) spherical particles where each unit cell follows the pattern of a 2:1 trimer: S-W-S. The configuration at the left boundary is driven by a harmonic in-time actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modesmore » and the states dictated by the linear drive collide in a saddle-node bifurcation as the driving amplitude is increased, beyond which the dynamics of the system becomes chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental full-field visualization of the time-periodic structures.« less

The nonlinear differential equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos

NASA Astrophysics Data System (ADS)

Hide, Raymond

1997-02-01

This paper discusses the derivation of the autonomous sets of dimensionless nonlinear ordinary differential equations (ODE's) that govern the behaviour of a hierarchy of related electro-mechanical self-exciting Faraday-disk homopolar dynamo systems driven by steady mechanical couples. Each system comprises N interacting units which could be arranged in a ring or lattice. Within each unit and connected in parallel or in series with the coil are electric motors driven into motion by the dynamo, all having linear characteristics, so that nonlinearity arises entirely through the coupling between components. By introducing simple extra terms into the equations it is possible to represent biasing effects arising from impressed electromotive forces due to thermoelectric or chemical processes and from the presence of ambient magnetic fields. Dissipation in the system is due not only to ohmic heating but also to mechanical friction in the disk and the motors, with the latter agency, no matter how weak, playing an unexpectedly crucial rôle in the production of régimes of chaotic behaviour. This has already been demonstrated in recent work on a case of a single unit incorporating just one series motor, which is governed by a novel autonomous set of nonlinear ODE's with three time-dependent variables and four control parameters. It will be of mathematical as well as geophysical and astrophysical interest to investigate systematically phase and amplitude locking and other types of behaviour in the more complicated cases that arise when N > 1, which can typically involve up to 6 N dependent variables and 19 N-5 control parameters. Even the simplest members of the hierarchy, with N as low as 1, 2 or 3, could prove useful as physically-realistic low-dimensional models in theoretical studies of fluctuating stellar and planetary magnetic fields. Geomagnetic polarity reversals could be affected by the presence of the Earth's solid metallic inner core, driven like an electric motor by currents generated by self-exciting magnetohydrodynamic (MHD) dynamo action involving motional induction associated with buoyancy-driven flow in the liquid metallic outer core. The study of biased disk dynamos could bear on the theory of the magnetic fields of natural systems where a significant background field is present (e.g., Galilean satellites of Jupiter) or when the action of motional induction is modified by electromotive forces produced by other mechanisms, such as thermoelectric processes, as in certain stars.

Analysis of Nonlinear Dynamics in Linear Compressors Driven by Linear Motors

NASA Astrophysics Data System (ADS)

Chen, Liangyuan

2018-03-01

The analysis of dynamic characteristics of the mechatronics system is of great significance for the linear motor design and control. Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically based on the linearized and nonlinear models. First, the influence factors considering the nonlinear gas force load were analyzed. Then, a simple linearized model was set up to analyze the influence on the stroke and resonance frequency. Finally, the nonlinear model was set up to analyze the effects of piston mass, spring stiffness, driving force as an example of design parameter variation. The simulating results show that the stroke can be obtained by adjusting the excitation amplitude, frequency and other adjustments, the equilibrium position can be adjusted by adjusting the DC input, and to make the more efficient operation, the operating frequency must always equal to the resonance frequency.

A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal

NASA Astrophysics Data System (ADS)

Coudeyras, N.; Sinou, J.-J.; Nacivet, S.

2009-01-01

Brake squeal noise is still an issue since it generates high warranty costs for the automotive industry and irritation for customers. Key parameters must be known in order to reduce it. Stability analysis is a common method of studying nonlinear phenomena and has been widely used by the scientific and the engineering communities for solving disc brake squeal problems. This type of analysis provides areas of stability versus instability for driven parameters, thereby making it possible to define design criteria. Nevertheless, this technique does not permit obtaining the vibrating state of the brake system and nonlinear methods have to be employed. Temporal integration is a well-known method for computing the dynamic solution but as it is time consuming, nonlinear methods such as the Harmonic Balance Method (HBM) are preferred. This paper presents a novel nonlinear method called the Constrained Harmonic Balance Method (CHBM) that works for nonlinear systems subject to flutter instability. An additional constraint-based condition is proposed that omits the static equilibrium point (i.e. the trivial static solution of the nonlinear problem that would be obtained by applying the classical HBM) and therefore focuses on predicting both the Fourier coefficients and the fundamental frequency of the stationary nonlinear system. The effectiveness of the proposed nonlinear approach is illustrated by an analysis of disc brake squeal. The brake system under consideration is a reduced finite element model of a pad and a disc. Both stability and nonlinear analyses are performed and the results are compared with a classical variable order solver integration algorithm. Therefore, the objectives of the following paper are to present not only an extension of the HBM (CHBM) but also to demonstrate an application to the specific problem of disc brake squeal with extensively parametric studies that investigate the effects of the friction coefficient, piston pressure, nonlinear stiffness and structural damping.

Chaos as an intermittently forced linear system.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

Near Optimal Event-Triggered Control of Nonlinear Discrete-Time Systems Using Neurodynamic Programming.

PubMed

Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani

2016-09-01

This paper presents an event-triggered near optimal control of uncertain nonlinear discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor-critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.

Use of the dispersion ratio in estimating the nonlinear properties of an object of diagnosis

NASA Technical Reports Server (NTRS)

Balitskiy, F. Y.; Genkin, M. D.; Ivanova, M. A.; Kobrinskiy, A. A.; Sokolova, A. G.

1973-01-01

An experimental investigation for estimating the nonlinearity of a diagnostic object was carried out on a single-stage, spur gear reducer. The linearity of the properties of spur gearing (including the linearity of its mode of operation) was tested. Torsional vibrations of the driven wheel and transverse (to the meshing plane) vibrations of the drive wheel on its support were taken as the two outputs of the object to be analyzed. The results of the investigation showed that the degree of nonlinearity of a reducing gear is essentially connected with its operating mode, so that different mathematical models of it can correspond to different values of the system parameters.

Nonlinear Alfvén wave propagating in ideal MHD plasmas

NASA Astrophysics Data System (ADS)

Zheng, Jugao; Chen, Yinhua; Yu, Mingyang

2016-01-01

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

Paucity of attractors in nonlinear systems driven with complex signals.

PubMed

Pethel, Shawn D; Blakely, Jonathan N

2011-04-01

We study the probability of multistability in a quadratic map driven repeatedly by a random signal of length N, where N is taken as a measure of the signal complexity. We first establish analytically that the number of coexisting attractors is bounded above by N. We then numerically estimate the probability p of a randomly chosen signal resulting in a multistable response as a function of N. Interestingly, with increasing drive signal complexity the system exhibits a paucity of attractors. That is, almost any drive signal beyond a certain complexity level will result in a single attractor response (p=0). This mechanism may play a role in allowing sensitive multistable systems to respond consistently to external influences.

Consistency properties of chaotic systems driven by time-delayed feedback

NASA Astrophysics Data System (ADS)

Jüngling, T.; Soriano, M. C.; Oliver, N.; Porte, X.; Fischer, I.

2018-04-01

Consistency refers to the property of an externally driven dynamical system to respond in similar ways to similar inputs. In a delay system, the delayed feedback can be considered as an external drive to the undelayed subsystem. We analyze the degree of consistency in a generic chaotic system with delayed feedback by means of the auxiliary system approach. In this scheme an identical copy of the nonlinear node is driven by exactly the same signal as the original, allowing us to verify complete consistency via complete synchronization. In the past, the phenomenon of synchronization in delay-coupled chaotic systems has been widely studied using correlation functions. Here, we analytically derive relationships between characteristic signatures of the correlation functions in such systems and unequivocally relate them to the degree of consistency. The analytical framework is illustrated and supported by numerical calculations of the logistic map with delayed feedback for different replica configurations. We further apply the formalism to time series from an experiment based on a semiconductor laser with a double fiber-optical feedback loop. The experiment constitutes a high-quality replica scheme for studying consistency of the delay-driven laser and confirms the general theoretical results.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

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

High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity.

PubMed

Reed, M D; DiCarlo, L; Johnson, B R; Sun, L; Schuster, D I; Frunzio, L; Schoelkopf, R J

2010-10-22

We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that, in the strongly driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.

Nonlinear Friction Compensation of Ball Screw Driven Stage Based on Variable Natural Length Spring Model and Disturbance Observer

NASA Astrophysics Data System (ADS)

Asaumi, Hiroyoshi; Fujimoto, Hiroshi

Ball screw driven stages are used for industrial equipments such as machine tools and semiconductor equipments. Fast and precise positioning is necessary to enhance productivity and microfabrication technology of the system. The rolling friction of the ball screw driven stage deteriorate the positioning performance. Therefore, the control system based on the friction model is necessary. In this paper, we propose variable natural length spring model (VNLS model) as the friction model. VNLS model is simple and easy to implement as friction controller. Next, we propose multi variable natural length spring model (MVNLS model) as the friction model. MVNLS model can represent friction characteristic of the stage precisely. Moreover, the control system based on MVNLS model and disturbance observer is proposed. Finally, the simulation results and experimental results show the advantages of the proposed method.

Nonlinear structure formation in ion-temperature-gradient driven drift waves in pair-ion plasma with nonthermal electron distribution

NASA Astrophysics Data System (ADS)

Razzaq, Javaria; Haque, Q.; Khan, Majid; Bhatti, Adnan Mehmood; Kamran, M.; Mirza, Arshad M.

2018-02-01

Nonlinear structure formation in ion-temperature-gradient (ITG) driven waves is investigated in pair-ion plasma comprising ions and nonthermal electrons (kappa, Cairns). By using the transport equations of the Braginskii model, a new set of nonlinear equations are derived. A linear dispersion relation is obtained and discussed analytically as well as numerically. It is shown that the nonthermal population of electrons affects both the linear and nonlinear characteristics of the ITG mode in pair-ion plasma. This work will be useful in tokamaks and stellarators where non-Maxwellian population of electrons may exist due to resonant frequency heating, electron cyclotron heating, runaway electrons, etc.

Jump Resonance in Fractional Order Circuits

NASA Astrophysics Data System (ADS)

Buscarino, Arturo; Caponetto, Riccardo; Famoso, Carlo; Fortuna, Luigi

The occurrence of an hysteretic loop in the frequency response of a driven nonlinear system is a phenomenon deeply investigated in nonlinear control theory. Such a phenomenon, which is linked to the multistable behavior of the system, is called jump resonance, since the magnitude of the frequency response is subjected to an abrupt jump up/down with respect to the increasing/decreasing of the frequency of the driving signal. In this paper, we aim at investigating fractional order nonlinear systems showing jump resonance, that is systems in which the order of the derivative is noninteger and their frequency response has a magnitude that is a multivalued function in a given range of frequencies. Furthermore, a strategy for designing fractional order systems showing jump resonance is presented along with the procedure to design and implement an analog circuit based on the approximation of the fractional order derivative. An extensive numerical analysis allows one to assess that the phenomenon is robust to the difference in the derivative order, enlightening the first example of a system with order lower than two which is able to demonstrate a jump resonance behavior.

Analysis of the power flow in nonlinear oscillators driven by random excitation using the first Wiener kernel

NASA Astrophysics Data System (ADS)

Hawes, D. H.; Langley, R. S.

2018-01-01

Random excitation of mechanical systems occurs in a wide variety of structures and, in some applications, calculation of the power dissipated by such a system will be of interest. In this paper, using the Wiener series, a general methodology is developed for calculating the power dissipated by a general nonlinear multi-degree-of freedom oscillatory system excited by random Gaussian base motion of any spectrum. The Wiener series method is most commonly applied to systems with white noise inputs, but can be extended to encompass a general non-white input. From the extended series a simple expression for the power dissipated can be derived in terms of the first term, or kernel, of the series and the spectrum of the input. Calculation of the first kernel can be performed either via numerical simulations or from experimental data and a useful property of the kernel, namely that the integral over its frequency domain representation is proportional to the oscillating mass, is derived. The resulting equations offer a simple conceptual analysis of the power flow in nonlinear randomly excited systems and hence assist the design of any system where power dissipation is a consideration. The results are validated both numerically and experimentally using a base-excited cantilever beam with a nonlinear restoring force produced by magnets.

Traveling wave solution of driven nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-09-01

The traveling solitary and cnoidal wave solutions of the one dimensional driven nonlinear Schrödinger equation with a generalized form of nonlinearity are presented in this paper. We examine the modulation of nonlinear solitary excitations in two known weakly nonlinear models of classic oscillators, namely, the Helmholtz and Duffing oscillators and envelope structure formations for different oscillator and driver parameters. It is shown that two distinct regimes of subcritical and supercritical modulations may occur for nonlinear excitations with propagation speeds v <√{4 F0 } and v >√{4 F0 } , respectively, in which F0 is the driver force strength. The envelope soliton and cnoidal waves in these regimes are observed to be fundamentally different. The effect of pseudoenergy on the structure of the modulated envelope excitations is studied in detail for both sub- and supercritical modulation types. The current model for traveling envelope excitations may be easily extended to pseudopotentials with full nonlinearity relevant to more realistic gases, fluids, and plasmas.

Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2017-03-01

We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.

Precipitation and floodiness

NASA Astrophysics Data System (ADS)

Stephens, E.; Day, J. J.; Pappenberger, F.; Cloke, H.

2015-12-01

There are a number of factors that lead to nonlinearity between precipitation anomalies and flood hazard; this nonlinearity is a pertinent issue for applications that use a precipitation forecast as a proxy for imminent flood hazard. We assessed the degree of this nonlinearity for the first time using a recently developed global-scale hydrological model driven by the ERA-Interim/Land precipitation reanalysis (1980-2010). We introduced new indices to assess large-scale flood hazard, or floodiness, and quantified the link between monthly precipitation, river discharge, and floodiness anomalies at the global and regional scales. The results show that monthly floodiness is not well correlated with precipitation, therefore demonstrating the value of hydrometeorological systems for providing floodiness forecasts for decision-makers. A method is described for forecasting floodiness using the Global Flood Awareness System, building a climatology of regional floodiness from which to forecast floodiness anomalies out to 2 weeks.

Differential Activity-Driven Instabilities in Biphasic Active Matter

NASA Astrophysics Data System (ADS)

Weber, Christoph A.; Rycroft, Chris H.; Mahadevan, L.

2018-06-01

Active stresses can cause instabilities in contractile gels and living tissues. Here we provide a generic hydrodynamic theory that treats these systems as a mixture of two phases of varying activity and different mechanical properties. We find that differential activity between the phases causes a uniform mixture to undergo a demixing instability. We follow the nonlinear evolution of the instability and characterize a phase diagram of the resulting patterns. Our study complements other instability mechanisms in mixtures driven by differential adhesion, differential diffusion, differential growth, and differential motion.

Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

NASA Astrophysics Data System (ADS)

Pozharskiy, Dmitry

In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

Adaptive Neural Output Feedback Control for Nonstrict-Feedback Stochastic Nonlinear Systems With Unknown Backlash-Like Hysteresis and Unknown Control Directions.

PubMed

Yu, Zhaoxu; Li, Shugang; Yu, Zhaosheng; Li, Fangfei

2018-04-01

This paper investigates the problem of output feedback adaptive stabilization for a class of nonstrict-feedback stochastic nonlinear systems with both unknown backlashlike hysteresis and unknown control directions. A new linear state transformation is applied to the original system, and then, control design for the new system becomes feasible. By combining the neural network's (NN's) parameterization, variable separation technique, and Nussbaum gain function method, an input-driven observer-based adaptive NN control scheme, which involves only one parameter to be updated, is developed for such systems. All closed-loop signals are bounded in probability and the error signals remain semiglobally bounded in the fourth moment (or mean square). Finally, the effectiveness and the applicability of the proposed control design are verified by two simulation examples.

Cross-diffusion-driven hydrodynamic instabilities in a double-layer system: General classification and nonlinear simulations

NASA Astrophysics Data System (ADS)

Budroni, M. A.

2015-12-01

Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.

Nonlinear Internal Waves on the Inner Shelf: Observations Using a Distributed Temperature Sensing (DTS) System.

NASA Astrophysics Data System (ADS)

Davis, K. A.; Reid, E. C.; Cohen, A. L.

2016-02-01

Internal waves propagating across the continental slope and shelf are transformed by the competing effects of nonlinear steepening and dispersive spreading, forming nonlinear internal waves (NLIWs) that can penetrate onto the shallow inner shelf, often appearing in the form of bottom-propagating nonlinear internal bores or boluses. NLIWs play a significant role in nearshore dynamics with baroclinic current amplitudes on the order of that of wind- and surface wave-driven flows and rapid temperature changes on the order of annual ranges. In June 2014 we used a Distributed Temperature Sensing (DTS) system to give a continuous cross-shelf view of nonlinear internal wave dynamics on the forereef of Dongsha Atoll, a coral reef in the northern South China Sea. A DTS system measures temperature continuously along the length of an optical fiber, resolving meter-to-kilometer spatial scales. This unique view of cross-shelf temperature structure made it possible to observe internal wave reflection, variable propagation speed across the shelf, bolus formation and dissipation. Additionally, we used the DTS data to track internal waves across the shallow fore reef and onto the reef flat and to quantify spatial patterns in temperature variability. Shoaling internal waves are an important process affecting physical variability and water properties on the reef.

Non-classical light generated by quantum-noise-driven cavity optomechanics.

PubMed

Brooks, Daniel W C; Botter, Thierry; Schreppler, Sydney; Purdy, Thomas P; Brahms, Nathan; Stamper-Kurn, Dan M

2012-08-23

Optomechanical systems, in which light drives and is affected by the motion of a massive object, will comprise a new framework for nonlinear quantum optics, with applications ranging from the storage and transduction of quantum information to enhanced detection sensitivity in gravitational wave detectors. However, quantum optical effects in optomechanical systems have remained obscure, because their detection requires the object’s motion to be dominated by vacuum fluctuations in the optical radiation pressure; so far, direct observations have been stymied by technical and thermal noise. Here we report an implementation of cavity optomechanics using ultracold atoms in which the collective atomic motion is dominantly driven by quantum fluctuations in radiation pressure. The back-action of this motion onto the cavity light field produces ponderomotive squeezing. We detect this quantum phenomenon by measuring sub-shot-noise optical squeezing. Furthermore, the system acts as a low-power, high-gain, nonlinear parametric amplifier for optical fluctuations, demonstrating a gain of 20 dB with a pump corresponding to an average of only seven intracavity photons. These findings may pave the way for low-power quantum optical devices, surpassing quantum limits on position and force sensing, and the control and measurement of motion in quantum gases.

Meaning as a Nonlinear Effect: The Birth of Cool

ERIC Educational Resources Information Center

Blommaert, Jan

2015-01-01

Saussurean and Chomskyan "conduit" views of meaning in communication, dominant in much of expert and lay linguistic semantics, presuppose a simple, closed and linear system in which outcomes can be predicted and explained in terms of finite sets of rules. Summarizing critical traditions of scholarship, notably those driven by Bateson's…

A Process Dynamics and Control Experiment for the Undergraduate Laboratory

ERIC Educational Resources Information Center

Spencer, Jordan L.

2009-01-01

This paper describes a process control experiment. The apparatus includes a three-vessel glass flow system with a variable flow configuration, means for feeding dye solution controlled by a stepper-motor driven valve, and a flow spectrophotometer. Students use impulse response data and nonlinear regression to estimate three parameters of a model…

Theory of parametrically amplified electron-phonon superconductivity

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

Babadi, Mehrtash; Knap, Michael; Martin, Ivar

2017-07-01

Ultrafast optical manipulation of ordered phases in strongly correlated materials is a topic of significant theoretical, experimental, and technological interest. Inspired by a recent experiment on light-induced superconductivity in fullerenes [M. Mitrano et al., Nature (London) 530, 461 (2016)], we develop a comprehensive theory of light-induced superconductivity in driven electron-phonon systemswith lattice nonlinearities. In analogy with the operation of parametric amplifiers, we show how the interplay between the external drive and lattice nonlinearities lead to significantly enhanced effective electron-phonon couplings. We provide a detailed and unbiased study of the nonequilibrium dynamics of the driven system using the real-time Green's functionmore » technique. To this end, we develop a Floquet generalization of the Migdal-Eliashberg theory and derive a numerically tractable set of quantum Floquet-Boltzmann kinetic equations for the coupled electron-phonon system. We study the role of parametric phonon generation and electronic heating in destroying the transient superconducting state. Finally, we predict the transient formation of electronic Floquet bands in time-and angle-resolved photoemission spectroscopy experiments as a consequence of the proposed mechanism.« less

A Novel Position Compensation Scheme for Cable-Pulley Mechanisms Used in Laparoscopic Surgical Robots

PubMed Central

Liang, Yunlei; Du, Zhijiang; Sun, Lining

2017-01-01

The tendon driven mechanism using a cable and pulley to transmit power is adopted by many surgical robots. However, backlash hysteresis objectively exists in cable-pulley mechanisms, and this nonlinear problem is a great challenge in precise position control during the surgical procedure. Previous studies mainly focused on the transmission characteristics of the cable-driven system and constructed transmission models under particular assumptions to solve nonlinear problems. However, these approaches are limited because the modeling process is complex and the transmission models lack general applicability. This paper presents a novel position compensation control scheme to reduce the impact of backlash hysteresis on the positioning accuracy of surgical robots’ end-effectors. In this paper, a position compensation scheme using a support vector machine based on feedforward control is presented to reduce the position tracking error. To validate the proposed approach, experimental validations are conducted on our cable-pulley system and comparative experiments are carried out. The results show remarkable improvements in the performance of reducing the positioning error for the use of the proposed scheme. PMID:28974011

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

NASA Astrophysics Data System (ADS)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

Alfvén Turbulence Driven by High-Dimensional Interior Crisis in the Solar Wind

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Rempel, E. L.; Macau, E. E. N.; Rosa, R. R.; Christiansen, F.

2003-09-01

Alfvén intermittent turbulence has been observed in the solar wind. It has been previously shown that the interplanetary Alfvén intermittent turbulence can appear due to a low-dimensional temporal chaos [1]. In this paper, we study the nonlinear spatiotemporal dynamics of Alfvén waves governed by the Kuramoto-Sivashinsky equation which describes the phase evolution of a large-amplitude Alfvén wave. We investigate the Alfvén turbulence driven by a high-dimensional interior crisis, which is a global bifurcation caused by the collision of a chaotic attractor with an unstable periodic orbit. This nonlinear phenomenon is analyzed using the numerical solutions of the model equation. The identification of the unstable periodic orbits and their invariant manifolds is fundamental for understanding the instability, chaos and turbulence in complex systems such as the solar wind plasma. The high-dimensional dynamical system approach to space environment turbulence developed in this paper can improve our interpretation of the origin and the nature of Alfvén turbulence observed in the solar wind.

Modification of optical properties by adiabatic shifting of resonances in a four-level atom

NASA Astrophysics Data System (ADS)

Dutta, Bibhas Kumar; Panchadhyayee, Pradipta

2018-04-01

We describe the linear and nonlinear optical properties of a four-level atomic system, after reducing it to an effective two-level atomic model under the condition of adiabatic shifting of resonances driven by two coherent off-resonant fields. The reduced form of the Hamiltonian corresponding to the two-level system is obtained by employing an adiabatic elimination procedure in the rate equations of the probability amplitudes for the proposed four-level model. For a weak probe field operating in the system, the nonlinear dependence of complex susceptibility on the Rabi frequencies and the detuning parameters of the off-resonant driving fields makes it possible to exhibit coherent control of single-photon and two-photon absorption and transparency, the evolution of enhanced Self-Kerr nonlinearity and noticeable dispersive switching. We have shown how the quantum interference results in the generic four-level model at the adiabatic limit. The present scheme describes the appearance of single-photon transparency without invoking any exact two-photon resonance.

Dual RBFNNs-Based Model-Free Adaptive Control With Aspen HYSYS Simulation.

PubMed

Zhu, Yuanming; Hou, Zhongsheng; Qian, Feng; Du, Wenli

2017-03-01

In this brief, we propose a new data-driven model-free adaptive control (MFAC) method with dual radial basis function neural networks (RBFNNs) for a class of discrete-time nonlinear systems. The main novelty lies in that it provides a systematic design method for controller structure by the direct usage of I/O data, rather than using the first-principle model or offline identified plant model. The controller structure is determined by equivalent-dynamic-linearization representation of the ideal nonlinear controller, and the controller parameters are tuned by the pseudogradient information extracted from the I/O data of the plant, which can deal with the unknown nonlinear system. The stability of the closed-loop control system and the stability of the training process for RBFNNs are guaranteed by rigorous theoretical analysis. Meanwhile, the effectiveness and the applicability of the proposed method are further demonstrated by the numerical example and Aspen HYSYS simulation of distillation column in crude styrene produce process.

Hydrodynamically induced oscillations and traffic dynamics in 1D microfludic networks

NASA Astrophysics Data System (ADS)

Bartolo, Denis; Jeanneret, Raphael

2011-03-01

We report on the traffic dynamics of particles driven through a minimal microfluidic network. Even in the minimal network consisting in a single loop, the traffic dynamics has proven to yield complex temporal patterns, including periodic, multi-periodic or chaotic sequences. This complex dynamics arises from the strongly nonlinear hydrodynamic interactions between the particles, that takes place at a junction. To better understand the consequences of this nontrivial coupling, we combined theoretical, numerical and experimental efforts and solved the 3-body problem in a 1D loop network. This apparently simple dynamical system revealed a rich and unexpected dynamics, including coherent spontaneous oscillations along closed orbits. Striking similarities between Hamiltonian systems and this driven dissipative system will be explained.

Transient chaos and crisis phenomena in butterfly valves driven by solenoid actuators

NASA Astrophysics Data System (ADS)

Naseradinmousavi, Peiman; Nataraj, C.

2012-11-01

Chilled water systems used in the industry and on board ships are critical for safe and reliable operation. It is hence important to understand the fundamental physics of these systems. This paper focuses in particular on a critical part of the automation system, namely, actuators and valves that are used in so-called "smart valve" systems. The system is strongly nonlinear, and necessitates a nonlinear dynamic analysis to be able to predict all critical phenomena that affect effective operation and efficient design. The derived mathematical model includes electromagnetics, fluid mechanics, and mechanical dynamics. Nondimensionalization has been carried out in order to reduce the large number of parameters to a few critical independent sets to help carry out a broad parametric analysis. The system stability analysis is then carried out with the aid of the tools from nonlinear dynamic analysis. This reveals that the system is unstable in a certain region of the parameter space. The system is also shown to exhibit crisis and transient chaotic responses; this is characterized using Lyapunov exponents and power spectra. Knowledge and avoidance of these dangerous regimes is necessary for successful and safe operation.

Nonlinear resonances and antiresonances of a forced sonic vacuum

DOE PAGES

Pozharskiy, D.; Zhang, Y.; Williams, M. O.; ...

2015-12-23

We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., ofmore » period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) “nonlinear spectrum” in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). As a result, we rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.« less

Spontaneous symmetry breaking in coupled parametrically driven waveguides.

PubMed

Dror, Nir; Malomed, Boris A

2009-01-01

We introduce a system of linearly coupled parametrically driven damped nonlinear Schrödinger equations, which models a laser based on a nonlinear dual-core waveguide with parametric amplification symmetrically applied to both cores. The model may also be realized in terms of parallel ferromagnetic films, in which the parametric gain is provided by an external field. We analyze spontaneous symmetry breaking (SSB) of fundamental and multiple solitons in this system, which was not studied systematically before in linearly coupled dissipative systems with intrinsic nonlinearity. For fundamental solitons, the analysis reveals three distinct SSB scenarios. Unlike the standard dual-core-fiber model, the present system gives rise to a vast bistability region, which may be relevant to applications. Other noteworthy findings are restabilization of the symmetric soliton after it was destabilized by the SSB bifurcation, and the existence of a generic situation with all solitons unstable in the single-component (decoupled) model, while both symmetric and asymmetric solitons may be stable in the coupled system. The stability of the asymmetric solitons is identified via direct simulations, while for symmetric and antisymmetric ones the stability is verified too through the computation of stability eigenvalues, families of antisymmetric solitons being entirely unstable. In this way, full stability maps for the symmetric solitons are produced. We also investigate the SSB bifurcation of two-soliton bound states (it breaks the symmetry between the two components, while the two peaks in the shape of the soliton remain mutually symmetric). The family of the asymmetric double-peak states may decouple from its symmetric counterpart, being no longer connected to it by the bifurcation, with a large portion of the asymmetric family remaining stable.

Generation of high-field narrowband terahertz radiation by counterpropagating plasma wakefields

NASA Astrophysics Data System (ADS)

Timofeev, I. V.; Annenkov, V. V.; Volchok, E. P.

2017-10-01

It is found that nonlinear interaction of plasma wakefields driven by counterpropagating laser or particle beams can efficiently generate high-power electromagnetic radiation at the second harmonic of the plasma frequency. Using a simple analytical theory and particle-in-cell simulations, we show that this phenomenon can be attractive for producing high-field ( ˜10 MV/cm) tunable terahertz radiation with a narrow line width. For laser drivers produced by existing petawatt-class systems, this nonlinear process opens the way to the generation of gigawatt, multi-millijoule terahertz pulses which are not presently available for any other generating schemes.

Generating higher-order quantum dissipation from lower-order parametric processes

NASA Astrophysics Data System (ADS)

Mundhada, S. O.; Grimm, A.; Touzard, S.; Vool, U.; Shankar, S.; Devoret, M. H.; Mirrahimi, M.

2017-06-01

The stabilisation of quantum manifolds is at the heart of error-protected quantum information storage and manipulation. Nonlinear driven-dissipative processes achieve such stabilisation in a hardware efficient manner. Josephson circuits with parametric pump drives implement these nonlinear interactions. In this article, we propose a scheme to engineer a four-photon drive and dissipation on a harmonic oscillator by cascading experimentally demonstrated two-photon processes. This would stabilise a four-dimensional degenerate manifold in a superconducting resonator. We analyse the performance of the scheme using numerical simulations of a realisable system with experimentally achievable parameters.

Thermal conductance of suspended nanoribbons: interplay between strain and interatomic potential nonlinearity

NASA Astrophysics Data System (ADS)

Barreto, Roberto; Florencia Carusela, M.; Monastra, Alejandro G.

2017-10-01

We investigate the role that nonlinearity in the interatomic potential has on the thermal conductance of a suspended nanoribbon when it is subjected to a longitudinal strain. To focus on the first cubic and quartic nonlinear terms of a general potential, we propose an atomic system based on an α-β Fermi-Pasta-Ulam nearest neighbor interaction. We perform classical molecular dynamics simulations to investigate the contribution of longitudinal, transversal and flexural modes to the thermal conductance as a function of the α-β parameters and the applied strain. We compare the cases where atoms are allowed to vibrate only in plane (2D) with the case of vibrations in and out of plane (3D). We find that the dependence of conductance on α and β relies on a crossover phenomenon between linear/nonlinear delocalized/localized flexural and transversal modes, driven by an on/off switch of the strain.

Nonlinear flow response of soft hair beds

NASA Astrophysics Data System (ADS)

Alvarado, José; Comtet, Jean; de Langre, Emmanuel; Hosoi, A. E.

2017-10-01

We are `hairy' on the inside: beds of passive fibres anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. These hairs are soft enough to deform in response to stresses from fluid flows. Yet fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem that is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear-driven Stokes flows. We characterize this system with a theoretical model that accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers towards the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter that controls nonlinear behaviour. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps.

Deterministic representation of chaos with application to turbulence

NASA Technical Reports Server (NTRS)

Zak, M.

1987-01-01

Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.

Steady-state mechanical squeezing and ground-state cooling of a Duffing anharmonic oscillator in an optomechanical cavity assisted by a nonlinear medium

NASA Astrophysics Data System (ADS)

Momeni, F.; Naderi, M. H.

2018-05-01

In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.

Measuring system for the determination of nonlinear elastic and electromechanical properties in solids

NASA Astrophysics Data System (ADS)

Straube, U.; Beige, H.

1999-03-01

An arbitrary waveform generator was introduced to produce pulse bursts with improved time jitter for the generation of ultrasound pulses. The problem of pulse amplification was solved using a ceramic power triode driven by a power FET amplifier. The construction of these special amplifier stages is mainly considered in this paper.

Nonlinear Decoupling Control With ANFIS-Based Unmodeled Dynamics Compensation for a Class of Complex Industrial Processes.

PubMed

Zhang, Yajun; Chai, Tianyou; Wang, Hong; Wang, Dianhui; Chen, Xinkai

2018-06-01

Complex industrial processes are multivariable and generally exhibit strong coupling among their control loops with heavy nonlinear nature. These make it very difficult to obtain an accurate model. As a result, the conventional and data-driven control methods are difficult to apply. Using a twin-tank level control system as an example, a novel multivariable decoupling control algorithm with adaptive neural-fuzzy inference system (ANFIS)-based unmodeled dynamics (UD) compensation is proposed in this paper for a class of complex industrial processes. At first, a nonlinear multivariable decoupling controller with UD compensation is introduced. Different from the existing methods, the decomposition estimation algorithm using ANFIS is employed to estimate the UD, and the desired estimating and decoupling control effects are achieved. Second, the proposed method does not require the complicated switching mechanism which has been commonly used in the literature. This significantly simplifies the obtained decoupling algorithm and its realization. Third, based on some new lemmas and theorems, the conditions on the stability and convergence of the closed-loop system are analyzed to show the uniform boundedness of all the variables. This is then followed by the summary on experimental tests on a heavily coupled nonlinear twin-tank system that demonstrates the effectiveness and the practicability of the proposed method.

Optical response in a laser-driven quantum pseudodot system

NASA Astrophysics Data System (ADS)

Kilic, D. Gul; Sakiroglu, S.; Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sokmen, I.

2017-03-01

We investigate theoretically the intense laser-induced optical absorption coefficients and refractive index changes in a two-dimensional quantum pseudodot system under an uniform magnetic field. The effects of non-resonant, monochromatic intense laser field upon the system are treated within the framework of high-frequency Floquet approach in which the system is supposed to be governed by a laser-dressed potential. Linear and nonlinear absorption coefficients and relative changes in the refractive index are obtained by means of the compact-density matrix approach and iterative method. The results of numerical calculations for a typical GaAs quantum dot reveal that the optical response depends strongly on the magnitude of external magnetic field and characteristic parameters of the confinement potential. Moreover, we have demonstrated that the intense laser field modifies the confinement and thereby causes remarkable changes in the linear and nonlinear optical properties of the system.

Hybrid simulation of fishbone instabilities in the EAST tokamak

DOE PAGES

Shen, Wei; Wang, Feng; Fu, G. Y.; ...

2017-08-11

Hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in the experimental advanced superconducting tokamak (EAST) experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. Our results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a beta-induced Alfvenmore » eigenmode (BAE) with much higher frequency. This BAE is driven by higher energy beam ions. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. Furthermore, for the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution.« less

Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback

NASA Astrophysics Data System (ADS)

Marchewka, Chad; Larsen, Paul; Bhattacharjee, Sudeep; Booske, John; Sengele, Sean; Ryskin, Nikita; Titov, Vladimir

2006-01-01

The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube (TWT) amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the TWT output power back to the input in a delayed feedback configuration. A driver wave provides a constant external force to the system making it behave like a forced nonlinear oscillator. The effects of the feedback bandwidth, intensity, and phase are described. The study illuminates the different transitions to chaos and the effect of parameters such as the frequency and intensity of the driver wave. The detuning frequency, i.e., difference frequency between the driver wave and the natural oscillation of the system, has been identified as being an important physical parameter for controlling evolution to chaos. Among the observed routes to chaos, besides the more common period doubling, a new route called loss of frequency locking occurs when the driving frequency is adjacent to a natural oscillation mode. The feedback bandwidth controls the nonlinear dynamics of the system, particularly the number of natural oscillation modes. A computational model has been developed to simulate the experiments and reasonably good agreement is obtained between them. Experiments are described that demonstrate the feasibility of chaotic communications using two TWTs, where one is operated as a driven chaotic oscillator and the other as a time-delayed, open-loop amplifier.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

PubMed

Metzler, Holger; Müller, Markus; Sierra, Carlos A

2018-02-06

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

Influence of helical external driven current on nonlinear resistive tearing mode evolution and saturation in tokamaks

NASA Astrophysics Data System (ADS)

Zhang, W.; Wang, S.; Ma, Z. W.

2017-06-01

The influences of helical driven currents on nonlinear resistive tearing mode evolution and saturation are studied by using a three-dimensional toroidal resistive magnetohydrodynamic code (CLT). We carried out three types of helical driven currents: stationary, time-dependent amplitude, and thickness. It is found that the helical driven current is much more efficient than the Gaussian driven current used in our previous study [S. Wang et al., Phys. Plasmas 23(5), 052503 (2016)]. The stationary helical driven current cannot persistently control tearing mode instabilities. For the time-dependent helical driven current with f c d = 0.01 and δ c d < 0.04 , the island size can be reduced to its saturated level that is about one third of the initial island size. However, if the total driven current increases to about 7% of the total plasma current, tearing mode instabilities will rebound again due to the excitation of the triple tearing mode. For the helical driven current with time dependent strength and thickness, the reduction speed of the radial perturbation component of the magnetic field increases with an increase in the driven current and then saturates at a quite low level. The tearing mode is always controlled even for a large driven current.

Shear-flow driven dissipative instability and investigation of nonlinear drift-vortex modes in dusty plasmas with non-thermal ion population

NASA Astrophysics Data System (ADS)

Gul-e-Ali, Masood, W.; Mirza, Arshad M.

2017-12-01

The shear flow in dust dynamics driven waves in combination with the dust-neutral drag is studied in a plasma comprising of ions, electrons, and dust. Non-thermal population of ions is considered, which has been observed by many satellite missions. It is found that the dissipative instability produced by dust sheared flow and dust-neutral drag gets modified by the presence of nonthermal ions. It is found that the dissipative instability enhances for the Cairns distribution, whereas the kappa distribution arrests the growth of this instability. In the nonlinear regime, the formation of vortices in the system is studied. It is found that the nonthermal population of ions significantly alters these structures in comparison with their Maxwellian counterpart. The results obtained in this paper may have relevance in the planetary magnetospheres where the dust particles are present and non-Maxwellian distribution of particles have been observed by Freja and Viking satellites.

Towards classification of the bifurcation structure of a spherical cavitation bubble.

PubMed

Behnia, Sohrab; Sojahrood, Amin Jafari; Soltanpoor, Wiria; Sarkhosh, Leila

2009-12-01

We focus on a single cavitation bubble driven by ultrasound, a system which is a specimen of forced nonlinear oscillators and is characterized by its extreme sensitivity to the initial conditions. The driven radial oscillations of the bubble are considered to be implicated by the principles of chaos physics and owing to specific ranges of control parameters, can be periodic or chaotic. Despite the growing number of investigations on its dynamics, there is not yet an inclusive yardstick to sort the dynamical behavior of the bubble into classes; also, the response oscillations are so complex that long term prediction on the behavior becomes difficult to accomplish. In this study, the nonlinear dynamics of a bubble oscillator was treated numerically and the simulations were proceeded with bifurcation diagrams. The calculated bifurcation diagrams were compared in an attempt to classify the bubble dynamic characteristics when varying the control parameters. The comparison reveals distinctive bifurcation patterns as a consequence of driving the systems with unequal ratios of R(0)lambda (where R(0) is the bubble initial radius and lambda is the wavelength of the driving ultrasonic wave). Results indicated that systems having the equal ratio of R(0)lambda, share remarkable similarities in their bifurcating behavior and can be classified under a unit category.

Thermally and electrically controllable multiple high harmonics generation by harmonically driven quasi-two-dimensional electron gas

NASA Astrophysics Data System (ADS)

Maglevanny, I. I.; Smolar, V. A.; Karyakina, T. I.

2018-06-01

In this paper, we consider the activation processes in nonlinear meta-stable system based on a lateral (quasi-two-dimensional) superlattice and study the dynamics of such a system externally driven by a harmonic force. The internal control parameters are the longitudinal applied electric field and the sample temperature. The spontaneous transverse electric field is considered as an order parameter. The forced violations of order parameter are considered as a response of a system to periodic driving. We investigate the cooperative effects of self-organization and high harmonic forcing from the viewpoint of catastrophe theory and show the possibility of generation of third and higher odd harmonics in output signal that lead to distortion of its wave front. A higher harmonics detection strategy is further proposed and explained in detail by exploring the influences of system parameters on the response output of the system that are discussed through numerical simulations.

Nonlinear Magnus-induced dynamics and Shapiro spikes for ac and dc driven skyrmions on periodic quasi-one-dimensional substrates

NASA Astrophysics Data System (ADS)

Reichhardt, Charles; Reichhardt, Cynthia J. Olson

We numerically examine skyrmions interacting with a periodic quasi-one-dimensional substrate. When we drive the skyrmions perpendicular to the substrate periodicity direction, a rich variety of nonlinear Magnus-induced effects arise, in contrast to an overdamped system that shows only a linear velocity-force curve for this geometry. The skyrmion velocity-force curve is strongly nonlinear and we observe a Magnus-induced speed-up effect when the pinning causes the Magnus velocity response to align with the dissipative response. At higher applied drives these components decouple, resulting in strong negative differential conductivity. For skyrmions under combined ac and dc driving, we find a new class of phase locking phenomena in which the velocity-force curves contain a series of what we call Shapiro spikes, distinct from the Shapiro steps observed in overdamped systems. There are also regimes in which the skyrmion moves in the direction opposite to the applied dc drive to give negative mobility.

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

PubMed

Suslov, Sergey A

2010-02-01

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

Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

NASA Astrophysics Data System (ADS)

Sarma, Bijita; Sarma, Amarendra K.

2018-04-01

Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

How Non-Linearity and Grade-Level Differences Complicate the Validation of Observation Protocols

ERIC Educational Resources Information Center

Lazarev, Valeriy; Newman, Denis

2013-01-01

Teacher evaluation is currently a major policy issue at all levels of the K-12 system driven in large part by current US Department of Education requirements. The main objective of this study is to explore the patterns of relationship between observational scores and value-added measures of teacher performance in math classrooms and the variation…

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

NASA Astrophysics Data System (ADS)

Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

2017-06-01

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

Linking actin networks and cell membrane via a reaction-diffusion-elastic description of nonlinear filopodia initiation.

PubMed

Ben Isaac, Eyal; Manor, Uri; Kachar, Bechara; Yochelis, Arik; Gov, Nir S

2013-08-01

Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations.

Nonlinear dynamic modeling for smart material electro-hydraulic actuator development

NASA Astrophysics Data System (ADS)

Larson, John P.; Dapino, Marcelo J.

2013-03-01

Smart material electro-hydraulic actuators use hydraulic rectification by one-way check valves to amplify the motion of smart materials, such as magnetostrictives and piezoelectrics, in order to create compact, lightweight actuators. A piston pump driven by a smart material is combined with a hydraulic cylinder to form a self-contained, power-by-wire actuator that can be used in place of a conventional hydraulic system without the need for hydraulic lines and a centralized pump. The performance of an experimental actuator driven by a 12.7 mm diameter, 114 mm length Terfenol-D rod is evaluated over a range of applied input frequencies, loads, and currents. The peak performance achieved is 37 W, moving a 220 N load at a rate of 17 cm/s and producing a blocked pressure of 12.5 MPa. Additional tests are conducted to quantify the dynamic behavior of the one-way reed valves using a scanning laser vibrometer to identify the frequency response of the reeds and the effect of the valve seat and fluid mass loading. A lumped-parameter model is developed for the system that includes valve inertia and fluid response nonlinearities, and the model results are compared with the experimental data.

Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

PubMed

Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul

2012-09-01

In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.

Charging power optimization for nonlinear vibration energy harvesting systems subjected to arbitrary, persistent base excitations

NASA Astrophysics Data System (ADS)

Dai, Quanqi; Harne, Ryan L.

2018-01-01

The vibrations of mechanical systems and structures are often a combination of periodic and random motions. Emerging interest to exploit nonlinearities in vibration energy harvesting systems for charging microelectronics may be challenged by such reality due to the potential to transition between favorable and unfavorable dynamic regimes for DC power delivery. Therefore, a need exists to devise an optimization method whereby charging power from nonlinear energy harvesters remains maximized when excitation conditions are neither purely harmonic nor purely random, which have been the attention of past research. This study meets the need by building from an analytical approach that characterizes the dynamic response of nonlinear energy harvesting platforms subjected to combined harmonic and stochastic base accelerations. Here, analytical expressions are formulated and validated to optimize charging power while the influences of the relative proportions of excitation types are concurrently assessed. It is found that about a 2 times deviation in optimal resistive loads can reduce the charging power by 20% when the system is more prominently driven by harmonic base accelerations, whereas a greater proportion of stochastic excitation results in a 11% reduction in power for the same resistance deviation. In addition, the results reveal that when the frequency of a predominantly harmonic excitation deviates by 50% from optimal conditions the charging power reduces by 70%, whereas the same frequency deviation for a more stochastically dominated excitation reduce total DC power by only 20%. These results underscore the need for maximizing direct current power delivery for nonlinear energy harvesting systems in practical operating environments.

Parameterized data-driven fuzzy model based optimal control of a semi-batch reactor.

PubMed

Kamesh, Reddi; Rani, K Yamuna

2016-09-01

A parameterized data-driven fuzzy (PDDF) model structure is proposed for semi-batch processes, and its application for optimal control is illustrated. The orthonormally parameterized input trajectories, initial states and process parameters are the inputs to the model, which predicts the output trajectories in terms of Fourier coefficients. Fuzzy rules are formulated based on the signs of a linear data-driven model, while the defuzzification step incorporates a linear regression model to shift the domain from input to output domain. The fuzzy model is employed to formulate an optimal control problem for single rate as well as multi-rate systems. Simulation study on a multivariable semi-batch reactor system reveals that the proposed PDDF modeling approach is capable of capturing the nonlinear and time-varying behavior inherent in the semi-batch system fairly accurately, and the results of operating trajectory optimization using the proposed model are found to be comparable to the results obtained using the exact first principles model, and are also found to be comparable to or better than parameterized data-driven artificial neural network model based optimization results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

(2 + 1)-dimensional bright optical solitons in metamaterials with Kerr, power and parabolic law nonlinearities

NASA Astrophysics Data System (ADS)

Boubir, Badreddine

2018-06-01

In this paper, we investigate the dynamics of bright optical solitons in nonlinear metamaterials governed by a (2 + 1)-dimensional nonlinear Schrödinger equation. Three types of nonlinearities have been considered, Kerr law, power law and parabolic law. We based on the solitary wave ansatz method to find these optical soliton solutions. All necessary parametric conditions for their existence are driven.

Nonlinear flow response of soft hair beds

NASA Astrophysics Data System (ADS)

Alvarado, José

2017-11-01

We are hairy inside: beds of passive fibers anchored to a surface and immersed in fluids are prevalent in many biological systems, including intestines, tongues, and blood vessels. Such hairs are soft enough to deform in response to stresses from fluid flows. Fluid stresses are in turn affected by hair deformation, leading to a coupled elastoviscous problem which is poorly understood. Here we investigate a biomimetic model system of elastomer hair beds subject to shear- driven Stokes flows. We characterize this system with a theoretical model which accounts for the large-deformation flow response of hair beds. Hair bending results in a drag-reducing nonlinearity because the hair tip lowers toward the base, widening the gap through which fluid flows. When hairs are cantilevered at an angle subnormal to the surface, flow against the grain bends hairs away from the base, narrowing the gap. The flow response of angled hair beds is axially asymmetric and amounts to a rectification nonlinearity. We identify an elastoviscous parameter which controls nonlinear behavior. Our study raises the hypothesis that biological hairy surfaces function to reduce fluid drag. Furthermore, angled hairs may be incorporated in the design of integrated microfluidic components, such as diodes and pumps. J.A. acknowledges support the U. S. Army Research Office under Grant Number W911NF-14-1-0396.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

Nonreciprocal wave scattering on nonlinear string-coupled oscillators

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

Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it; Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino; Pikovsky, Arkady

2014-12-01

We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaoticmore » scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.« less

Experimental observation of the generation of cutoff solitons in a discrete L C nonlinear electrical line

NASA Astrophysics Data System (ADS)

Koon, K. Tse Ve; Marquié, P.; Dinda, P. Tchofo

2014-11-01

We address the problem of supratransmission of waves in a discrete nonlinear system, driven at one end by a periodic excitation at a frequency lying above the phonon band edge. In an experimental electrical transmission line made of 200 inductance-capacitance LC cells, we establish the existence of a voltage threshold for a supratransmission enabling the generation and propagation of cut-off solitons within the line. The decisive role of modulational instability in the onset and development of the process of generation of cut-off solitons is clearly highlighted. The phenomenon of dissipation is identified as being particularly harmful for the soliton generation, but we show that its impact can be managed by a proper choice of the amplitude of the voltage excitation of the system.

Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion

NASA Astrophysics Data System (ADS)

Krumm, F.; Vogel, W.

2018-04-01

In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time evolution of the nonclassicality of the motional quantum state.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions.

PubMed

Shpielberg, O; Akkermans, E

2016-06-17

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Le Chatelier Principle for Out-of-Equilibrium and Boundary-Driven Systems: Application to Dynamical Phase Transitions

NASA Astrophysics Data System (ADS)

Shpielberg, O.; Akkermans, E.

2016-06-01

A stability analysis is presented for boundary-driven and out-of-equilibrium systems in the framework of the hydrodynamic macroscopic fluctuation theory. A Hamiltonian description is proposed which allows us to thermodynamically interpret the additivity principle. A necessary and sufficient condition for the validity of the additivity principle is obtained as an extension of the Le Chatelier principle. These stability conditions result from a diagonal quadratic form obtained using the cumulant generating function. This approach allows us to provide a proof for the stability of the weakly asymmetric exclusion process and to reduce the search for stability to the solution of two coupled linear ordinary differential equations instead of nonlinear partial differential equations. Additional potential applications of these results are discussed in the realm of classical and quantum systems.

Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

Recurrence plots revisited

NASA Astrophysics Data System (ADS)

Casdagli, M. C.

1997-09-01

We show that recurrence plots (RPs) give detailed characterizations of time series generated by dynamical systems driven by slowly varying external forces. For deterministic systems we show that RPs of the time series can be used to reconstruct the RP of the driving force if it varies sufficiently slowly. If the driving force is one-dimensional, its functional form can then be inferred up to an invertible coordinate transformation. The same results hold for stochastic systems if the RP of the time series is suitably averaged and transformed. These results are used to investigate the nonlinear prediction of time series generated by dynamical systems driven by slowly varying external forces. We also consider the problem of detecting a small change in the driving force, and propose a surrogate data technique for assessing statistical significance. Numerically simulated time series and a time series of respiration rates recorded from a subject with sleep apnea are used as illustrative examples.

Self-consistent Langmuir waves in resonantly driven thermal plasmas

NASA Astrophysics Data System (ADS)

Lindberg, R. R.; Charman, A. E.; Wurtele, J. S.

2007-12-01

The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed in the limit that the growth of the electrostatic wave is slow compared to the bounce frequency. Using simple physical arguments, the nonlinear distribution function is shown to be nearly invariant in the canonical particle action, provided both a spatially uniform term and higher-order spatial harmonics are included along with the fundamental in the longitudinal electric field. Requirements of self-consistency with the electrostatic potential yield the basic properties of the nonlinear distribution function, including a frequency shift that agrees closely with driven, electrostatic particle simulations over a range of temperatures. This extends earlier work on nonlinear Langmuir waves by Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] and Dewar [R. L. Dewar, Phys. Plasmas 15, 712 (1972)], and could form the basis of a reduced kinetic treatment of plasma dynamics for accelerator applications or Raman backscatter.

Magnetoplasmonic RF mixing and nonlinear frequency generation

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

Firby, C. J., E-mail: firby@ualberta.ca; Elezzabi, A. Y.

2016-07-04

We present the design of a magnetoplasmonic Mach-Zehnder interferometer (MZI) modulator facilitating radio-frequency (RF) mixing and nonlinear frequency generation. This is achieved by forming the MZI arms from long-range dielectric-loaded plasmonic waveguides containing bismuth-substituted yttrium iron garnet (Bi:YIG). The magnetization of the Bi:YIG can be driven in the nonlinear regime by RF magnetic fields produced around adjacent transmission lines. Correspondingly, the nonlinear temporal dynamics of the transverse magnetization component are mapped onto the nonreciprocal phase shift in the MZI arms, and onto the output optical intensity signal. We show that this tunable mechanism can generate harmonics, frequency splitting, and frequencymore » down-conversion with a single RF excitation, as well as RF mixing when driven by two RF signals. This magnetoplasmonic component can reduce the number of electrical sources required to generate distinct optical modulation frequencies and is anticipated to satisfy important applications in integrated optics.« less

Dimer with gain and loss: Integrability and {P}{T}-symmetry restoration

NASA Astrophysics Data System (ADS)

Barashenkov, I. V.; Pelinovsky, D. E.; Dubard, P.

2015-08-01

A {P}{T}-symmetric nonlinear Schrödinger dimer is a two-site discrete nonlinear Schrödinger equation with one site losing and the other one gaining energy at the same rate. In this paper, two four-parameter families of cubic {P}{T}-symmetric dimers are constructed as gain-loss extensions of their conservative, Hamiltonian, counterparts. We prove that all these damped-driven equations define completely integrable Hamiltonian systems. The second aim of our study is to identify nonlinearities that give rise to the spontaneous {P}{T}-symmetry restoration. When the symmetry of the underlying linear dimer is broken and an unstable small perturbation starts to grow, the nonlinear coupling of the required type will divert an increasingly large percentage of energy from the gaining to the losing site. As a result, the exponential growth will be saturated and all trajectories remain trapped in a finite part of the phase space regardless of the value of the gain-loss coefficient.

Control strategies for systems with limited actuators

NASA Technical Reports Server (NTRS)

Marcopoli, Vincent R.; Phillips, Stephen M.

1994-01-01

This work investigates the effects of actuator saturation in multi-input, multi-output (MIMO) control systems. The adverse system behavior introduced by the saturation nonlinearity is viewed here as resulting from two mechanisms: controller windup - a problem caused by the discrepancy between the limited actuator commands and the corresponding control signals, and directionality - the problem of how to use nonlimited actuators when a limited condition exists. The tracking mode and Hanus methods are two common strategies for dealing with the windup problem. It is seen that while these methods alleviate windup, performance problems remain due to plant directionality. Though high gain conventional antiwindup as well as more general linear methods have the potential to address both windup and directionality, no systematic design method for these schemes has emerged; most approaches used in practice are application driven. An alternative method of addressing the directionality problem is presented which involves the introduction of a control direction preserving nonlinearity to the Hanus antiwindup system. A nonlinearity is subsequently proposed which reduces the conservation inherent in the former direction-preserving approach, improving performance. The concept of multivariable sensitivity is seen to play a key role in the success of the new method.

A variational approach to probing extreme events in turbulent dynamical systems

PubMed Central

Farazmand, Mohammad; Sapsis, Themistoklis P.

2017-01-01

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

Nonlinear dynamics of confined thin liquid-vapor bilayer systems with phase change

NASA Astrophysics Data System (ADS)

Kanatani, Kentaro; Oron, Alexander

2011-03-01

We numerically investigate the nonlinear evolution of the interface of a thin liquid-vapor bilayer system confined by rigid horizontal walls from both below and above. The lateral variation of the vapor pressure arising from phase change is taken into account in the present analysis. When the liquid (vapor) is heated (cooled) and gravity acts toward the liquid, the deflection of the interface monotonically grows, leading to a rupture of the vapor layer, whereas nonruptured stationary states are found when the liquid (vapor) is cooled (heated) and gravity acts toward the vapor. In the latter case, vapor-flow-driven convective cells are found in the liquid phase in the stationary state. The average vapor pressure and interface temperature deviate from their equilibrium values once the interface departs from the flat equilibrium state. Thermocapillarity does not have a significant effect near the thermodynamic equilibrium, but becomes important if the system significantly deviates from it.

Nonlinear structures and anomalous transport in partially magnetized E×B plasmas

DOE PAGES

Janhunen, Salomon; Smolyakov, Andrei; Chapurin, Oleksandr; ...

2017-12-29

Nonlinear dynamics of the electron-cyclotron instability driven by the electron E x B current in a crossed electric and magnetic field is studied. In the nonlinear regime, the instability proceeds by developing a large amplitude coherent wave driven by the energy input from the fundamental cyclotron resonance. Further evolution shows the formation of the long wavelength envelope akin to the modulational instability. Simultaneously, the ion density shows the development of a high-k content responsible for wave focusing and sharp peaks on the periodic cnoidal wave structure. Here, it is shown that the anomalous electron transport (along the direction of themore » applied electric field) is dominated by the long wavelength part of the turbulent spectrum.« less

Random perturbations of a periodically driven nonlinear oscillator: escape from a resonance zone

NASA Astrophysics Data System (ADS)

Lingala, Nishanth; Sri Namachchivaya, N.; Pavlyukevich, Ilya

2017-04-01

For nonlinear oscillators, frequency of oscillations depends on the oscillation amplitude. When a nonlinear oscillator is periodically driven, the phase space consists of many resonance zones where the oscillator frequency and the driving frequency are commensurable. It is well known that, a small subset of initial conditions can lead to capture in one of the resonance zones. In this paper we study the effect of weak noise on the escape from a resonance zone. Using averaging techniques we obtain the mean exit time from a resonance zone and study the dependence of the exit rate on the parameters of the oscillator. Paper dedicated to Professor Peter W Sauer of University of Illinois on the occasion of his 70th birthday.

Dynamic Modeling and Very Short-term Prediction of Wind Power Output Using Box-Cox Transformation

NASA Astrophysics Data System (ADS)

Urata, Kengo; Inoue, Masaki; Murayama, Dai; Adachi, Shuichi

2016-09-01

We propose a statistical modeling method of wind power output for very short-term prediction. The modeling method with a nonlinear model has cascade structure composed of two parts. One is a linear dynamic part that is driven by a Gaussian white noise and described by an autoregressive model. The other is a nonlinear static part that is driven by the output of the linear part. This nonlinear part is designed for output distribution matching: we shape the distribution of the model output to match with that of the wind power output. The constructed model is utilized for one-step ahead prediction of the wind power output. Furthermore, we study the relation between the prediction accuracy and the prediction horizon.

Bubble, Drop and Particle Unit (BDPU)

NASA Technical Reports Server (NTRS)

1998-01-01

This section of the Life and Microgravity Spacelab (LMS) publication includes the following articles entitled: (1) Oscillatory Thermocapillary Instability; (2) Thermocapillary Convection in Multilayer Systems; (3) Bubble and Drop Interaction with Solidification Front; (4) A Liquid Electrohydrodynamics Experiment; (5) Boiling on Small Plate Heaters under Microgravity and a Comparison with Earth Gravity; (6) Thermocapillary Migration and Interactions of Bubbles and Drops; and (7) Nonlinear Surface Tension Driven Bubble Migration

Nanophotonic Devices in Silicon for Nonlinear Optics

DTIC Science & Technology

2010-10-15

record performance  Demonstration of world‟s lowest loss slot waveguides, made in a DOD-trusted foundry (BAE Systems)  Design study showing...highly-cited design study.  Design study on analog links using the above modulators.  Demonstration of the first silicon waveguides for the mid...Hochberg. Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links. Optics Express 2010

Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

PubMed

Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland

2013-05-10

We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Nonlinear heat transport in ferromagnetic-quantum dot-superconducting systems

NASA Astrophysics Data System (ADS)

Hwang, Sun-Yong; Sánchez, David

2018-03-01

We analyze the heat current traversing a quantum dot sandwiched between a ferromagnetic and a superconducting electrode. The heat flow generated in response to a voltage bias presents rectification as a function of the gate potential applied to the quantum dot. Remarkably, in the thermally driven case the heat shows a strong diode effect with large asymmetry ratios that can be externally tuned with magnetic fields or spin-polarized tunneling. Our results thus demonstrate the importance of hybrid systems as promising candidates for thermal applications.

Mixed-mode oscillations in memristor emulator based Liénard system

NASA Astrophysics Data System (ADS)

Kingston, S. Leo; Suresh, K.; Thamilmaran, K.

2018-04-01

We report the existence of mixed-mode oscillations in memristor emulator based Liénard system which is externally driven by sinusoidal force. The charge and flux relationship of memristor emulator device explored based on the smooth cubic nonlinear element. The system exhibits the successive period adding sequences of mixed-mode oscillations in the wide parameter region. The electronics circuit of the memristor emulator is successfully implemented through PSpice simulation and mixed mode oscillations are observed through PSpice experiment and the obtained results are qualitatively matches with the numerical simulation.

Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming

USGS Publications Warehouse

Yu, X.; Hsu, T.-J.; Hanes, D.M.

2010-01-01

Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.

Proceedings of the 2nd Experimental Chaos Conference

NASA Astrophysics Data System (ADS)

Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

1995-02-01

The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud

Recent progress of the Laser-driven Ion-beam Trace Probe

NASA Astrophysics Data System (ADS)

Yang, Xiaoyi; Xiao, Chijie; Chen, Yihang; Xu, Tianchao; Yu, Yi; Xu, Min; Wang, Long; Lin, Chen; Wang, Xiaogang

2017-10-01

The Laser-driven Ion-beam Trace Probe (LITP) is a new method to diagnose the poloidal magnetic field and radial electric field in tokamaks. Recently significant progresses have been made as follows. 1) The experimental system has been set up on the PKU Plasma Test (PPT) linear device and begun to validate the principle of LITP, including the ion source, the ion detector and the poloidal magnetic field cable. Preliminary experimental results matched the theoretical prediction well. 2) The reconstruction principle has been improved including the nonlinear effect. 3) Tomography methods have been applied in the reconstruction codes. Now the laser-driven ion-beam accelerator has been setup on the PPT device, and further test of LITP will start soon. After that a prototype of LITP system will be designed and setup on the HL-2A tokamak device. This work was supported by the CHINA MOST under 2012YQ030142, ITER-CHINA program 2015GB120001 and National Natural Science Foundation of China under 11575014 and 11375053.

Signal Processing in Periodically Forced Gradient Frequency Neural Networks

PubMed Central

Kim, Ji Chul; Large, Edward W.

2015-01-01

Oscillatory instability at the Hopf bifurcation is a dynamical phenomenon that has been suggested to characterize active non-linear processes observed in the auditory system. Networks of oscillators poised near Hopf bifurcation points and tuned to tonotopically distributed frequencies have been used as models of auditory processing at various levels, but systematic investigation of the dynamical properties of such oscillatory networks is still lacking. Here we provide a dynamical systems analysis of a canonical model for gradient frequency neural networks driven by a periodic signal. We use linear stability analysis to identify various driven behaviors of canonical oscillators for all possible ranges of model and forcing parameters. The analysis shows that canonical oscillators exhibit qualitatively different sets of driven states and transitions for different regimes of model parameters. We classify the parameter regimes into four main categories based on their distinct signal processing capabilities. This analysis will lead to deeper understanding of the diverse behaviors of neural systems under periodic forcing and can inform the design of oscillatory network models of auditory signal processing. PMID:26733858

Semiconductor quantum well irradiated by a two-mode electromagnetic field as a terahertz emitter

NASA Astrophysics Data System (ADS)

Mandal, S.; Liew, T. C. H.; Kibis, O. V.

2018-04-01

We study theoretically the nonlinear optical properties of a semiconductor quantum well (QW) irradiated by a two-mode electromagnetic wave consisting of a strong resonant dressing field and a weak off-resonant driving field. In the considered strongly coupled electron-field system, the dressing field opens dynamic Stark gaps in the electron energy spectrum of the QW, whereas the driving field induces electron oscillations in the QW plane. Since the gapped electron spectrum restricts the amplitude of the oscillations, the emission of a frequency comb from the QW appears. Therefore, the doubly driven QW operates as a nonlinear optical element which can be used, particularly, for optically controlled generation of terahertz radiation.

Development of control strategies for safe microburst penetration: A progress report

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1987-01-01

A single-engine, propeller-driven, general-aviation model was incorporated into the nonlinear simulation and into the linear analysis of root loci and frequency response. Full-scale wind tunnel data provided its aerodynamic model, and the thrust model included the airspeed dependent effects of power and propeller efficiency. Also, the parameters of the Jet Transport model were changed to correspond more closely to the Boeing 727. In order to study their effects on steady-state repsonse to vertical wind inputs, altitude and total specific energy (air-relative and inertial) feedback capabilities were added to the nonlinear and linear models. Multiloop system design goals were defined. Attempts were made to develop controllers which achieved these goals.

Characteristics of a four element gyromagnetic nonlinear transmission line array high power microwave source.

PubMed

Johnson, J M; Reale, D V; Krile, J T; Garcia, R S; Cravey, W H; Neuber, A A; Dickens, J C; Mankowski, J J

2016-05-01

In this paper, a solid-state four element array gyromagnetic nonlinear transmission line high power microwave system is presented as well as a detailed description of its subsystems and general output capabilities. This frequency agile S-band source is easily adjusted from 2-4 GHz by way of a DC driven biasing magnetic field and is capable of generating electric fields of 7.8 kV/m at 10 m correlating to 4.2 MW of RF power with pulse repetition frequencies up to 1 kHz. Beam steering of the array at angles of ±16.7° is also demonstrated, and the associated general radiation pattern is detailed.

Characteristics of a four element gyromagnetic nonlinear transmission line array high power microwave source

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

Johnson, J. M., E-mail: jared.johnson@ttu.edu; Reale, D. V.; Garcia, R. S.

2016-05-15

In this paper, a solid-state four element array gyromagnetic nonlinear transmission line high power microwave system is presented as well as a detailed description of its subsystems and general output capabilities. This frequency agile S-band source is easily adjusted from 2-4 GHz by way of a DC driven biasing magnetic field and is capable of generating electric fields of 7.8 kV/m at 10 m correlating to 4.2 MW of RF power with pulse repetition frequencies up to 1 kHz. Beam steering of the array at angles of ±16.7° is also demonstrated, and the associated general radiation pattern is detailed.

Growth and nonlinear response of driven water bells

NASA Astrophysics Data System (ADS)

Kolinski, John M.; Aharoni, Hillel; Fineberg, Jay; Sharon, Eran

2017-04-01

A water bell forms when a fluid jet impacts upon a target and separates into a two-dimensional sheet. Depending on the angle of separation from the target, the sheet can curve into a variety of different geometries. We show analytically that harmonic perturbations of water bells have linear wave solutions with geometry-dependent growth. We test the predictions of this model experimentally with a custom target system, and observe growth in agreement with the model below a critical forcing amplitude. Once the critical forcing amplitude is exceeded, a nonlinear transcritical bifurcation occurs; the response amplitude increases linearly with increasing forcing amplitude, albeit with a fundamentally different spatial form, and distinct nodes appear in the amplitude envelope.

Autonomous Rhythmic Drug Delivery Systems Based on Chemical and Biochemomechanical Oscillators

NASA Astrophysics Data System (ADS)

Siegel, Ronald A.

While many drug delivery systems target constant, or zero-order drug release, certain drugs and hormones must be delivered in rhythmic pulses in order to achieve their optimal effect. Here we describe studies with two model autonomous rhythmic delivery systems. The first system is driven by a pH oscillator that modulates the ionization state of a model drug, benzoic acid, which can permeate through a lipophilic membrane when the drug is uncharged. The second system is based on a nonlinear negative feedback instability that arises from coupling of swelling of a hydrogel membrane to an enzymatic reaction, with the hydrogel controlling access of substrate to the enzyme, and the enzyme's product controlling the hydrogel's swelling state. The latter system, whose autonomous oscillations are driven by glucose at constant external activity, is shown to deliver gonadotropin releasing hormone (GnRH) in rhythmic pulses, with periodicity of the same order as observed in sexually mature adult humans. Relevant experimental results and some mathematical models are reviewed.

Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond

PubMed Central

Ge, Hao; Qian, Hong

2011-01-01

A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the ‘free energy function’, Lee–Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network. PMID:20466813

Nonlinear mechanical resonators for ultra-sensitive mass detection

NASA Astrophysics Data System (ADS)

Datskos, P. G.; Lavrik, N. V.

2014-10-01

The fundamental sensitivity limit of an appropriately scaled down mechanical resonator can approach one atomic mass unit when only thermal noise is present in the system. However, operation of such nanoscale mechanical resonators is very challenging due to minuteness of their oscillation amplitudes and presence of multiple noise sources in real experimental environments. In order to surmount these challenges, we use microscale cantilever resonators driven to large amplitudes, far beyond their nonlinear instability onset. Our experiments show that such a nonlinear cantilever resonator, described analytically as a Duffing oscillator, has mass sensing performance comparable to that of much smaller resonators operating in a linear regime. We demonstrate femtogram level mass sensing that relies on a bifurcation point tracking that does not require any complex readout means. Our approaches enable straightforward detection of mass changes that are near the fundamental limit imposed by thermo-mechanical fluctuations.

Input signal shaping based on harmonic frequency response function for suppressing nonlinear optical frequency in frequency-scanning interferometry

NASA Astrophysics Data System (ADS)

Zhu, Yu; Liu, Zhigang; Deng, Wen; Deng, Zhongwen

2018-05-01

Frequency-scanning interferometry (FSI) using an external cavity diode laser (ECDL) is essential for many applications of the absolute distance measurement. However, owing to the hysteresis and creep of the piezoelectric actuator inherent in the ECDL, the optical frequency scanning exhibits a nonlinearity that seriously affects the phase extraction accuracy of the interference signal and results in the reduction of the measurement accuracy. To suppress the optical frequency nonlinearity, a harmonic frequency synthesis method for shaping the desired input signal instead of the original triangular wave is presented. The effectiveness of the presented shaping method is demonstrated through the comparison of the experimental results. Compared with an incremental Renishaw interferometer, the standard deviation of the displacement measurement of the FSI system is less than 2.4 μm when driven by the shaped signal.

The Dynamics of Small-Scale Turbulence Driven Flows

NASA Astrophysics Data System (ADS)

Beer, M. A.; Hammett, G. W.

1997-11-01

The dynamics of small-scale fluctuation driven flows are of great interest for micro-instability driven turbulence, since nonlinear toroidal simulations have shown that these flows play an important role in the regulation of the turbulence and transport levels. The gyrofluid treatment of these flows was shown to be accurate for times shorter than a bounce time.(Beer, M. A., Ph. D. thesis, Princeton University (1995).) Since the decorrelation times of the turbulence are generally shorter than a bounce time, our original hypothesis was that this description was adequate. Recent work(Hinton, F. L., Rosenbluth, M. N., and Waltz, R. E., International Sherwood Fusion Theory Conference (1997).) pointed out possible problems with this hypothesis, emphasizing the existence of a linearly undamped component of the flow which could build up in time and lower the final turbulence level. While our original gyrofluid model reproduces some aspects of the linear flow, there are differences between the long time gyrofluid and kinetic linear results in some cases. On the other hand, if the long time behavior of these flows is dominated by nonlinear damping (which seems reasonable), then the existing nonlinear gyrofluid simulations may be sufficiently accurate. We test these possibilities by modifying the gyrofluid description of these flows and diagnosing the flow evolution in nonlinear simulations.

Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes

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

Bass, Eric M.; Waltz, R. E.

Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEMmore » peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.« less

Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes

DOE PAGES

Bass, Eric M.; Waltz, R. E.

2017-12-08

Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEMmore » peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.« less

Fluctuations and correlations in modulation instability

NASA Astrophysics Data System (ADS)

Solli, D. R.; Herink, G.; Jalali, B.; Ropers, C.

2012-07-01

Stochastically driven nonlinear processes are responsible for spontaneous pattern formation and instabilities in numerous natural and artificial systems, including well-known examples such as sand ripples, cloud formations, water waves, animal pigmentation and heart rhythms. Technologically, a type of such self-amplification drives free-electron lasers and optical supercontinuum sources whose radiation qualities, however, suffer from the stochastic origins. Through time-resolved observations, we identify intrinsic properties of these fluctuations that are hidden in ensemble measurements. We acquire single-shot spectra of modulation instability produced by laser pulses in glass fibre at megahertz real-time capture rates. The temporally confined nature of the gain physically limits the number of amplified modes, which form an antibunched arrangement as identified from a statistical analysis of the data. These dynamics provide an example of pattern competition and interaction in confined nonlinear systems.

Low-noise phase of a two-dimensional active nematic system

NASA Astrophysics Data System (ADS)

Shankar, Suraj; Ramaswamy, Sriram; Marchetti, M. Cristina

2018-01-01

We consider a collection of self-driven apolar particles on a substrate that organize into an active nematic phase at sufficiently high density or low noise. Using the dynamical renormalization group, we systematically study the two-dimensional fluctuating ordered phase in a coarse-grained hydrodynamic description involving both the nematic director and the conserved density field. In the presence of noise, we show that the system always displays only quasi-long-ranged orientational order beyond a crossover scale. A careful analysis of the nonlinearities permitted by symmetry reveals that activity is dangerously irrelevant over the linearized description, allowing giant number fluctuations to persist although now with strong finite-size effects and a nonuniversal scaling exponent. Nonlinear effects from the active currents lead to power-law correlations in the density field, thereby preventing macroscopic phase separation in the thermodynamic limit.

Sweep excitation with order tracking: A new tactic for beam crack analysis

NASA Astrophysics Data System (ADS)

Wei, Dongdong; Wang, KeSheng; Zhang, Mian; Zuo, Ming J.

2018-04-01

Crack detection in beams and beam-like structures is an important issue in industry and has attracted numerous investigations. A local crack leads to global system dynamics changes and produce non-linear vibration responses. Many researchers have studied these non-linearities for beam crack diagnosis. However, most reported methods are based on impact excitation and constant frequency excitation. Few studies have focused on crack detection through external sweep excitation which unleashes abundant dynamic characteristics of the system. Together with a signal resampling technique inspired by Computed Order Tracking, this paper utilize vibration responses under sweep excitations to diagnose crack status of beams. A data driven method for crack depth evaluation is proposed and window based harmonics extracting approaches are studied. The effectiveness of sweep excitation and the proposed method is experimentally validated.

Nonlinear simulations of beam-driven Compressional Alfv´en Eigenmodes in NSTX

DOE PAGES

Belova, Elena V.; Gorelenkov, N. N.; Crocker, N. A.; ...

2017-03-10

We present results for the 3D nonlinear simulations of neutral-beam-driven compressional Alfv´en eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX). Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n = 4 - 9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfv´en wave (KAW) that occurs on the high-field side at the Alfv´en resonance location. We frequently observe high-frequency Alfv´en eigenmodes in beam-heated NSTX plasmas, and have been linkedmore » to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. Furthermore, a set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.« less

Nonlinear simulations of beam-driven Compressional Alfv´en Eigenmodes in NSTX

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

Belova, Elena V.; Gorelenkov, N. N.; Crocker, N. A.

We present results for the 3D nonlinear simulations of neutral-beam-driven compressional Alfv´en eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX). Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n = 4 - 9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfv´en wave (KAW) that occurs on the high-field side at the Alfv´en resonance location. We frequently observe high-frequency Alfv´en eigenmodes in beam-heated NSTX plasmas, and have been linkedmore » to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. Furthermore, a set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.« less

A necessary condition for dispersal driven growth of populations with discrete patch dynamics.

PubMed

Guiver, Chris; Packman, David; Townley, Stuart

2017-07-07

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Minimum fuel control of a vehicle with a continuously variable transmission. [control system simulation

NASA Technical Reports Server (NTRS)

Burghart, J. H.; Donoghue, J. F.

1980-01-01

The design and evaluation of a control system for a sedan with a heat engine and a continuously variable transmission, is considered in a effort to minimize fuel consumption and achieve satisfactory dynamic response of vehicle variables as the vehicle is driven over a standard driving cycle. Even though the vehicle system was highly nonlinear, attention was restricted to linear control algorithms which could be easily understood and implemented demonstrated by simulation. Simulation results also revealed that the vehicle could exhibit unexpected dynamic behavior which must be taken into account in any control system design.

On the performance of voltage stepping for the simulation of adaptive, nonlinear integrate-and-fire neuronal networks.

PubMed

Kaabi, Mohamed Ghaith; Tonnelier, Arnaud; Martinez, Dominique

2011-05-01

In traditional event-driven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrate-and-fire model. In a recent paper, Zheng, Tonnelier, and Martinez (2009) introduced an approximate event-driven strategy, named voltage stepping, that allows the generic simulation of nonlinear spiking neurons. Promising results were achieved in the simulation of single quadratic integrate-and-fire neurons. Here, we assess the performance of voltage stepping in network simulations by considering more complex neurons (quadratic integrate-and-fire neurons with adaptation) coupled with multiple synapses. To handle the discrete nature of synaptic interactions, we recast voltage stepping in a general framework, the discrete event system specification. The efficiency of the method is assessed through simulations and comparisons with a modified time-stepping scheme of the Runge-Kutta type. We demonstrated numerically that the original order of voltage stepping is preserved when simulating connected spiking neurons, independent of the network activity and connectivity.

Optical spatial solitons: historical overview and recent advances.

PubMed

Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N

2012-08-01

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Higgs Mode in the d -Wave Superconductor Bi2Sr2CaCu2O8 +x Driven by an Intense Terahertz Pulse

NASA Astrophysics Data System (ADS)

Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I.; Matsunaga, Ryusuke; Schneeloch, John; Zhong, Ruidan D.; Gu, Genda D.; Aoki, Hideo; Gallais, Yann; Shimano, Ryo

2018-03-01

We investigate the terahertz (THz)-pulse-driven nonlinear response in the d -wave cuprate superconductor Bi2Sr2CaCu2O8 +x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We observe an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is markedly enhanced below Tc . The corresponding third-order nonlinear effect exhibits both A1 g and B1 g symmetry components, which are decomposed from polarization-resolved measurements. A comparison with a BCS calculation of the nonlinear susceptibility indicates that the A1 g component is associated with the Higgs mode of the d -wave order parameter.

Higgs Mode in the d -Wave Superconductor Bi 2 Sr 2 CaCu 2 O 8 + x Driven by an Intense Terahertz Pulse

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

Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I.

We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi 2Sr 2CaCu 2O 8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below Tc. The corresponding third-order nonlinear effect exhibits both A 1g and B 1g symmetry components, which are decomposed from polarization-resolved measurements. Comparison with a BCS calculation of the nonlinear susceptibility indicates that the A 1g component is associated with the Higgs mode of the d-wave order parameter.

Higgs Mode in the d -Wave Superconductor Bi 2 Sr 2 CaCu 2 O 8 + x Driven by an Intense Terahertz Pulse

DOE PAGES

Katsumi, Kota; Tsuji, Naoto; Hamada, Yuki I.; ...

2018-03-14

We investigated the terahertz (THz)-pulse driven nonlinear response in the d-wave cuprate superconductor Bi 2Sr 2CaCu 2O 8+x (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We have observed an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is strongly enhanced below Tc. The corresponding third-order nonlinear effect exhibits both A 1g and B 1g symmetry components, which are decomposed from polarization-resolved measurements. Comparison with a BCS calculation of the nonlinear susceptibility indicates that the A 1g component is associated with the Higgs mode of the d-wave order parameter.

Excitation of a nonlinear plasma ion wake by intense energy sources with applications to the crunch-in regime

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

Sahai, Aakash A.

We show the excitation of a nonlinear ion-wake mode by plasma electron modes in the bubble regime driven by intense energy sources, using analytical theory and simulations. The ion wake is shown to be a driven nonlinear ion-acoustic wave in the form of a long-lived cylindrical ion soliton which limits the repetition rate of a plasma-based particle accelerator in the bubble regime. We present the application of this evacuated and radially outwards propagating ion-wake channel with an electron skin-depth scale radius for the “crunch-in” regime of hollow-channel plasma. It is shown that the time-asymmetric focusing force phases in the bubblemore » couple to ion motion significantly differently than in the linear electron mode. The electron compression in the back of the bubble sucks in the ions whereas the space charge within the bubble cavity expels them, driving a cylindrical ion-soliton structure at the bubble radius. Once formed, the soliton is sustained and driven radially outwards by the thermal pressure of the wake energy in electrons. Particle-in-cell simulations are used to study the ion-wake soliton structure, its driven propagation and its use for positron acceleration in the crunch-in regime.« less

Excitation of a nonlinear plasma ion wake by intense energy sources with applications to the crunch-in regime

DOE PAGES

Sahai, Aakash A.

2017-08-23

We show the excitation of a nonlinear ion-wake mode by plasma electron modes in the bubble regime driven by intense energy sources, using analytical theory and simulations. The ion wake is shown to be a driven nonlinear ion-acoustic wave in the form of a long-lived cylindrical ion soliton which limits the repetition rate of a plasma-based particle accelerator in the bubble regime. We present the application of this evacuated and radially outwards propagating ion-wake channel with an electron skin-depth scale radius for the “crunch-in” regime of hollow-channel plasma. It is shown that the time-asymmetric focusing force phases in the bubblemore » couple to ion motion significantly differently than in the linear electron mode. The electron compression in the back of the bubble sucks in the ions whereas the space charge within the bubble cavity expels them, driving a cylindrical ion-soliton structure at the bubble radius. Once formed, the soliton is sustained and driven radially outwards by the thermal pressure of the wake energy in electrons. Particle-in-cell simulations are used to study the ion-wake soliton structure, its driven propagation and its use for positron acceleration in the crunch-in regime.« less

Average dynamics of a finite set of coupled phase oscillators

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

Dima, Germán C., E-mail: gdima@df.uba.ar; Mindlin, Gabriel B.

2014-06-15

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.

Average dynamics of a finite set of coupled phase oscillators

PubMed Central

Dima, Germán C.; Mindlin, Gabriel B.

2014-01-01

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate. PMID:24985426

Average dynamics of a finite set of coupled phase oscillators.

PubMed

Dima, Germán C; Mindlin, Gabriel B

2014-06-01

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.

Cellular automata in photonic cavity arrays.

PubMed

Li, Jing; Liew, T C H

2016-10-31

We propose theoretically a photonic Turing machine based on cellular automata in arrays of nonlinear cavities coupled with artificial gauge fields. The state of the system is recorded making use of the bistability of driven cavities, in which losses are fully compensated by an external continuous drive. The sequential update of the automaton layers is achieved automatically, by the local switching of bistable states, without requiring any additional synchronization or temporal control.

Data-Driven Nonlinear Subspace Modeling for Prediction and Control of Molten Iron Quality Indices in Blast Furnace Ironmaking

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

Zhou, Ping; Song, Heda; Wang, Hong

Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multi-phase and multi-field coupling and large time delay occur during its operation. In BF operation, the molten iron temperature (MIT) as well as Si, P and S contents of molten iron are the most essential molten iron quality (MIQ) indices, whose measurement, modeling and control have always been important issues in metallurgic engineering and automation field. This paper develops a novel data-driven nonlinear state space modeling for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques. First, to improvemore » modeling efficiency, a data-driven hybrid method combining canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modeling inputs from multitudinous factors would affect the MIQ indices. Then, a Hammerstein model for the prediction of MIQ indices is established using the LS-SVM based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method to fit the complex nonlinear kernel function. Compared to the original Hammerstein model, this simplified model can not only significantly reduce the computational complexity, but also has almost the same reliability and accuracy for a stable prediction of MIQ indices. Last, in order to verify the practicability of the developed model, it is applied in designing a genetic algorithm based nonlinear predictive controller for multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approach.« less

Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

NASA Astrophysics Data System (ADS)

Whelan, G. G.; Pueschel, M. J.; Terry, P. W.

2018-04-01

The physical causes for the strong stabilizing effect of finite plasma β on ion-temperature-gradient-driven turbulence, which far exceeds quasilinear estimates, are identified from nonlinear gyrokinetic simulations. The primary contribution stems from a resonance of frequencies in the dominant nonlinear interaction between the unstable mode, the stable mode, and zonal flows, which maximizes the triplet correlation time and therefore the energy transfer efficiency. A modification to mixing-length transport estimates is constructed, which reproduces nonlinear heat fluxes throughout the examined β range.

Data-Driven Modeling of Complex Systems by means of a Dynamical ANN

NASA Astrophysics Data System (ADS)

Seleznev, A.; Mukhin, D.; Gavrilov, A.; Loskutov, E.; Feigin, A.

2017-12-01

The data-driven methods for modeling and prognosis of complex dynamical systems become more and more popular in various fields due to growth of high-resolution data. We distinguish the two basic steps in such an approach: (i) determining the phase subspace of the system, or embedding, from available time series and (ii) constructing an evolution operator acting in this reduced subspace. In this work we suggest a novel approach combining these two steps by means of construction of an artificial neural network (ANN) with special topology. The proposed ANN-based model, on the one hand, projects the data onto a low-dimensional manifold, and, on the other hand, models a dynamical system on this manifold. Actually, this is a recurrent multilayer ANN which has internal dynamics and capable of generating time series. Very important point of the proposed methodology is the optimization of the model allowing us to avoid overfitting: we use Bayesian criterion to optimize the ANN structure and estimate both the degree of evolution operator nonlinearity and the complexity of nonlinear manifold which the data are projected on. The proposed modeling technique will be applied to the analysis of high-dimensional dynamical systems: Lorenz'96 model of atmospheric turbulence, producing high-dimensional space-time chaos, and quasi-geostrophic three-layer model of the Earth's atmosphere with the natural orography, describing the dynamics of synoptical vortexes as well as mesoscale blocking systems. The possibility of application of the proposed methodology to analyze real measured data is also discussed. The study was supported by the Russian Science Foundation (grant #16-12-10198).

Subharmonics, Chaos, and Beyond

NASA Technical Reports Server (NTRS)

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

2011-01-01

While studying finite amplitude ultrasonic wave resonance in a one dimensional liquid-filled cavity, which is formed by a narrow band transducer and a plane reflector, subharmonics of the driver's frequency were observed in addition to the expected harmonic structure. Subsequently it was realized that the system was one of the many examples where parametric resonance takes place and in which the observed subharmonics are parametrically generated. Parametric resonance occurs in any physical system which has a periodically modulated natural frequency. The generation mechanism also requires a sufficiently high threshold value of the driving amplitude so that the system becomes increasingly nonlinear in response. The nonlinear features were recently investigated and are the objective of this presentation. An ultrasonic interferometer with optical precision was built. The transducers were compressional undamped quartz and Lithium Niobate crystals ranging from 1-10 Mhz, and driven by a high power amplifier. Both an optical diffraction system and a receive transducer attached to an aligned reflector with lapped flat and parallel surfaces were used to observe the generated frequency components in the cavity.

Chaos and Beyond in a Water Filled Ultrasonic Resonance System

NASA Technical Reports Server (NTRS)

Lazlo, Adler; Yost, W.; Cantrell, John H.

2013-01-01

Finite amplitude ultrasonic wave resonances in a one-dimensional liquid-filled cavity, formed by a narrow band transducer and a plane reflector, are reported. The resonances are observed to include not only the expected harmonic and subharmonic signals (1,2) but chaotic signals as well. The generation mechanism requires attaining a threshold value of the driving amplitude that the liquid-filled cavity system becomes sufficiently nonlinear in response. The nonlinear features of the system were recently investigated via the construction of an ultrasonic interferometer having optical precision. The transducers were compressional, undamped quartz and lithium niobate crystals having the frequency range 1-10 MHz, driven by a high power amplifier. Both an optical diffraction system to characterize the diffraction pattern of laser light normally incident to the cavity and a receiving transducer attached to an aligned reflector with lapped flat and parallel surfaces were used to assess the generated resonance response in the cavity. At least 5 regions of excitation are identified.

A Robust Control of Two-Wheeled Mobile Manipulator with Underactuated Joint by Nonlinear Backstepping Method

NASA Astrophysics Data System (ADS)

Acar, Cihan; Murakami, Toshiyuki

In this paper, a robust control of two-wheeled mobile manipulator with underactuated joint is considered. Two-wheeled mobile manipulators are dynamically balanced two-wheeled driven systems that do not have any caster or extra wheels to stabilize their body. Two-wheeled mobile manipulators mainly have an important feature that makes them more flexible and agile than the statically stable mobile manipulators. However, two-wheeled mobile manipulator is an underactuated system due to its two-wheeled structure. Therefore, it is required to stabilize the underactuated passive body and, at the same time, control the position of the center of gravity (CoG) of the manipulator in this system. To realize this, nonlinear backstepping based control method with virtual double inverted pendulum model is proposed in this paper. Backstepping is used with sliding mode to increase the robustness of the system against modeling errors and other perturbations. Then robust acceleration control is also achieved by utilizing disturbance observer. Performance of the proposed method is evaluated by several experiments.

Four-wave mixing in an asymmetric double quantum dot molecule

NASA Astrophysics Data System (ADS)

Kosionis, Spyridon G.

2018-06-01

The four-wave mixing (FWM) effect of a weak probe field, in an asymmetric semiconductor double quantum dot (QD) structure driven by a strong pump field is theoretically studied. Similarly to the case of examining several other nonlinear optical processes, the nonlinear differential equations of the density matrix elements are used, under the rotating wave approximation. By suitably tuning the intensity and the frequency of the pump field as well as by changing the value of the applied bias voltage, a procedure used to properly adjust the electron tunneling coupling, we control the FWM in the same way as several other nonlinear optical processes of the system. While in the weak electron tunneling regime, the impact of the pump field intensity on the FWM is proven to be of crucial importance, for even higher rates of the electron tunneling it is evident that the intensity of the pump field has only a slight impact on the form of the FWM spectrum. The number of the spectral peaks, depends on the relation between specific parameters of the system.

Soliton Trains Induced by Adaptive Shaping with Periodic Traps in Four-Level Ultracold Atom Systems

NASA Astrophysics Data System (ADS)

Djouom Tchenkoue, M. L.; Welakuh Mbangheku, D.; Dikandé, Alain M.

2017-06-01

It is well known that an optical trap can be imprinted by a light field in an ultracold-atom system embedded in an optical cavity, and driven by three different coherent fields. Of the three fields coexisting in the optical cavity there is an intense control field that induces a giant Kerr nonlinearity via electromagnetically-induced transparency, and another field that creates a periodic optical grating of strength proportional to the square of the associated Rabi frequency. In this work elliptic-soliton solutions to the nonlinear equation governing the propagation of the probe field are considered, with emphasis on the possible generation of optical soliton trains forming a discrete spectrum with well defined quantum numbers. The problem is treated assuming two distinct types of periodic optical gratings and taking into account the negative and positive signs of detunings (detuning above or below resonance). Results predict that the competition between the self-phase and cross-phase modulation nonlinearities gives rise to a rich family of temporal soliton train modes characterized by distinct quantum numbers.

Engineering high-order nonlinear dissipation for quantum superconducting circuits

NASA Astrophysics Data System (ADS)

Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

Intelligence rules of hysteresis in the feedforward trajectory control of piezoelectrically-driven nanostagers

NASA Astrophysics Data System (ADS)

Bashash, Saeid; Jalili, Nader

2007-02-01

Piezoelectrically-driven nanostagers have limited performance in a variety of feedforward and feedback positioning applications because of their nonlinear hysteretic response to input voltage. The hysteresis phenomenon is well known for its complex and multi-path behavior. To realize the underlying physics of this phenomenon and to develop an efficient compensation strategy, the intelligence properties of hysteresis with the effects of non-local memories are discussed here. Through performing a set of experiments on a piezoelectrically-driven nanostager with a high resolution capacitive position sensor, it is shown that for the precise prediction of the hysteresis path, certain memory units are required to store the previous hysteresis trajectory data. Based on the experimental observations, a constitutive memory-based mathematical modeling framework is developed and trained for the precise prediction of the hysteresis path for arbitrarily assigned input profiles. Using the inverse hysteresis model, a feedforward control strategy is then developed and implemented on the nanostager to compensate for the ever-present nonlinearity. Experimental results demonstrate that the controller remarkably eliminates the nonlinear effect, if memory units are sufficiently chosen for the inverse model.

Combining Load and Motor Encoders to Compensate Nonlinear Disturbances for High Precision Tracking Control of Gear-Driven Gimbal

PubMed Central

Tang, Tao; Chen, Sisi; Huang, Xuanlin; Yang, Tao; Qi, Bo

2018-01-01

High-performance position control can be improved by the compensation of disturbances for a gear-driven control system. This paper presents a mode-free disturbance observer (DOB) based on sensor-fusion to reduce some errors related disturbances for a gear-driven gimbal. This DOB uses the rate deviation to detect disturbances for implementation of a high-gain compensator. In comparison with the angular position signal the rate deviation between load and motor can exhibits the disturbances exiting in the gear-driven gimbal quickly. Due to high bandwidth of the motor rate closed loop, the inverse model of the plant is not necessary to implement DOB. Besides, this DOB requires neither complex modeling of plant nor the use of additive sensors. Without rate sensors providing angular rate, the rate deviation is easily detected by encoders mounted on the side of motor and load, respectively. Extensive experiments are provided to demonstrate the benefits of the proposed algorithm. PMID:29498643

Combining Load and Motor Encoders to Compensate Nonlinear Disturbances for High Precision Tracking Control of Gear-Driven Gimbal.

PubMed

Tang, Tao; Chen, Sisi; Huang, Xuanlin; Yang, Tao; Qi, Bo

2018-03-02

High-performance position control can be improved by the compensation of disturbances for a gear-driven control system. This paper presents a mode-free disturbance observer (DOB) based on sensor-fusion to reduce some errors related disturbances for a gear-driven gimbal. This DOB uses the rate deviation to detect disturbances for implementation of a high-gain compensator. In comparison with the angular position signal the rate deviation between load and motor can exhibits the disturbances exiting in the gear-driven gimbal quickly. Due to high bandwidth of the motor rate closed loop, the inverse model of the plant is not necessary to implement DOB. Besides, this DOB requires neither complex modeling of plant nor the use of additive sensors. Without rate sensors providing angular rate, the rate deviation is easily detected by encoders mounted on the side of motor and load, respectively. Extensive experiments are provided to demonstrate the benefits of the proposed algorithm.

Non-linear Interactions between Niño region 3 and the Southern Amazon

NASA Astrophysics Data System (ADS)

Ramos, A. M. D. T.; Builes-Jaramillo, L. A.; Poveda, G.; Goswami, B.; Macau, E. E. N.; Kurths, J.; Marwan, N.

2016-12-01

Identifying causal relations from the observational dataset has posed great challenges in data-driven inference study. However, complex system framework offers promising approaches to tackle such problems. Here we propose a new data-driven causality inference method using the framework of recurrence plots. We present the Recurrence Measure of Conditional Dependence (RMCD) and its applications. The RMCD incorporates the recurrence behavior into the transfer entropy theory. Therefore, it quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the potential driver and present on the potential driven, except for any contribution that has already been in the past of the driven. We apply this methodology to some paradigmatic models and to investigate the possible influence of the Pacific Ocean temperatures on the South West Amazon for the 2010 and 2005 droughts. The results reveal that for the 2005 drought there is not a significant signal of dependence from the Pacific Ocean and that for 2010 there is a signal of dependence of around 200 days. These outcomes are confirmed by the traditional climatological analysis of these episodes available in the literature and show the accuracy of RMCD inferring causal relations in climate systems.

An optimized strain demodulation method for PZT driven fiber Fabry-Perot tunable filter

NASA Astrophysics Data System (ADS)

Sheng, Wenjuan; Peng, G. D.; Liu, Yang; Yang, Ning

2015-08-01

An optimized strain-demodulation-method based on piezo-electrical transducer (PZT) driven fiber Fabry-Perot (FFP) filter is proposed and experimentally demonstrated. Using a parallel processing mode to drive the PZT continuously, the hysteresis effect is eliminated, and the system demodulation rate is increased. Furthermore, an AC-DC compensation method is developed to address the intrinsic nonlinear relationship between the displacement and voltage of PZT. The experimental results show that the actual demodulation rate is improved from 15 Hz to 30 Hz, the random error of the strain measurement is decreased by 95%, and the deviation between the test values after compensation and the theoretical values is less than 1 pm/με.

Averaged variational principle for autoresonant Bernstein-Greene-Kruskal modes

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

Khain, P.; Friedland, L.

2010-10-15

Whitham's averaged variational principle is applied in studying dynamics of formation of autoresonant (continuously phase-locked) Bernstein-Greene-Kruskal (BGK) modes in a plasma driven by a chirped frequency ponderomotive wave. A flat-top electron velocity distribution is used as a model allowing a variational formulation within the water bag theory. The corresponding Lagrangian, averaged over the fast phase variable yields evolution equations for the slow field variables, allows uniform description of all stages of excitation of driven-chirped BGK modes, and predicts modulational stability of these nonlinear phase-space structures. Numerical solutions of the system of slow variational equations are in good agreement with Vlasov-Poissonmore » simulations.« less

Processes on the emergent landscapes of biochemical reaction networks and heterogeneous cell population dynamics: differentiation in living matters

PubMed Central

Li, Fangting

2017-01-01

The notion of an attractor has been widely employed in thinking about the nonlinear dynamics of organisms and biological phenomena as systems and as processes. The notion of a landscape with valleys and mountains encoding multiple attractors, however, has a rigorous foundation only for closed, thermodynamically non-driven, chemical systems, such as a protein. Recent advances in the theory of nonlinear stochastic dynamical systems and its applications to mesoscopic reaction networks, one reaction at a time, have provided a new basis for a landscape of open, driven biochemical reaction systems under sustained chemostat. The theory is equally applicable not only to intracellular dynamics of biochemical regulatory networks within an individual cell but also to tissue dynamics of heterogeneous interacting cell populations. The landscape for an individual cell, applicable to a population of isogenic non-interacting cells under the same environmental conditions, is defined on the counting space of intracellular chemical compositions x = (x1,x2, … ,xN) in a cell, where xℓ is the concentration of the ℓth biochemical species. Equivalently, for heterogeneous cell population dynamics xℓ is the number density of cells of the ℓth cell type. One of the insights derived from the landscape perspective is that the life history of an individual organism, which occurs on the hillsides of a landscape, is nearly deterministic and ‘programmed’, while population-wise an asynchronous non-equilibrium steady state resides mostly in the lowlands of the landscape. We argue that a dynamic ‘blue-sky’ bifurcation, as a representation of Waddington's landscape, is a more robust mechanism for a cell fate decision and subsequent differentiation than the widely pictured pitch-fork bifurcation. We revisit, in terms of the chemostatic driving forces upon active, living matter, the notions of near-equilibrium thermodynamic branches versus far-from-equilibrium states. The emergent landscape perspective permits a quantitative discussion of a wide range of biological phenomena as nonlinear, stochastic dynamics. PMID:28490602

Soliton interactions and the formation of solitonic patterns

NASA Astrophysics Data System (ADS)

Sears, Suzanne M.

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

Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability

NASA Astrophysics Data System (ADS)

Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Seleznev, A.; Loskutov, E.

2017-12-01

We study abilities of data-driven stochastic models constructed by nonlinear dynamical decomposition of spatially distributed data to quantitative (short-term) forecast of climate characteristics. We compare two data processing techniques: (i) widely used empirical orthogonal function approach, and (ii) nonlinear dynamical modes (NDMs) framework [1,2]. We also make comparison of two kinds of the prognostic models: (i) traditional autoregression (linear) model and (ii) model in the form of random ("stochastic") nonlinear dynamical system [3]. We apply all combinations of the above-mentioned data mining techniques and kinds of models to short-term forecasts of climate indices based on sea surface temperature (SST) data. We use NOAA_ERSST_V4 dataset (monthly SST with space resolution 20 × 20) covering the tropical belt and starting from the year 1960. We demonstrate that NDM-based nonlinear model shows better prediction skill versus EOF-based linear and nonlinear models. Finally we discuss capability of NDM-based nonlinear model for long-term (decadal) prediction of climate variability. [1] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J., 2016: Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators.

PubMed

Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao

2014-10-06

Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.

Power-Law Modeling of Cancer Cell Fates Driven by Signaling Data to Reveal Drug Effects

PubMed Central

Zhang, Fan; Wu, Min; Kwoh, Chee Keong; Zheng, Jie

2016-01-01

Extracellular signals are captured and transmitted by signaling proteins inside a cell. An important type of cellular responses to the signals is the cell fate decision, e.g., apoptosis. However, the underlying mechanisms of cell fate regulation are still unclear, thus comprehensive and detailed kinetic models are not yet available. Alternatively, data-driven models are promising to bridge signaling data with the phenotypic measurements of cell fates. The traditional linear model for data-driven modeling of signaling pathways has its limitations because it assumes that the a cell fate is proportional to the activities of signaling proteins, which is unlikely in the complex biological systems. Therefore, we propose a power-law model to relate the activities of all the measured signaling proteins to the probabilities of cell fates. In our experiments, we compared our nonlinear power-law model with the linear model on three cancer datasets with phosphoproteomics and cell fate measurements, which demonstrated that the nonlinear model has superior performance on cell fates prediction. By in silico simulation of virtual protein knock-down, the proposed model is able to reveal drug effects which can complement traditional approaches such as binding affinity analysis. Moreover, our model is able to capture cell line specific information to distinguish one cell line from another in cell fate prediction. Our results show that the power-law data-driven model is able to perform better in cell fate prediction and provide more insights into the signaling pathways for cancer cell fates than the linear model. PMID:27764199

A Mathematical Motivation for Complex-Valued Convolutional Networks.

PubMed

Tygert, Mark; Bruna, Joan; Chintala, Soumith; LeCun, Yann; Piantino, Serkan; Szlam, Arthur

2016-05-01

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors, followed by (2) taking the absolute value of every entry of the resulting vectors, followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as data-driven multiscale windowed power spectra, data-driven multiscale windowed absolute spectra, data-driven multiwavelet absolute values, or (in their most general configuration) data-driven nonlinear multiwavelet packets. Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (e.g., logistic or tanh) nonlinearities, or max pooling, for example, do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

Bound-Electron Nonlinearity Beyond the Ionization Threshold.

PubMed

Wahlstrand, J K; Zahedpour, S; Bahl, A; Kolesik, M; Milchberg, H M

2018-05-04

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

Bound-Electron Nonlinearity Beyond the Ionization Threshold

NASA Astrophysics Data System (ADS)

Wahlstrand, J. K.; Zahedpour, S.; Bahl, A.; Kolesik, M.; Milchberg, H. M.

2018-05-01

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

High amplitude nonlinear acoustic wave driven flow fields in cylindrical and conical resonators.

PubMed

Antao, Dion Savio; Farouk, Bakhtier

2013-08-01

A high fidelity computational fluid dynamic model is used to simulate the flow, pressure, and density fields generated in a cylindrical and a conical resonator by a vibrating end wall/piston producing high-amplitude standing waves. The waves in the conical resonator are found to be shock-less and can generate peak acoustic overpressures that exceed the initial undisturbed pressure by two to three times. A cylindrical (consonant) acoustic resonator has limitations to the output response observed at one end when the opposite end is acoustically excited. In the conical geometry (dissonant acoustic resonator) the linear acoustic input is converted to high energy un-shocked nonlinear acoustic output. The model is validated using past numerical results of standing waves in cylindrical resonators. The nonlinear nature of the harmonic response in the conical resonator system is further investigated for two different working fluids (carbon dioxide and argon) operating at various values of piston amplitude. The high amplitude nonlinear oscillations observed in the conical resonator can potentially enhance the performance of pulse tube thermoacoustic refrigerators and these conical resonators can be used as efficient mixers.

Nonlinear optical polymers for electro-optic signal processing

NASA Technical Reports Server (NTRS)

Lindsay, Geoffrey A.

1991-01-01

Photonics is an emerging technology, slated for rapid growth in communications systems, sensors, imagers, and computers. Its growth is driven by the need for speed, reliability, and low cost. New nonlinear polymeric materials will be a key technology in the new wave of photonics devices. Electron-conjubated polymeric materials offer large electro-optic figures of merit, ease of processing into films and fibers, ruggedness, low cost, and a plethora of design options. Several new broad classes of second-order nonlinear optical polymers were developed at the Navy's Michelson Laboratory at China Lake, California. Polar alignment in thin film waveguides was achieved by electric-field poling and Langmuir-Blodgett processing. Our polymers have high softening temperatures and good aging properties. While most of the films can be photobleached with ultraviolet (UV) light, some have excellent stability in the 500-1600 nm range, and UV stability in the 290-310 nm range. The optical nonlinear response of these polymers is subpicosecond. Electro-optic switches, frequency doublers, light modulators, and optical data storage media are some of the device applications anticipated for these polymers.

Predictability of rogue events.

PubMed

Birkholz, Simon; Brée, Carsten; Demircan, Ayhan; Steinmeyer, Günter

2015-05-29

Using experimental data from three different rogue wave supporting systems, determinism, and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the Draupner platform in the North Sea as well as time series from two optical systems in our analysis. One of the latter was measured in the infrared tail of optical fiber supercontinua, the other in the fluence profiles of multifilaments. All three data sets exhibit extreme-value statistics and exceed the significant wave height in the respective system by a factor larger than 2. Nonlinear time series analysis indicates a different degree of determinism in the systems. The optical fiber scenario is found to be driven by quantum noise whereas rogue waves emerge as a consequence of turbulence in the others. With the large number of rogue events observed in the multifilament system, we can systematically explore the predictability of such events in a turbulent system. We observe that rogue events do not necessarily appear without a warning, but are often preceded by a short phase of relative order. This surprising finding sheds some new light on the fascinating phenomenon of rogue waves.

Method for generating a plasma wave to accelerate electrons

DOEpatents

Umstadter, D.; Esarey, E.; Kim, J.K.

1997-06-10

The invention provides a method and apparatus for generating large amplitude nonlinear plasma waves, driven by an optimized train of independently adjustable, intense laser pulses. In the method, optimal pulse widths, interpulse spacing, and intensity profiles of each pulse are determined for each pulse in a series of pulses. A resonant region of the plasma wave phase space is found where the plasma wave is driven most efficiently by the laser pulses. The accelerator system of the invention comprises several parts: the laser system, with its pulse-shaping subsystem; the electron gun system, also called beam source, which preferably comprises photo cathode electron source and RF-LINAC accelerator; electron photo-cathode triggering system; the electron diagnostics; and the feedback system between the electron diagnostics and the laser system. The system also includes plasma source including vacuum chamber, magnetic lens, and magnetic field means. The laser system produces a train of pulses that has been optimized to maximize the axial electric field amplitude of the plasma wave, and thus the electron acceleration, using the method of the invention. 21 figs.

Method for generating a plasma wave to accelerate electrons

DOEpatents

Umstadter, Donald; Esarey, Eric; Kim, Joon K.

1997-01-01

The invention provides a method and apparatus for generating large amplitude nonlinear plasma waves, driven by an optimized train of independently adjustable, intense laser pulses. In the method, optimal pulse widths, interpulse spacing, and intensity profiles of each pulse are determined for each pulse in a series of pulses. A resonant region of the plasma wave phase space is found where the plasma wave is driven most efficiently by the laser pulses. The accelerator system of the invention comprises several parts: the laser system, with its pulse-shaping subsystem; the electron gun system, also called beam source, which preferably comprises photo cathode electron source and RF-LINAC accelerator; electron photo-cathode triggering system; the electron diagnostics; and the feedback system between the electron diagnostics and the laser system. The system also includes plasma source including vacuum chamber, magnetic lens, and magnetic field means. The laser system produces a train of pulses that has been optimized to maximize the axial electric field amplitude of the plasma wave, and thus the electron acceleration, using the method of the invention.

Magnetic curvature effects on plasma interchange turbulence

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

Li, B., E-mail: bli@pku.edu.cn; Liao, X.; Sun, C. K.

2016-06-15

The magnetic curvature effects on plasma interchange turbulence and transport in the Z-pinch and dipole-like systems are explored with two-fluid global simulations. By comparing the transport levels in the systems with a different magnetic curvature, we show that the interchange-mode driven transport strongly depends on the magnetic geometry. For the system with large magnetic curvature, the pressure and density profiles are strongly peaked in a marginally stable state and the nonlinear evolution of interchange modes produces the global convective cells in the azimuthal direction, which lead to the low level of turbulent convective transport.

Time reversal of arbitrary photonic temporal modes via nonlinear optical frequency conversion

NASA Astrophysics Data System (ADS)

Raymer, Michael G.; Reddy, Dileep V.; van Enk, Steven J.; McKinstrie, Colin J.

2018-05-01

Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is ‘blind’ reversal of a photon’s temporal wave packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. The process used may be sum-frequency generation or four-wave Bragg scattering. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only single-photon ones) of an unknown wave packet.

All-optical reservoir computer based on saturation of absorption.

PubMed

Dejonckheere, Antoine; Duport, François; Smerieri, Anteo; Fang, Li; Oudar, Jean-Louis; Haelterman, Marc; Massar, Serge

2014-05-05

Reservoir computing is a new bio-inspired computation paradigm. It exploits a dynamical system driven by a time-dependent input to carry out computation. For efficient information processing, only a few parameters of the reservoir needs to be tuned, which makes it a promising framework for hardware implementation. Recently, electronic, opto-electronic and all-optical experimental reservoir computers were reported. In those implementations, the nonlinear response of the reservoir is provided by active devices such as optoelectronic modulators or optical amplifiers. By contrast, we propose here the first reservoir computer based on a fully passive nonlinearity, namely the saturable absorption of a semiconductor mirror. Our experimental setup constitutes an important step towards the development of ultrafast low-consumption analog computers.

Characterizing driver-response relationships in marine pelagic ecosystems for improved ocean management.

PubMed

Hunsicker, Mary E; Kappel, Carrie V; Selkoe, Kimberly A; Halpern, Benjamin S; Scarborough, Courtney; Mease, Lindley; Amrhein, Alisan

2016-04-01

Scientists and resource managers often use methods and tools that assume ecosystem components respond linearly to environmental drivers and human stressors. However, a growing body of literature demonstrates that many relationships are-non-linear, where small changes in a driver prompt a disproportionately large ecological response. We aim to provide a comprehensive assessment of the relationships between drivers and ecosystem components to identify where and when non-linearities are likely to occur. We focused our analyses on one of the best-studied marine systems, pelagic ecosystems, which allowed us to apply robust statistical techniques on a large pool of previously published studies. In this synthesis, we (1) conduct a wide literature review on single driver-response relationships in pelagic systems, (2) use statistical models to identify the degree of non-linearity in these relationships, and (3) assess whether general patterns exist in the strengths and shapes of non-linear relationships across drivers. Overall we found that non-linearities are common in pelagic ecosystems, comprising at least 52% of all driver-response relation- ships. This is likely an underestimate, as papers with higher quality data and analytical approaches reported non-linear relationships at a higher frequency (on average 11% more). Consequently, in the absence of evidence for a linear relationship, it is safer to assume a relationship is non-linear. Strong non-linearities can lead to greater ecological and socioeconomic consequences if they are unknown (and/or unanticipated), but if known they may provide clear thresholds to inform management targets. In pelagic systems, strongly non-linear relationships are often driven by climate and trophodynamic variables but are also associated with local stressors, such as overfishing and pollution, that can be more easily controlled by managers. Even when marine resource managers cannot influence ecosystem change, they can use information about threshold responses to guide how other stressors are managed and to adapt to new ocean conditions. As methods to detect and reduce uncertainty around threshold values improve, managers will be able to better understand and account for ubiquitous non-linear relationships.

Friction self-oscillation decrease in nonlinear system of locomotive traction drive

NASA Astrophysics Data System (ADS)

Antipin, D. Ya; Vorobiyov, V. I.; Izmerov, O. V.; Shorokhov, S. G.; Bondarenko, D. A.

2017-02-01

The problems of the friction self-oscillation decrease in a nonlinear system of a locomotive traction drive are considered. It is determined that the self-oscillation amplitude decrease in a locomotive wheel pair during boxing in traction drives with an elastic linkage between an armature of a traction electric motor and gearing can be achieved due to drive damping capacity during impact vibro-damping in an axle reduction gear with a hard driven gear. The self-oscillation amplitude reduction in a wheel pair in the designs of locomotive traction drives with the location of elastic elements between a wheel pair and gearing can be obtained owing to the application of drive inertial masses as an anti-vibrator. On the basis of the carried out investigations, a design variant of a self-oscillation shock absorber of a traction electric motor framework on a reduction gear suspension with an absorber located beyond a wheel-motor unit was offered.

Simulation of high-energy radiation belt electron fluxes using NARMAX-VERB coupled codes

PubMed Central

Pakhotin, I P; Drozdov, A Y; Shprits, Y Y; Boynton, R J; Subbotin, D A; Balikhin, M A

2014-01-01

This study presents a fusion of data-driven and physics-driven methodologies of energetic electron flux forecasting in the outer radiation belt. Data-driven NARMAX (Nonlinear AutoRegressive Moving Averages with eXogenous inputs) model predictions for geosynchronous orbit fluxes have been used as an outer boundary condition to drive the physics-based Versatile Electron Radiation Belt (VERB) code, to simulate energetic electron fluxes in the outer radiation belt environment. The coupled system has been tested for three extended time periods totalling several weeks of observations. The time periods involved periods of quiet, moderate, and strong geomagnetic activity and captured a range of dynamics typical of the radiation belts. The model has successfully simulated energetic electron fluxes for various magnetospheric conditions. Physical mechanisms that may be responsible for the discrepancies between the model results and observations are discussed. PMID:26167432

Nonlinear unitary transformations of space-variant polarized light fields from self-induced geometric-phase optical elements

NASA Astrophysics Data System (ADS)

Kravets, Nina; Brasselet, Etienne

2018-01-01

We propose to couple the optical orientational nonlinearities of liquid crystals with their ability to self-organize to tailor them to control space-variant-polarized optical fields in a nonlinear manner. Experimental demonstration is made using a liquid crystal light valve that behaves like a light-driven geometric phase optical element. We also unveil two original nonlinear optical processes, namely self-induced separability and nonseparability. These results contribute to the advancement of nonlinear singular optics that is still in its infancy despite 25 years of effort, which may foster the development of nonlinear protocols to manipulate high-dimensional optical information both in the classical and quantum regimes.

Data-driven non-Markovian closure models

NASA Astrophysics Data System (ADS)

Kondrashov, Dmitri; Chekroun, Mickaël D.; Ghil, Michael

2015-03-01

This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with the optimal closures predicted by the Mori-Zwanzig (MZ) formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a generalization and a time-continuous limit of existing multilevel, regression-based approaches to closure in a data-driven setting; these approaches include empirical model reduction (EMR), as well as more recent multi-layer modeling. It is shown that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the MZ formalism. A simple correlation-based stopping criterion for an EMR-MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are derived on the structure of the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. The EMR-MSM methodology is first applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. It is shown that the resulting closure model with energy-conserving nonlinearities efficiently captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lotka-Volterra model of population dynamics in its chaotic regime. The challenges here include the rarity of strange attractors in the model's parameter space and the existence of multiple attractor basins with fractal boundaries. The positivity constraint on the solutions' components replaces here the quadratic-energy-preserving constraint of fluid-flow problems and it successfully prevents blow-up.

Parametric Symmetry Breaking in a Nonlinear Resonator

NASA Astrophysics Data System (ADS)

Leuch, Anina; Papariello, Luca; Zilberberg, Oded; Degen, Christian L.; Chitra, R.; Eichler, Alexander

2016-11-01

Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far-from-equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we investigate a resonating system subject to a fundamental interplay between intrinsic nonlinearities and a combination of several driving forces. We have constructed a controllable and robust realization of such a system using a macroscopic doubly clamped string. We experimentally observe a hitherto unseen double hysteresis in both the amplitude and the phase of the resonator's response function and present a theoretical model that is in excellent agreement with the experiment. Our work unveils that the double hysteresis is a manifestation of an out-of-equilibrium symmetry breaking between parametric phase states. Such a fundamental phenomenon, in the most ubiquitous building block of nature, paves the way for the investigation of new dynamical phases of matter in parametrically driven many-body systems and motivates applications ranging from ultrasensitive force detection to low-energy computing memory units.

Quantum dynamics of a Josephson junction driven cavity mode system in the presence of voltage bias noise

NASA Astrophysics Data System (ADS)

Wang, Hui; Blencowe, M. P.; Armour, A. D.; Rimberg, A. J.

2017-09-01

We give a semiclassical analysis of the average photon number as well as photon number variance (Fano factor F ) for a Josephson junction (JJ) embedded microwave cavity system, where the JJ is subject to a fluctuating (i.e., noisy) bias voltage with finite dc average. Through the ac Josephson effect, the dc voltage bias drives the effectively nonlinear microwave cavity mode into an amplitude squeezed state (F <1 ), as has been established previously [Armour et al., Phys. Rev. Lett. 111, 247001 (2013), 10.1103/PhysRevLett.111.247001], but bias noise acts to degrade this squeezing. We find that the sensitivity of the Fano factor to bias voltage noise depends qualitatively on which stable fixed point regime the system is in for the corresponding classical nonlinear steady-state dynamics. Furthermore, we show that the impact of voltage bias noise is most significant when the cavity is excited to states with large average photon number.

Theory of nonclassical photonic states in driven-dissipative circuit quantum electrodynamics

NASA Astrophysics Data System (ADS)

Elliott, Matthew

Superconducting circuits provide an architecture upon which cavity quantum electrodynamics (QED) can be implemented at microwave frequencies in a highly tunable environment. Known as circuit QED, these systems can achieve larger nonlinearities, stronger coupling and greater controllability than can be achieved in cavity QED, all in a customisable, solid state device, making this technology an exciting test bed for both quantum optics and quantum information processing. These new parameter regimes open up new avenues for quantum technology, while also allowing older quantum optics results to finally be tested. In particular is is now possible to experimentally produce nonclassical states, such as squeezed and Schrodinger cat states, relatively simply in these devices. Using open quantum systems methods, in this thesis we investigate four problems which involve the use of nonclassical states in circuit QED. First we investigate the effects of a Kerr nonlinearity on the ability to preserve transported squeezed states in a superconducting cavity, and whether this setup permits us to generate, and perform tomography, of a highly squeezed field using a qubit, with possible applications in the characterisation of sources of squeezed microwaves. Second, we present a novel scheme for the amplification of cat states using a coupled qubit and external microwave drives, inspired by the stimulated Raman adiabatic passage. This scheme differs from similar techniques in circuit QED in that it is deterministic and therefore compatible with a protocol for stabilising cat states without the need for complex dissipation engineering. Next we use solutions of Fokker-Planck equations to study the exact steady-state response of two nonlinear systems: a transmon qubit coupled to a readout resonator, where we find good agreement with experiments and see simultaneous bistability of the cavity and transmon; and a parametrically driven nonlinear resonator, where we compare the classical and quantum phases of the system and discuss applications in the generation of squeezed states and stabilisation of cat states. Finally, we investigate the use of two different types of superconducting qubits in a single experiment, seeing that this enables engineering of the self- and cross-Kerr effects in a line of cavities. This could provide a valuable means of entangling cavity states, in addition to a resource for quantum simulation.

Buckling Causes Nonlinear Dynamics of Filamentous Viruses Driven through Nanopores.

PubMed

McMullen, Angus; de Haan, Hendrick W; Tang, Jay X; Stein, Derek

2018-02-16

Measurements and Langevin dynamics simulations of filamentous viruses driven through solid-state nanopores reveal a superlinear rise in the translocation velocity with driving force. The mobility also scales with the length of the virus in a nontrivial way that depends on the force. These dynamics are consequences of the buckling of the leading portion of a virus as it emerges from the nanopore and is put under compressive stress by the viscous forces it encounters. The leading tip of a buckled virus stalls and this reduces the total viscous drag force. We present a scaling theory that connects the solid mechanics to the nonlinear dynamics of polyelectrolytes translocating nanopores.

Buckling Causes Nonlinear Dynamics of Filamentous Viruses Driven through Nanopores

NASA Astrophysics Data System (ADS)

McMullen, Angus; de Haan, Hendrick W.; Tang, Jay X.; Stein, Derek

2018-02-01

Measurements and Langevin dynamics simulations of filamentous viruses driven through solid-state nanopores reveal a superlinear rise in the translocation velocity with driving force. The mobility also scales with the length of the virus in a nontrivial way that depends on the force. These dynamics are consequences of the buckling of the leading portion of a virus as it emerges from the nanopore and is put under compressive stress by the viscous forces it encounters. The leading tip of a buckled virus stalls and this reduces the total viscous drag force. We present a scaling theory that connects the solid mechanics to the nonlinear dynamics of polyelectrolytes translocating nanopores.

Nonlinear disturbance observer based sliding mode control of a cable-driven rehabilitation robot.

PubMed

Niu, Jie; Yang, Qianqian; Chen, Guangtao; Song, Rong

2017-07-01

This paper introduces a cable-driven robot for upper-limb rehabilitation. Kinematic and dynamic of this rehabilitation robot is analyzed. A sliding mode controller combined with a nonlinear disturbance observer is proposed to control this robot in the presence of disturbances. Simulation is carried out to prove the effectiveness of the proposed control scheme, and the results of the proposed controller is compared with a PID controller and a traditional sliding mode controller. Results show that the proposed controller can effectively improve the tracking performance as compared with the other two controllers and cause lower chattering as compared with a traditional sliding mode controller.

Singularity-driven second- and third-harmonic generation at {epsilon}-near-zero crossing points

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

Vincenti, M. A.; Ceglia, D. de; Ciattoni, A.

We show an alternative path to efficient second- and third-harmonic generation in proximity of the zero crossing points of the dielectric permittivity in conjunction with low absorption. Under these circumstances, any material, either natural or artificial, will show similar degrees of field enhancement followed by strong harmonic generation, without resorting to any resonant mechanism. The results presented in this paper provide a general demonstration of the potential that the zero-crossing-point condition holds for nonlinear optical phenomena. We investigate a generic Lorentz medium and demonstrate that a singularity-driven enhancement of the electric field may be achieved even in extremely thin layersmore » of material. We also discuss the role of nonlinear surface sources in a realistic scenario where a 20-nm layer of CaF{sub 2} is excited at 21 {mu}m, where {epsilon}{approx} 0. Finally, we show similar behavior in an artificial composite material that includes absorbing dyes in the visible range, provide a general tool for the improvement of harmonic generation using the {epsilon}{approx} 0 condition, and illustrate that this singularity-driven enhancement of the field lowers the thresholds for a plethora of nonlinear optical phenomena.« less

Saturation of energetic-particle-driven geodesic acoustic modes due to wave-particle nonlinearity

NASA Astrophysics Data System (ADS)

Biancalani, A.; Chavdarovski, I.; Qiu, Z.; Bottino, A.; Del Sarto, D.; Ghizzo, A.; Gürcan, Ö.; Morel, P.; Novikau, I.

2017-12-01

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. As a main result, the formula for the saturation level is provided. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e. the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

Aspect ratio effects on limited scrape-off layer plasma turbulence

NASA Astrophysics Data System (ADS)

Jolliet, Sébastien; Halpern, Federico D.; Loizu, Joaquim; Mosetto, Annamaria; Ricci, Paolo

2014-02-01

The drift-reduced Braginskii model describing turbulence in the tokamak scrape-off layer is written for a general magnetic configuration with a limiter. The equilibrium is then specified for a circular concentric magnetic geometry retaining aspect ratio effects. Simulations are then carried out with the help of the global, flux-driven fluid three-dimensional code GBS [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. Linearly, both simulations and simplified analytical models reveal a stabilization of ballooning modes. Nonlinearly, flux-driven nonlinear simulations give a pressure characteristic length whose trends are correctly captured by the gradient removal theory [Ricci and Rogers, Phys. Plasmas 20, 010702 (2013)], that assumes the profile flattening from the linear modes as the saturation mechanism. More specifically, the linear stabilization of ballooning modes is reflected by a 15% increase in the steady-state pressure gradient obtained from GBS nonlinear simulations when going from an infinite to a realistic aspect ratio.

Mechanical-magnetic-electric coupled behaviors for stress-driven Terfenol-D energy harvester

NASA Astrophysics Data System (ADS)

Cao, Shuying; Zheng, Jiaju; Wang, Bowen; Pan, Ruzheng; Zhao, Ran; Weng, Ling; Sun, Ying; Liu, Chengcheng

2017-05-01

The stress-driven Terfernol-D energy harvester exhibits the nonlinear mechanical-magnetic-electric coupled (MMEC) behaviors and the eddy current effects. To analyze and design the device, it is necessary to establish an accurate model of the device. Based on the effective magnetic field expression, the constitutive equations with eddy currents and variable coefficients, and the dynamic equations, a nonlinear dynamic MMEC model for the device is founded. Comparisons between the measured and calculated results show that the model can describe the nonlinear coupled curves of magnetization versus stress and strain versus stress under different bias fields, and can provide the reasonable data trends of piezomagnetic coefficients, Young's modulus and relative permeability for Terfenol-D. Moreover, the calculated power results show that the model can determine the optimal bias conditions, optimal resistance, suitable proof mass, suitable slices for the maximum energy extraction of the device under broad stress amplitude and broad frequency.

Kinetic theory and Vlasov simulation of nonlinear ion-acoustic waves in multi-ion species plasmas.

PubMed

Chapman, T; Berger, R L; Brunner, S; Williams, E A

2013-05-10

The theory of damping and nonlinear frequency shifts from particles resonant with ion-acoustic waves (IAWs) is presented for multi-ion species plasma and compared to driven wave Vlasov simulations. Two distinct IAW modes may be supported in multi-ion species plasmas, broadly classified as fast and slow by their phase velocity relative to the constituent ion thermal velocities. In current fusion-relevant long pulse experiments, the ion to electron temperature ratio, T(i)/T(e), is expected to reach a level such that the least damped and thus more readily driven mode is the slow mode, with both linear and nonlinear properties that are shown to differ significantly from the fast mode. The lighter ion species of the slow mode is found to make no significant contribution to the IAW frequency shift despite typically being the dominant contributor to the Landau damping.

Data-based adjoint and H2 optimal control of the Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Banks, Michael; Bodony, Daniel

2017-11-01

Equation-free, reduced-order methods of control are desirable when the governing system of interest is of very high dimension or the control is to be applied to a physical experiment. Two-phase flow optimal control problems, our target application, fit these criteria. Dynamic Mode Decomposition (DMD) is a data-driven method for model reduction that can be used to resolve the dynamics of very high dimensional systems and project the dynamics onto a smaller, more manageable basis. We evaluate the effectiveness of DMD-based forward and adjoint operator estimation when applied to H2 optimal control approaches applied to the linear and nonlinear Ginzburg-Landau equation. Perspectives on applying the data-driven adjoint to two phase flow control will be given. Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program, under Grant Number N00014-16-1-2617.

Design and experiment of data-driven modeling and flutter control of a prototype wing

NASA Astrophysics Data System (ADS)

Lum, Kai-Yew; Xu, Cai-Lin; Lu, Zhenbo; Lai, Kwok-Leung; Cui, Yongdong

2017-06-01

This paper presents an approach for data-driven modeling of aeroelasticity and its application to flutter control design of a wind-tunnel wing model. Modeling is centered on system identification of unsteady aerodynamic loads using computational fluid dynamics data, and adopts a nonlinear multivariable extension of the Hammerstein-Wiener system. The formulation is in modal coordinates of the elastic structure, and yields a reduced-order model of the aeroelastic feedback loop that is parametrized by airspeed. Flutter suppression is thus cast as a robust stabilization problem over uncertain airspeed, for which a low-order H∞ controller is computed. The paper discusses in detail parameter sensitivity and observability of the model, the former to justify the chosen model structure, and the latter to provide a criterion for physical sensor placement. Wind tunnel experiments confirm the validity of the modeling approach and the effectiveness of the control design.

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

PubMed

Hammi, Oualid

2014-01-01

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

Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing

NASA Astrophysics Data System (ADS)

Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley

2017-08-01

At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such memristors into the hardware of a Hopfield computing network can greatly improve the efficiency and accuracy of converging to a solution for computationally difficult problems.

Modeling stick-slip-separation dynamics in a bimodal standing wave ultrasonic motor

NASA Astrophysics Data System (ADS)

Li, Xiang; Yao, Zhiyuan; Lv, Qibao; Liu, Zhen

2016-11-01

Ultrasonic motor (USM) is an electromechanical coupling system with ultrasonic vibration, which is driven by the frictional contact force between the stator (vibrating body) and the rotor/slider (driven body). Stick-slip motion can occur at the contact interface when USM is operating, which may affect the performance of the motor. This paper develops a physically-based model to investigate the complex stick-slip-separation dynamics in a bimodal standing wave ultrasonic motor. The model includes both friction nonlinearity and intermittent separation nonlinearity of the system. Utilizing Hamilton's principle and assumed mode method, the dynamic equations of the stator are deduced. Based on the dynamics of the stator and the slider, sticking force during the stick phase is derived, which is used to examine the stick-to-slip transition. Furthermore, the stick-slip-separation kinematics is analyzed by establishing analytical criteria that predict the transition between stick, slip and separation of the interface. Stick-slip-separation motion is observed in the resulting model, and numerical simulations are performed to study the influence of parameters on the range of possible motions. Results show that stick-slip motion can occur with greater preload and smaller voltage amplitude. Furthermore, a dimensionless parameter is proposed to predict the occurrence of stick-slip versus slip-separation motions, and its role in designing ultrasonic motors is discussed. It is shown that slip-separation motion is favorable for the slider velocity.

Phase reduction approach to synchronisation of nonlinear oscillators

NASA Astrophysics Data System (ADS)

Nakao, Hiroya

2016-04-01

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.

Computational Study of Breathing-type Processes in Driven, Confined, Granular Alignments

DTIC Science & Technology

2012-04-17

Government of India, Title: : “Newton’s cradle, Fermi, Pasta , Ulam chain & the nonlinear many body frontier,” June 29, 2011 2. Physics Seminar, Indian...Institute of Science, Bangalore, India, Title: “Newton’s cradle, Fermi, Pasta , Ulam chain & the nonlinear many body frontier,” June 30, 2011 3. Physics...Department Colloquium, SUNY Buffalo, Title: “Newton’s cradle, Fermi, Pasta , Ulam chain & the nonlinear many body frontier,” January 20, 2011. 4

Direct Numerical Simulation of Fingering Instabilities in Coating Flows

NASA Astrophysics Data System (ADS)

Eres, Murat H.; Schwartz, Leonard W.

1998-11-01

We consider stability and finger formation in free surface flows. Gravity driven downhill drainage and temperature gradient driven climbing flows are two examples of such problems. The former situation occurs when a mound of viscous liquid on a vertical wall is allowed to flow. Constant surface shear stress due to temperature gradients (Marangoni stress) can initiate the latter problem. The evolution equations are derived using the lubrication approximation. We also include the effects of finite-contact angles in the evolution equations using a disjoining pressure model. Evolution equations for both problems are solved using an efficient alternating-direction-implicit method. For both problems a one-dimensional base state is established, that is steady in a moving reference frame. This base state is unstable to transverse perturbations. The transverse wavenumbers for the most rapidly growing modes are found through direct numerical solution of the nonlinear evolution equations, and are compared with published experimental results. For a range of finite equilibrium contact angles, the fingers can grow without limit leading to semi-finite steady fingers in a moving coordinate system. A computer generated movie of the nonlinear simulation results, for several sets of input parameters, will be shown.

Frequency Combs in a Lumped-Element Josephson-Junction Circuit

NASA Astrophysics Data System (ADS)

Khan, Saeed; Türeci, Hakan E.

2018-04-01

We investigate the dynamics of a microwave-driven Josephson junction capacitively coupled to a lumped-element L C oscillator. In the regime of driving where the Josephson junction can be approximated as a Kerr oscillator, this minimal nonlinear system has been previously shown to exhibit a bistability in phase and amplitude. In the present study, we characterize the full phase diagram and show that besides a parameter regime exhibiting bistability, there is also a regime of self-oscillations characterized by a frequency comb in its spectrum. We discuss the mechanism of comb generation which appears to be different from those studied in microcavity frequency combs and mode-locked lasers. We then address the fate of the comblike spectrum in the regime of strong quantum fluctuations, reached when nonlinearity becomes the dominant scale with respect to dissipation. We find that the nonlinearity responsible for the emergence of the frequency combs also leads to its dephasing, leading to broadening and ultimate disappearance of sharp spectral peaks. Our study explores the fundamental question of the impact of quantum fluctuations for quantum systems which do not possess a stable fixed point in the classical limit.

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

DOE PAGES

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

2017-11-09

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

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

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

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

Scholbrock, A. K.; Fleming, P. A.; Fingersh, L. J.

Wind turbines are complex, nonlinear, dynamic systems driven by aerodynamic, gravitational, centrifugal, and gyroscopic forces. The aerodynamics of wind turbines are nonlinear, unsteady, and complex. Turbine rotors are subjected to a chaotic three-dimensional (3-D) turbulent wind inflow field with imbedded coherent vortices that drive fatigue loads and reduce lifetime. In order to reduce cost of energy, future large multimegawatt turbines must be designed with lighter weight structures, using active controls to mitigate fatigue loads, maximize energy capture, and add active damping to maintain stability for these dynamically active structures operating in a complex environment. Researchers at the National Renewable Energymore » Laboratory (NREL) and University of Stuttgart are designing, implementing, and testing advanced feed-back and feed-forward controls in order to reduce the cost of energy for wind turbines.« less

Nonlinear Entanglement and its Application to Generating Cat States

NASA Astrophysics Data System (ADS)

Shen, Y.; Assad, S. M.; Grosse, N. B.; Li, X. Y.; Reid, M. D.; Lam, P. K.

2015-03-01

The Einstein-Podolsky-Rosen (EPR) paradox, which was formulated to argue for the incompleteness of quantum mechanics, has since metamorphosed into a resource for quantum information. The EPR entanglement describes the strength of linear correlations between two objects in terms of a pair of conjugate observables in relation to the Heisenberg uncertainty limit. We propose that entanglement can be extended to include nonlinear correlations. We examine two driven harmonic oscillators that are coupled via third-order nonlinearity can exhibit quadraticlike nonlinear entanglement which, after a projective measurement on one of the oscillators, collapses the other into a cat state of tunable size.

Nonlinear entanglement and its application to generating cat States.

PubMed

Shen, Y; Assad, S M; Grosse, N B; Li, X Y; Reid, M D; Lam, P K

2015-03-13

The Einstein-Podolsky-Rosen (EPR) paradox, which was formulated to argue for the incompleteness of quantum mechanics, has since metamorphosed into a resource for quantum information. The EPR entanglement describes the strength of linear correlations between two objects in terms of a pair of conjugate observables in relation to the Heisenberg uncertainty limit. We propose that entanglement can be extended to include nonlinear correlations. We examine two driven harmonic oscillators that are coupled via third-order nonlinearity can exhibit quadraticlike nonlinear entanglement which, after a projective measurement on one of the oscillators, collapses the other into a cat state of tunable size.

Tangled nonlinear driven chain reactions of all optical singularities

NASA Astrophysics Data System (ADS)

Vasil'ev, V. I.; Soskin, M. S.

2012-03-01

Dynamics of polarization optical singularities chain reactions in generic elliptically polarized speckle fields created in photorefractive crystal LiNbO3 was investigated in details Induced speckle field develops in the tens of minutes scale due to photorefractive 'optical damage effect' induced by incident beam of He-Ne laser. It was shown that polarization singularities develop through topological chain reactions of developing speckle fields driven by photorefractive nonlinearities induced by incident laser beam. All optical singularities (C points, optical vortices, optical diabolos,) are defined by instantaneous topological structure of the output wavefront and are tangled by singular optics lows. Therefore, they have develop in tangled way by six topological chain reactions driven by nonlinear processes in used nonlinear medium (photorefractive LiNbO3:Fe in our case): C-points and optical diabolos for right (left) polarized components domains with orthogonally left (right) polarized optical vortices underlying them. All elements of chain reactions consist from loop and chain links when nucleated singularities annihilated directly or with alien singularities in 1:9 ratio. The topological reason of statistics was established by low probability of far enough separation of born singularities pair from existing neighbor singularities during loop trajectories. Topology of developing speckle field was measured and analyzed by dynamic stokes polarimetry with few seconds' resolution. The hierarchy of singularities govern scenario of tangled chain reactions was defined. The useful space-time data about peculiarities of optical damage evolution were obtained from existence and parameters of 'islands of stability' in developing speckle fields.

Preface

NASA Astrophysics Data System (ADS)

Zhuge, Qunbi; Chen, Xi

2018-02-01

Global IP traffic is predicted to increase nearly threefold over the next 5 years, driven by emerging high-bandwidth-demanding applications, such as cloud computing, 5G wireless, high-definition video streaming, and virtual reality. This results in a continuously increasing demand on the capacity of backbone optical networks. During the past decade, advanced digital signal processing (DSP), modulation formats, and forward error correction (FEC) were commercially realized to exploit the capacity potential of long-haul fiber channels, and have increased per channel data rate from 10 Gb/s to 400 Gb/s. DSP has played a crucial role in coherent transceivers to accommodate channel impairments including chromatic dispersion (CD), polarization mode dispersion (PMD), laser phase noise, fiber nonlinearities, clock jitter, and so forth. The advance of DSP has also enabled innovations in modulation formats to increase spectral efficiency, improve linear/nonlinear noise tolerance, and realize flexible bandwidth. Moving forward to next generation 1 Tb/s systems on conventional single mode fiber (SMF) platform, more innovations in DSP techniques are needed to further reduce cost per bit, increase network efficiency, and close the gap to the Shannon limit. To further increase capacity per fiber, spatial-division multiplexing (SDM) systems can be used. DSP techniques such as advanced channel equalization methods and distortion compensation can help SDM systems to achieve higher system capacity. In the area of short-reach transmission, the rapid increase of data center network traffic has driven the development of optical technologies for both intra- and inter-data center interconnects (DCI). In particular, DSP has been exploited in intensity-modulation direct detection (IM/DD) systems to realize 400 Gb/s pluggable optical transceivers. In addition, multi-dimensional direct detection modulation schemes are being investigated to increase the data rate per wavelength targeting 1 Tb/s interface.

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

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

Wu, Yimin; Lv, Hui, E-mail: lvhui207@gmail.com

In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.

Frontogenesis driven by horizontally quadratic distributions of density

NASA Technical Reports Server (NTRS)

Jacqmin, David

1991-01-01

Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.

Nonlinear fishbone dynamics in spherical tokamaks

DOE Data Explorer

Wang, Feng [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Dalian Univ Technol, Sch Phys & Optoelect Technol, Minist Educ, Key Lab Mat Modificat Laser Ion & Electron Beams, Dalian 116024, Peoples R China.; Fu, G.Y. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Institute for Fusion Theory and Simulation and Department of Physics Hangzhou, Zhejiang University, Hangzhou, 310027, People's Republic of China; Shen, Wei [Institute of Plasma Physics, Chinese Academy of Science, Hefei 230031, People's Republic of China

2017-01-01

Linear and nonlinear kinetic-MHD hybrid simulations have been carried out to investigate linear stability and nonlinear dynamics of beam-driven fishbone instability in spherical tokamak plasmas. Realistic NSTX parameters with finite toroidal rotation were used. The results show that the fishbone is driven by both trapped and passing particles. The instability drive of passing particles is comparable to that of trapped particles in the linear regime. The effects of rotation are destabilizing and a new region of instability appears at higher q min (>1.5) values, q min being the minimum of safety factor profile. In the nonlinear regime, the mode saturates due to flattening of beam ion distribution, and this persists after initial saturation while mode frequency chirps down in such a way that the resonant trapped particles move out radially and keep in resonance with the mode. Correspondingly, the flattening region of beam ion distribution expands radially outward. A substantial fraction of initially non-resonant trapped particles become resonant around the time of mode saturation and keep in resonance with the mode as frequency chirps down. On the other hand, the fraction of resonant passing particles is significantly smaller than that of trapped particles. Our analysis shows that trapped particles provide the main drive to the mode in the nonlinear regime.

Nonlinear fishbone dynamics in spherical tokamaks

DOE PAGES

Wang, Feng; Fu, G. Y.; Shen, Wei

2016-11-22

Linear and nonlinear kinetic-MHD hybrid simulations have been carried out to investigate linear stability and nonlinear dynamics of beam-driven fishbone instability in spherical tokamak plasmas. Realistic NSTX parameters with finite toroidal rotation were used. Our results show that the fishbone is driven by both trapped and passing particles. The instability drive of passing particles is comparable to that of trapped particles in the linear regime. The effects of rotation are destabilizing and a new region of instability appears at higher q min (>1.5) values, q min being the minimum of safety factor profile. In the nonlinear regime, the mode saturatesmore » due to flattening of beam ion distribution, and this persists after initial saturation while mode frequency chirps down in such a way that the resonant trapped particles move out radially and keep in resonance with the mode. Correspondingly, the flattening region of beam ion distribution expands radially outward. Furthermore, a substantial fraction of initially non-resonant trapped particles become resonant around the time of mode saturation and keep in resonance with the mode as frequency chirps down. On the other hand, the fraction of resonant passing particles is significantly smaller than that of trapped particles. Finally, our analysis shows that trapped particles provide the main drive to the mode in the nonlinear regime.« less

Solitons and Vortices of Shear-Flow-Modified Dust Acoustic Wave

NASA Astrophysics Data System (ADS)

Saeed, Usman; Saleem, Hamid; Shan, Shaukat Ali

2018-01-01

Shear-flow-driven instability and a modified nonlinear dust acoustic wave (mDAW) are investigated in a dusty plasma. In the nonlinear regime a one dimensional mDAW produces pulse-type solitons and in the two-dimensional case, the dipolar vortex solutions are obtained. This investigation is relevant to magnetospheres of planets such as Saturn and Jupiter as well as dusty interstellar clouds. Here, the theoretical model is applied to Saturn's F-rings, and shape of the nonlinear electric field structures is discussed.

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

PubMed Central

2014-01-01

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

Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

NASA Astrophysics Data System (ADS)

Wang, Lei; Feng, Enmin; Ye, Jianxiong; Xiu, Zhilong

The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.

The wavelength of supercritical surface tension driven Benard convection

NASA Technical Reports Server (NTRS)

Koschmieder, E. L.

1991-01-01

The size or the wavelength of moderately supercritical surface tension driven Benard convection has been investigated experimentally in a thin fluid layer of large aspect ratio. It has been found that the number of the hexagonal convection cells increases with increased temperature differences, up to 1.3 times the critical temperature difference. That means that the wavelength of surface tension driven convection decreases after onset of the instability for moderately nonlinear conditions. This result is in striking contrast to the well-known increase of the wavelength of buoyancy driven Rayleigh-Benard convection.

A framework for the automated data-driven constitutive characterization of composites

Treesearch

J.G. Michopoulos; John Hermanson; T. Furukawa; A. Iliopoulos

2010-01-01

We present advances on the development of a mechatronically and algorithmically automated framework for the data-driven identification of constitutive material models based on energy density considerations. These models can capture both the linear and nonlinear constitutive response of multiaxially loaded composite materials in a manner that accounts for progressive...

Using Recursive Regression to Explore Nonlinear Relationships and Interactions: A Tutorial Applied to a Multicultural Education Study

ERIC Educational Resources Information Center

Strang, Kenneth David

2009-01-01

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

Inverted Spring Pendulum Driven by a Periodic Force: Linear versus Nonlinear Analysis

ERIC Educational Resources Information Center

Arinstein, A.; Gitterman, M.

2008-01-01

We analyse the stability of the spring inverted pendulum with the vertical oscillations of the suspension point. An important factor in the stability analysis is the interaction between radial and oscillating modes. In addition to the small oscillations near the upper position, the nonlinearity of the problem leads to the appearance of limit-cycle…

Nonlinear optical effects of opening a gap in graphene

NASA Astrophysics Data System (ADS)

Carvalho, David N.; Biancalana, Fabio; Marini, Andrea

2018-05-01

Graphene possesses remarkable electronic, optical, and mechanical properties that have taken the research of two-dimensional relativistic condensed matter systems to prolific levels. However, the understanding of how its nonlinear optical properties are affected by relativisticlike effects has been broadly uncharted. It has been recently shown that highly nontrivial currents can be generated in free-standing samples, notably leading to the generation of even harmonics. Since graphene monolayers are centrosymmetric media, for which such harmonic generation at normal incidence is deemed inaccessible, this light-driven phenomenon is both startling and promising. More realistically, graphene samples are often deposited on a dielectric substrate, leading to additional intricate interactions. Here, we present a treatment to study this instance by gapping the spectrum and we show this leads to the appearance of a Berry phase in the carrier dynamics. We analyze the role of such a phase in the generated nonlinear current and conclude that it suppresses odd-harmonic generation. The pump energy can be tuned to the energy gap to yield interference among odd harmonics mediated by interband transitions, allowing even harmonics to be generated. Our results and general methodology pave the way for understanding the role of gap opening in the nonlinear optics of two-dimensional lattices.

Reconstructing latent dynamical noise for better forecasting observables

NASA Astrophysics Data System (ADS)

Hirata, Yoshito

2018-03-01

I propose a method for reconstructing multi-dimensional dynamical noise inspired by the embedding theorem of Muldoon et al. [Dyn. Stab. Syst. 13, 175 (1998)] by regarding multiple predictions as different observables. Then, applying the embedding theorem by Stark et al. [J. Nonlinear Sci. 13, 519 (2003)] for a forced system, I produce time series forecast by supplying the reconstructed past dynamical noise as auxiliary information. I demonstrate the proposed method on toy models driven by auto-regressive models or independent Gaussian noise.

Toward efficient aeroelastic energy harvesting through limit cycle shaping

NASA Astrophysics Data System (ADS)

Kirschmeier, Benjamin; Bryant, Matthew

2016-04-01

Increasing demand to harvest energy from renewable resources has caused significant research interest in unsteady aerodynamic and hydrodynamic phenomena. Apart from the traditional horizontal axis wind turbines, there has been significant growth in the study of bio-inspired oscillating wings for energy harvesting. These systems are being built to harvest electricity for wireless devices, as well as for large scale mega-watt power generation. Such systems can be driven by aeroelastic flutter phenomena which, beyond a critical wind speed, will cause the system to enter into limitcycle oscillations. When the airfoil enters large amplitude, high frequency motion, leading and trailing edge vortices form and, when properly synchronized with the airfoil kinematics, enhance the energy extraction efficiency of the device. A reduced order dynamic stall model is employed on a nonlinear aeroelastic structural model to investigate whether the parameters of a fully passive aeroelastic device can be tuned to produce limit cycle oscillations at desired kinematics. This process is done through an optimization technique to find the necessary structural parameters to achieve desired structural forces and moments corresponding to a target limit cycle. Structural nonlinearities are explored to determine the essential nonlinearities such that the system's limit cycle closely matches the desired kinematic trajectory. The results from this process demonstrate that it is possible to tune system parameters such that a desired limit cycle trajectory can be achieved. The simulations also demonstrate that the high efficiencies predicted by previous computational aerodynamics studies can be achieved in fully passive aeroelastic devices.

Magnetic effect for electrochemically driven cellular convection.

PubMed

Nakabayashi, S; Inokuma, K; Karantonis, A

1999-06-01

Hydrodynamic instability analogous to Rayleigh-Bénard convection is observed in an electrolytic solution between two parallel copper wire electrodes. The laser interferometric technique can reveal the dissipation structure created by the motion of the fluid, which is controlled electrochemically. It is shown that under the presence of horizontal magnetic field the roll cells move horizontally along the electrodes. The electrochemically driven convection is simply controlled and monitored by setting and measuring the electrochemical parameters and forms many kinds of spatiotemporal patterns, especially under the magnetic field. The phenomenon is modeled by considering a Boussinesq fluid under a concentration gradient. The stability of the resulting equations is studied by linear stability analysis. The time dependent nonlinear system is investigated numerically and the main features of the experimental response are reproduced.

Ion temperature gradient mode driven solitons and shocks

NASA Astrophysics Data System (ADS)

Zakir, U.; Adnan, Muhammad; Haque, Q.; Qamar, Anisa; Mirza, Arshad M.

2016-04-01

Ion temperature gradient (ITG) driven solitons and shocks are studied in a plasma having gradients in the equilibrium number density and equilibrium ion temperature. In the linear regime, it is found that the ion temperature and the ratio of the gradient scale lengths, ηi=Ln/LT , affect both the real frequency and the growth rate of the ITG driven wave instability. In the nonlinear regime, for the first time we derive a Korteweg de Vries-type equation for the ITG mode, which admits solitary wave solution. It is found that the ITG mode supports only compressive solitons. Further, it is noticed that the soliton amplitude and width are sensitive to the parameter ηi=Ln/LT . Second, in the presence of dissipation in the system, we obtain a Burger type equation, which admits the shock wave solution. This work may be useful to understand the low frequency electrostatic modes in inhomogeneous electron-ion plasma having density and ion temperature gradients. For illustration, the model has been applied to tokamak plasma.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

First Principles Modeling of the Performance of a Hydrogen-Peroxide-Driven Chem-E-Car

ERIC Educational Resources Information Center

Farhadi, Maryam; Azadi, Pooya; Zarinpanjeh, Nima

2009-01-01

In this study, performance of a hydrogen-peroxide-driven car has been simulated using basic conservation laws and a few numbers of auxiliary equations. A numerical method was implemented to solve sets of highly non-linear ordinary differential equations. Transient pressure and the corresponding traveled distance for three different car weights are…

Summary of Research 2002

DTIC Science & Technology

2005-01-01

dissipation, nonuniformity , and nonlinearity are included. A possible future objective is to theoretically investigate nonradiating sources in two and...dissipation, nonuniformity , and nonlinearity. The presence of any of these effects causes radiation to “leak” from the driven region. This radiation was...The utility of LWIR spectral imagery for plume detection was studied. PRESENTATION: Olsen, R.C., Ganer, J. and Van Dyke, E., “Terrain

Modeling of Nonlinear Beat Signals of TAE's

NASA Astrophysics Data System (ADS)

Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin

2012-03-01

Experiments on Alcator C-Mod reveal Toroidal Alfven Eigenmodes (TAE) together with signals at various beat frequencies, including those at twice the mode frequency. The beat frequencies are sidebands driven by quadratic nonlinear terms in the MHD equations. These nonlinear sidebands have not yet been quantified by any existing codes. We extend the AEGIS code to capture nonlinear effects by treating the nonlinear terms as a driving source in the linear MHD solver. Our goal is to compute the spatial structure of the sidebands for realistic geometry and q-profile, which can be directly compared with experiment in order to interpret the phase contrast imaging diagnostic measurements and to enable the quantitative determination of the Alfven wave amplitude in the plasma core

Nonlinear data-driven identification of polymer electrolyte membrane fuel cells for diagnostic purposes: A Volterra series approach

NASA Astrophysics Data System (ADS)

Ritzberger, D.; Jakubek, S.

2017-09-01

In this work, a data-driven identification method, based on polynomial nonlinear autoregressive models with exogenous inputs (NARX) and the Volterra series, is proposed to describe the dynamic and nonlinear voltage and current characteristics of polymer electrolyte membrane fuel cells (PEMFCs). The structure selection and parameter estimation of the NARX model is performed on broad-band voltage/current data. By transforming the time-domain NARX model into a Volterra series representation using the harmonic probing algorithm, a frequency-domain description of the linear and nonlinear dynamics is obtained. With the Volterra kernels corresponding to different operating conditions, information from existing diagnostic tools in the frequency domain such as electrochemical impedance spectroscopy (EIS) and total harmonic distortion analysis (THDA) are effectively combined. Additionally, the time-domain NARX model can be utilized for fault detection by evaluating the difference between measured and simulated output. To increase the fault detectability, an optimization problem is introduced which maximizes this output residual to obtain proper excitation frequencies. As a possible extension it is shown, that by optimizing the periodic signal shape itself that the fault detectability is further increased.

Depinning and heterogeneous dynamics of colloidal crystal layers under shear flow

NASA Astrophysics Data System (ADS)

Gerloff, Sascha; Klapp, Sabine H. L.

2016-12-01

Using Brownian dynamics (BD) simulations and an analytical approach we investigate the shear-induced, nonequilibrium dynamics of dense colloidal suspensions confined to a narrow slit-pore. Focusing on situations where the colloids arrange in well-defined layers with solidlike in-plane structure, the confined films display complex, nonlinear behavior such as collective depinning and local transport via density excitations. These phenomena are reminiscent of colloidal monolayers driven over a periodic substrate potential. In order to deepen this connection, we present an effective model that maps the dynamics of the shear-driven colloidal layers to the motion of a single particle driven over an effective substrate potential. This model allows us to estimate the critical shear rate of the depinning transition based on the equilibrium configuration, revealing the impact of important parameters, such as the slit-pore width and the interaction strength. We then turn to heterogeneous systems where a layer of small colloids is sheared with respect to bottom layers of large particles. For these incommensurate systems we find that the particle transport is dominated by density excitations resembling the so-called "kink" solutions of the Frenkel-Kontorova (FK) model. In contrast to the FK model, however, the corresponding "antikinks" do not move.

Tensegrity and motor-driven effective interactions in a model cytoskeleton

NASA Astrophysics Data System (ADS)

Wang, Shenshen; Wolynes, Peter G.

2012-04-01

Actomyosin networks are major structural components of the cell. They provide mechanical integrity and allow dynamic remodeling of eukaryotic cells, self-organizing into the diverse patterns essential for development. We provide a theoretical framework to investigate the intricate interplay between local force generation, network connectivity, and collective action of molecular motors. This framework is capable of accommodating both regular and heterogeneous pattern formation, arrested coarsening and macroscopic contraction in a unified manner. We model the actomyosin system as a motorized cat's cradle consisting of a crosslinked network of nonlinear elastic filaments subjected to spatially anti-correlated motor kicks acting on motorized (fibril) crosslinks. The phase diagram suggests there can be arrested phase separation which provides a natural explanation for the aggregation and coalescence of actomyosin condensates. Simulation studies confirm the theoretical picture that a nonequilibrium many-body system driven by correlated motor kicks can behave as if it were at an effective equilibrium, but with modified interactions that account for the correlation of the motor driven motions of the actively bonded nodes. Regular aster patterns are observed both in Brownian dynamics simulations at effective equilibrium and in the complete stochastic simulations. The results show that large-scale contraction requires correlated kicking.

Chaotic He-Ne laser

NASA Astrophysics Data System (ADS)

Kuusela, Tom A.

2017-09-01

A He-Ne laser is an example of a class A laser, which can be described by a single nonlinear differential equation of the complex electric field. This laser system has only one degree of freedom and is thus inherently stable. A He-Ne laser can be driven to the chaotic condition when a large fraction of the output beam is injected back to the laser. In practice, this can be done simply by adding an external mirror. In this situation, the laser system has infinite degrees of freedom and therefore it can have a chaotic attractor. We show the fundamental laser equations and perform elementary stability analysis. In experiments, the laser intensity variations are measured by a simple photodiode circuit. The laser output intensity time series is studied using nonlinear analysis tools which can be found freely on the internet. The results show that the laser system with feedback has an attractor of a reasonably high dimension and that the maximal Lyapunov exponent is positive, which is clear evidence of chaotic behaviour. The experimental setup and analysis steps are so simple that the studies can even be implemented in the undergraduate physics laboratory.

Adaptive estimation of nonlinear parameters of a nonholonomic spherical robot using a modified fuzzy-based speed gradient algorithm

NASA Astrophysics Data System (ADS)

Roozegar, Mehdi; Mahjoob, Mohammad J.; Ayati, Moosa

2017-05-01

This paper deals with adaptive estimation of the unknown parameters and states of a pendulum-driven spherical robot (PDSR), which is a nonlinear in parameters (NLP) chaotic system with parametric uncertainties. Firstly, the mathematical model of the robot is deduced by applying the Newton-Euler methodology for a system of rigid bodies. Then, based on the speed gradient (SG) algorithm, the states and unknown parameters of the robot are estimated online for different step length gains and initial conditions. The estimated parameters are updated adaptively according to the error between estimated and true state values. Since the errors of the estimated states and parameters as well as the convergence rates depend significantly on the value of step length gain, this gain should be chosen optimally. Hence, a heuristic fuzzy logic controller is employed to adjust the gain adaptively. Simulation results indicate that the proposed approach is highly encouraging for identification of this NLP chaotic system even if the initial conditions change and the uncertainties increase; therefore, it is reliable to be implemented on a real robot.

Multiple secondary islands formation in nonlinear evolution of double tearing mode simulations

NASA Astrophysics Data System (ADS)

Guo, W.; Ma, J.; Yu, Z.

2017-03-01

A new numerical code solving the conservative perturbed resistive magnetohydrodynamic (MHD) model is developed. Numerical tests of the ideal Kelvin-Helmholtz instability and the resistive double tearing mode (DTM) show its capability in solving linear and nonlinear MHD instabilities. The nonlinear DTM evolution in 2D geometry is numerically investigated with low guiding field B z 0 , short half-distance y 0 between the equilibrium current sheets, and small resistivity η. The interaction of islands on the two initial current sheets may generate an unstable flow driven current sheet with a high length-to-thickness aspect ratio (α), and multiple secondary islands can form. In general, the length-to-thickness aspect ratio α and the number of secondary islands increase with decreasing guide field B z 0 , decreasing half-distance y 0 , and increasing Lundquist number of the flow driven current sheet S L although the dependence may be non-monotonic. The reconnection rate dependence on S L , B z 0 , and y 0 is also investigated.

On the Origin of Time and the Universe

NASA Astrophysics Data System (ADS)

Jejjala, Vishnu; Kavic, Michael; Minic, Djordje; Tze, Chia-Hsiung

We present a novel solution to the low entropy and arrow of time puzzles of the initial state of the universe. Our approach derives from the physics of a specific generalization of Matrix theory put forth in earlier work as the basis for a quantum theory of gravity. The particular dynamical state space of this theory, the infinite-dimensional analogue of the Fubini-Study metric over a complex nonlinear Grassmannian, has recently been studied by Michor and Mumford. The geodesic distance between any two points on this space is zero. Here we show that this mathematical result translates to a description of a hot, zero entropy state and an arrow of time after the Big Bang. This is modeled as a far from equilibrium, large fluctuation driven, "freezing by heating" metastable ordered phase transition of a nonlinear dissipative dynamical system.

Electrohydraulic Synchronizing Servo Control of a Robotic Arm

NASA Astrophysics Data System (ADS)

Li, S.; Ruan, J.; Pei, X.; Yu, Z. Q.; Zhu, F. M.

2006-10-01

The large robotic arm is usually driven by the electrodraulic synchronizing control system. The electrodraulic synchronizing system is designed with the digital valve to eliminate the effect of the nonlinearities, such as hysteresis, saturation, definite resolution. The working principle of the electrodraulic synchronizing control system is introduced and the mathematical model is established through construction of flow rate equation, continuity equation, force equilibrium equation, etc. To obtain the high accuracy, the PID control is introduced in the system. Simulation analysis shows that the dynamic performance of the synchronizing system is good, and its steady state error is very small. To validate the results, the experimental set-up of the synchronizing system is built. The experiment makes it clear that the control system has high accuracy. The synchronizing system can be applied widely in practice.

Traffic and related self-driven many-particle systems

NASA Astrophysics Data System (ADS)

Helbing, Dirk

2001-10-01

Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Non-Linear Dynamics of Saturn's Rings

NASA Astrophysics Data System (ADS)

Esposito, L. W.

2016-12-01

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. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push 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. 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. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology 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).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 explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries determines the power law index, using results of numerical simulations in the tidal environment. Aggregates can explain many dynamic aspects of the rings and can renew rings by shielding and recycling the material within them, depending on how long the mass is sequestered. We can ask: Are Saturn's rings a chaotic non-linear driven system?

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 of the rings and can renew rings by shielding and recycling the material within them, depending on how long the mass is sequestered. We can ask: Are Saturn’s rings a chaotic non-linear driven system?

A numerical investigation on the influence of engine shape and mixing processes on wave engine performance

NASA Astrophysics Data System (ADS)

Erickson, Robert R.

Wave engines are a class of unsteady, air-breathing propulsion devices that use an intermittent combustion process to generate thrust. The inherently simple mechanical design of the wave engine allows for a relatively low cost per unit propulsion system, yet unsatisfactory overall performance has severely limited the development of commercially successful wave engines. The primary objective of this investigation was to develop a more detailed physical understanding of the influence of gas dynamic nonlinearities, unsteady combustion processes, and engine shape on overall wave engine performance. Within this study, several numerical models were developed and applied to wave engines and related applications. The first portion of this investigation examined the influence of duct shape on driven oscillations in acoustic compression devices, which represent a simplified physical system closely related in several ways to the wave engine. A numerical model based on an application of the Galerkin method was developed to simulate large amplitude, one-dimensional acoustic waves driven in closed ducts. Results from this portion of the investigation showed that gas-dynamic nonlinearities significantly influence the properties of driven oscillations by transferring acoustic energy from the fundamental driven mode into higher harmonic modes. The second portion of this investigation presented and analyzed results from a numerical model of wave engine dynamics based on the quasi one-dimensional conservation equations in addition to separate sub-models for mixing and heat release. This model was then used to perform parametric studies of the characteristics of mixing and engine shape. The objectives of these studies were to determine the influence of mixing characteristics and engine shape on overall wave engine performance and to develop insight into the physical processes controlling overall performance trends. Results from this model showed that wave engine performance was strongly dependent on the coupling between the unsteady heat release that drives oscillations in the engine and the characteristics that determine the acoustic properties of the engine such as engine shape and mean property gradients. Simulation results showed that average thrust generation decreased dramatically when the natural acoustic mode frequencies of the engine and the frequency content of the unsteady heat release were not aligned.

Hybrid simulation of fishbone instabilities in the EAST tokamak

NASA Astrophysics Data System (ADS)

Shen, Wei; Fu, Guoyong; Wang, Feng; Xu, Liqing; Li, Guoqiang; Liu, Chengyue; EAST Team

2017-10-01

Hybrid simulations with the global kinetic- MHD code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in EAST experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. The results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a BAE with much higher frequency. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. For the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution. This work is supported by the National Natural Science Foundation of China under Grant Nos. 11605245 and 11505022, and the CASHIPS Director's Fund under Grant No. YZJJ201510, and the Department of Energy Scientific Discovery through Advanced Computing (SciDAC) under Grant No. DE-AC02-09CH11466.

Seismic Retrofit for Electric Power Systems

DOE PAGES

Romero, Natalia; Nozick, Linda K.; Dobson, Ian; ...

2015-05-01

Our paper develops a two-stage stochastic program and solution procedure to optimize the selection of seismic retrofit strategies to increase the resilience of electric power systems against earthquake hazards. The model explicitly considers the range of earthquake events that are possible and, for each, an approximation of the distribution of damage experienced. Furthermore, this is important because electric power systems are spatially distributed and so their performance is driven by the distribution of component damage. We also test this solution procedure against the nonlinear integer solver in LINGO 13 and apply the formulation and solution strategy to the Eastern Interconnection,more » where seismic hazard stems from the New Madrid seismic zone.« less

Nonlinear optimal control policies for buoyancy-driven flows in the built environment

NASA Astrophysics Data System (ADS)

Nabi, Saleh; Grover, Piyush; Caulfield, Colm

2017-11-01

We consider optimal control of turbulent buoyancy-driven flows in the built environment, focusing on a model test case of displacement ventilation with a time-varying heat source. The flow is modeled using the unsteady Reynolds-averaged equations (URANS). To understand the stratification dynamics better, we derive a low-order partial-mixing ODE model extending the buoyancy-driven emptying filling box problem to the case of where both the heat source and the (controlled) inlet flow are time-varying. In the limit of a single step-change in the heat source strength, our model is consistent with that of Bower et al.. Our model considers the dynamics of both `filling' and `intruding' added layers due to a time-varying source and inlet flow. A nonlinear direct-adjoint-looping optimal control formulation yields time-varying values of temperature and velocity of the inlet flow that lead to `optimal' time-averaged temperature relative to appropriate objective functionals in a region of interest.

Large Spin-Wave Bullet in a Ferrimagnetic Insulator Driven by the Spin Hall Effect

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

Jungfleisch, M. B.; Zhang, W.; Sklenar, J.

2016-02-01

Due to its transverse nature, spin Hall effects (SHE) provide the possibility to excite and detect spin currents and magnetization dynamics even in magnetic insulators. Magnetic insulators are outstanding materials for the investigation of nonlinear phenomena and for novel low power spintronics applications because of their extremely low Gilbert damping. Here, we report on the direct imaging of electrically driven spin-torque ferromagnetic resonance (ST-FMR) in the ferrimagnetic insulator Y 3Fe 5O 12 based on the excitation and detection by SHEs. The driven spin dynamics in Y 3Fe 5O 12 is directly imaged by spatially-resolved microfocused Brillouin light scattering (BLS) spectroscopy.more » Previously, ST-FMR experiments assumed a uniform precession across the sample, which is not valid in our measurements. A strong spin-wave localization in the center of the sample is observed indicating the formation of a nonlinear, self-localized spin-wave `bullet'.« less

Nonlinear Decay of Alfvén Waves Driven by Interplaying Two- and Three-dimensional Nonlinear Interactions

NASA Astrophysics Data System (ADS)

Zhao, J. S.; Voitenko, Y.; De Keyser, J.; Wu, D. J.

2018-04-01

We study the decay of Alfvén waves in the solar wind, accounting for the joint operation of two-dimensional (2D) scalar and three-dimensional (3D) vector nonlinear interactions between Alfvén and slow waves. These interactions have previously been studied separately in long- and short-wavelength limits where they lead to 2D scalar and 3D vector decays, correspondingly. The joined action of the scalar and vector interactions shifts the transition between 2D and 3D decays to significantly smaller wavenumbers than was predicted by Zhao et al. who compared separate scalar and vector decays. In application to the broadband Alfvén waves in the solar wind, this means that the vector nonlinear coupling dominates in the extended wavenumber range 5 × 10‑4 ≲ ρ i k 0⊥ ≲ 1, where the decay is essentially 3D and nonlocal, generating product Alfvén and slow waves around the ion gyroscale. Here ρ i is the ion gyroradius, and k 0⊥ is the pump Alfvén wavenumber. It appears that, except for the smallest wavenumbers at and below {ρ }i{k}0\\perp ∼ {10}-4 in Channel I, the nonlinear decay of magnetohydrodynamic Alfvén waves propagating from the Sun is nonlocal and cannot generate counter-propagating Alfvén waves with similar scales needed for the turbulent cascade. Evaluation of the nonlinear frequency shift shows that product Alfvén waves can still be approximately described as normal Alfvénic eigenmodes. On the contrary, nonlinearly driven slow waves deviate considerably from normal modes and are therefore difficult to identify on the basis of their phase velocities and/or polarization.

"Big Bang" as a result result of the curvature-driven first-order phase transition in the early cold Universe

NASA Astrophysics Data System (ADS)

Pashitskii, E. A.; Pentegov, V. I.

We suggest that the "Big Bang" may be a result of the first-order phase transition driven by changing scalar curvature of the 4D space-time in the expanding cold Universe, filled with nonlinear scalar field φ and neutral matter with equation of state p = vɛ (where p and ɛ are pressure and energy density of matter). We consider a Lagrangian for scalar field in curved space-time with nonlinearity φ, which along with the quadratic term -ΣR|φ|2 (where Σ is interaction constant and R is scalar curvature) contains a term ΣR(φ +φ+) linear in φ. Due to this term the condition for the extrema of the potential energy of the scalar field is given by a cubic equation. Provided v > 1/3 the scalar curvature R = [κ(3v-1)ɛ - 4Γ (where κ and Γ are Einstein's gravitational and cosmological constants) decreases along with decreasing " in the process of the Universe's expansion, and at some critical value Rc < 0 a first-order phase transition occurs, driven by an "external field" parameter proportional to R. Given certain conditions the critical radius of the early Universe at the point of the first-order phase transition may reach arbitrary large values, so this scenario of unrestricted "inflation" of the Universe may be called "hyperinflation". Beyond the point of phase transition the system is rolling down into the potential minimum releasing the potential energy of scalar field with subsequent powerful heating of the Universe playing the role of "Big Bang".

Species coexistence through simultaneous fluctuation-dependent mechanisms.

PubMed

Letten, Andrew D; Dhami, Manpreet K; Ke, Po-Ju; Fukami, Tadashi

2018-06-12

Understanding the origins and maintenance of biodiversity remains one of biology's grand challenges. From theory and observational evidence, we know that variability in environmental conditions through time is likely critical to the coexistence of competing species. Nevertheless, experimental tests of fluctuation-driven coexistence are rare and have typically focused on just one of two potential mechanisms, the temporal storage effect, to the neglect of the theoretically equally plausible mechanism known as relative nonlinearity of competition. We combined experiments and simulations in a system of nectar yeasts to quantify the relative contribution of the two mechanisms to coexistence. Resource competition models parameterized from single-species assays predicted the outcomes of mixed-culture competition experiments with 83% accuracy. Model simulations revealed that both mechanisms have measurable effects on coexistence and that relative nonlinearity can be equal or greater in magnitude to the temporal storage effect. In addition, we show that their effect on coexistence can be both antagonistic and complementary. These results falsify the common assumption that relative nonlinearity is of negligible importance, and in doing so reveal the importance of testing coexistence mechanisms in combination.

3-D zebrafish embryo image filtering by nonlinear partial differential equations.

PubMed

Rizzi, Barbara; Campana, Matteo; Zanella, Cecilia; Melani, Camilo; Cunderlik, Robert; Krivá, Zuzana; Bourgine, Paul; Mikula, Karol; Peyriéras, Nadine; Sarti, Alessandro

2007-01-01

We discuss application of nonlinear PDE based methods to filtering of 3-D confocal images of embryogenesis. We focus on the mean curvature driven and the regularized Perona-Malik equations, where standard as well as newly suggested edge detectors are used. After presenting the related mathematical models, the practical results are given and discussed by visual inspection and quantitatively using the mean Hausdorff distance.

Master stability functions reveal diffusion-driven pattern formation in networks

NASA Astrophysics Data System (ADS)

Brechtel, Andreas; Gramlich, Philipp; Ritterskamp, Daniel; Drossel, Barbara; Gross, Thilo

2018-03-01

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

Order and disorder in traffic and self-driven many-particle systems

NASA Astrophysics Data System (ADS)

Helbing, Dirk

2002-07-01

During the last decade, physicists have identified various spatio-temporal patterns of motion in vehicle and pedestrian traffic. Moreover, by applying and extending methods from statistical physics and non-linear dynamics, these have been successfully explained by means of self-driven many-particle models. Some of the questions now understood are the following: Why are vehicles sometimes stopped by so-called "phantom traffic jams," although they all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction of the traffic volume cause a lasting traffic jam? What is the origin of fluctuations in traffic systems and which consequences do they have? Why do pedestrians moving in opposite directions normally organize in lanes, while nervous crowds are "freezing by heating?" Why do panicking pedestrians produce dangerous deadlocks?

Machine Learning-based discovery of closures for reduced models of dynamical systems

NASA Astrophysics Data System (ADS)

Pan, Shaowu; Duraisamy, Karthik

2017-11-01

Despite the successful application of machine learning (ML) in fields such as image processing and speech recognition, only a few attempts has been made toward employing ML to represent the dynamics of complex physical systems. Previous attempts mostly focus on parameter calibration or data-driven augmentation of existing models. In this work we present a ML framework to discover closure terms in reduced models of dynamical systems and provide insights into potential problems associated with data-driven modeling. Based on exact closure models for linear system, we propose a general linear closure framework from viewpoint of optimization. The framework is based on trapezoidal approximation of convolution term. Hyperparameters that need to be determined include temporal length of memory effect, number of sampling points, and dimensions of hidden states. To circumvent the explicit specification of memory effect, a general framework inspired from neural networks is also proposed. We conduct both a priori and posteriori evaluations of the resulting model on a number of non-linear dynamical systems. This work was supported in part by AFOSR under the project ``LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

Front fingering and complex dynamics driven by the interaction of buoyancy and diffusive instabilities.

PubMed

D'Hernoncourt, J; Merkin, J H; De Wit, A

2007-09-01

Traveling fronts can become transversally unstable either because of a diffusive instability arising when the key variables diffuse at sufficiently different rates or because of a buoyancy-driven Rayleigh-Taylor mechanism when the density jump across the front is statically unfavorable. The interaction between such diffusive and buoyancy instabilities of fronts is analyzed theoretically for a simple model system. Linear stability analysis and nonlinear simulations show that their interplay changes considerably the stability properties with regard to the pure Rayleigh-Taylor or diffusive instabilities of fronts. In particular, an instability scenario can arise which triggers convection around statically stable fronts as a result of differential diffusion. Moreover, spatiotemporal chaos can be observed when both buoyancy and diffusive effects cooperate to destabilize the front. Experimental conditions to test our predictions are suggested.

Convection- and SASI-driven flows in parametrized models of core-collapse supernova explosions

DOE PAGES

Endeve, E.; Cardall, C. Y.; Budiardja, R. D.; ...

2016-01-21

We present initial results from three-dimensional simulations of parametrized core-collapse supernova (CCSN) explosions obtained with our astrophysical simulation code General Astrophysical Simulation System (GenASIS). We are interested in nonlinear flows resulting from neutrino-driven convection and the standing accretion shock instability (SASI) in the CCSN environment prior to and during the explosion. By varying parameters in our model that control neutrino heating and shock dissociation, our simulations result in convection-dominated and SASI-dominated evolution. We describe this initial set of simulation results in some detail. To characterize the turbulent flows in the simulations, we compute and compare velocity power spectra from convection-dominatedmore » and SASI-dominated (both non-exploding and exploding) models. When compared to SASI-dominated models, convection-dominated models exhibit significantly more power on small spatial scales.« less

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

PubMed Central

Nitzan, Sarah H.; Zega, Valentina; Li, Mo; Ahn, Chae H.; Corigliano, Alberto; Kenny, Thomas W.; Horsley, David A.

2015-01-01

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes. PMID:25762243

Ultrasensitive detection enabled by nonlinear magnetization of nanomagnetic labels.

PubMed

Nikitin, M P; Orlov, A V; Sokolov, I L; Minakov, A A; Nikitin, P I; Ding, J; Bader, S D; Rozhkova, E A; Novosad, V

2018-06-21

Geometrically confined magnetic particles due to their unique response to external magnetic fields find a variety of applications, including magnetic guidance, heat and drug delivery, magneto-mechanical actuation, and contrast enhancement. Highly sensitive detection and imaging techniques based on the nonlinear properties of nanomagnets were recently proposed as innovative strong-translational potential methods applicable in complex, often opaque, biological systems. Here we report on the significant enhancement of the detection capability using optical-lithography-defined, ferromagnetic iron-nickel alloy disk-shaped particles. We show that an irreversible transition between strongly non-collinear (vortex) and single domain states, driven by an alternating magnetic field, translates into a nonlinear magnetic response that enables ultrasensitive detection of these particles. The record sensitivity of ∼3.5 × 10-9 emu, which is equivalent to ∼39 pg of magnetic material is demonstrated at room temperature for arrays of patterned disks. We also show that unbound disks suspended in the aqueous buffer can be successfully detected and quantified in real-time when administered into a live animal allowing for tracing of their biodistribution. The use of nanoscale ferromagnetic particles with engineered nonlinear properties opens prospects for further enhancing the sensitivity, scalability, and tunability of noise-free magnetic tag detection in high-background environments for various applications spanning from biosensing and medical imaging to anti-counterfeiting technologies.

Coherent Structures in Magnetic Confinement Systems

NASA Astrophysics Data System (ADS)

Horton, W.

2006-04-01

Coherent structures are long-lived, nonlinear localized solutions of the selfconsistient plasma-electromagnetic field equations. They contain appreciable energy density and control various transport and magnetic reconnection processes in plasmas. These structures are self-binding from the nonlinearity balancing, or overcoming, the wave dispersion of energy in smaller amplitude structures. The structures evolve out of the nonlinear interactions in various instabilities or external driving fields. The theoretical basis for these structures are reviewed giving examples from various plasma instabilities and their reduced descriptions from the appropriate partial differential equations. A classic example from drift waves is the formation of monopole, dipole and tripolar vortex structures which have been created in both laboratory and simulation experiments. For vortices, the long life-time and nonlinear interactions of the structures can be understood with conservation laws of angular momentum given by the vorticity field associated with dynamics. Other morphologies include mushrooms, Kelvin-Helmholtz vorticity roll-up, streamers and blobs. We show simulation movies of various examples drawn from ETG modes in NSTX, H-mode like shear flow layers in LAPD and the vortices measured with soft x-ray tomography in the GAMMA 10 tandem mirror. Coherent current-sheet structures form in driven magnetic reconnection layers and control the rate of transformation of magnetic energy to flow and thermal energy.

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

PubMed

Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A

2015-03-12

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

Impact of Seawater Nonlinearities on Nordic Seas Circulation

NASA Astrophysics Data System (ADS)

Helber, R. W.; Wallcraft, A. J.; Shriver, J. F.

2017-12-01

The Nordic Seas (Greenland, Iceland, and Norwegian Seas) form an ocean basin important for Arctic-mid-latitude climate linkages. Cold fresh water from the Arctic Ocean and warm salty water from the North Atlantic Ocean meet in the Nordic Seas, where a delicate balance between temperature and salinity variability results in deep water formation. Seawater non-linearities are stronger at low temperatures and salinities making high-latitude oceans highly subject to thermbaricity and cabbeling. This presentation highlights and quantifies the impact of seawater non-linearities on the Nordic Seas circulation. We use two layered ocean circulation models, the Hybrid Coordinate Ocean Model (HYOCM) and the Modular Ocean Model version 6 (MOM6), that enable accurate representation of processes along and across density or neutral density surfaces. Different equations-of-state and vertical coordinates are evaluated to clarify the impact of seawater non-linearities. Present Navy systems, however, do not capture some features in the Nrodic Seas vertical structure. For example, observations from the Greenland Sea reveal a subsurface temperature maximum that deepens from approximately 1500 m during 1998 to 1800 m during 2005. We demonstrate that in terms of density, salinity is the largest source of error in Nordic Seas Navy forecasts, regional scale models can represent mesoscale features driven by thermobaricity, vertical coordinates are a critical issue in Nordic Sea circulation modeling.

Spin-current emission governed by nonlinear spin dynamics.

PubMed

Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya

2015-10-16

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.

Spin-current emission governed by nonlinear spin dynamics

PubMed Central

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

Ocean circulation and climate during the past 120,000 years

NASA Astrophysics Data System (ADS)

Rahmstorf, Stefan

2002-09-01

Oceans cover more than two-thirds of our blue planet. The waters move in a global circulation system, driven by subtle density differences and transporting huge amounts of heat. Ocean circulation is thus an active and highly nonlinear player in the global climate game. Increasingly clear evidence implicates ocean circulation in abrupt and dramatic climate shifts, such as sudden temperature changes in Greenland on the order of 5-10 °C and massive surges of icebergs into the North Atlantic Ocean - events that have occurred repeatedly during the last glacial cycle.

Stochastic wave-function unravelling of the generalized Lindblad equation

NASA Astrophysics Data System (ADS)

Semin, V.; Semina, I.; Petruccione, F.

2017-12-01

We investigate generalized non-Markovian stochastic Schrödinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010), 10.1063/1.3514539]. We show that these SSEs can be translated in a nonlinear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath, and the results of the simulations are compared with the exact solution of the generalized master equation.

Propagation of electromagnetic soliton in a spin polarized current driven weak ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Gopi, D.

2017-11-01

We investigate the nonlinear spin dynamics of a spin polarized current driven anisotropic ferromagnetic nanowire with Dzyaloshinskii-Moriya interaction (DMI) under the influence of electromagnetic wave (EMW) propagating along the axis of the nanowire. The magnetization dynamics and electromagnetic wave propagation in the ferromagnetic nanowire with weak anti-symmetric interaction is governed by a coupled vector Landau-Lifshitz-Gilbert and Maxwell's equations. These coupled nonlinear vector equations are recasted into the extended derivative nonlinear Schrödinger (EDNLS) equation in the framework of reductive perturbation method. As it is well known, the modulational instability is a precursor for the emergence of localized envelope structures of various kinds, we compute the instability criteria for the weak ferromagnetic nanowire through linear stability analysis. Further, we invoke the homogeneous balance method to construct kink and anti-solitonic like electromagnetic (EM) soliton profiles for the EDNLS equation. We also explore the appreciable effect of the anti-symmetric weak interaction on the magnetization components of the propagating EM soliton. We find that the combination of spin-polarized current and the anti-symmetric DMI have a profound effect on the propagating EMW in a weak ferromagnetic nanowire. Thus, the anti-symmetric DMI in a spin polarized current driven ferromagnetic nanowire supports the lossless propagation of EM solitons, which may have potential applications in magnetic data storage devices.

Data-driven Climate Modeling and Prediction

NASA Astrophysics Data System (ADS)

Kondrashov, D. A.; Chekroun, M.

2016-12-01

Global climate models aim to simulate a broad range of spatio-temporal scales of climate variability with state vector having many millions of degrees of freedom. On the other hand, while detailed weather prediction out to a few days requires high numerical resolution, it is fairly clear that a major fraction of large-scale climate variability can be predicted in a much lower-dimensional phase space. Low-dimensional models can simulate and predict this fraction of climate variability, provided they are able to account for linear and nonlinear interactions between the modes representing large scales of climate dynamics, as well as their interactions with a much larger number of modes representing fast and small scales. This presentation will highlight several new applications by Multilayered Stochastic Modeling (MSM) [Kondrashov, Chekroun and Ghil, 2015] framework that has abundantly proven its efficiency in the modeling and real-time forecasting of various climate phenomena. MSM is a data-driven inverse modeling technique that aims to obtain a low-order nonlinear system of prognostic equations driven by stochastic forcing, and estimates both the dynamical operator and the properties of the driving noise from multivariate time series of observations or a high-end model's simulation. MSM leads to a system of stochastic differential equations (SDEs) involving hidden (auxiliary) variables of fast-small scales ranked by layers, which interact with the macroscopic (observed) variables of large-slow scales to model the dynamics of the latter, and thus convey memory effects. New MSM climate applications focus on development of computationally efficient low-order models by using data-adaptive decomposition methods that convey memory effects by time-embedding techniques, such as Multichannel Singular Spectrum Analysis (M-SSA) [Ghil et al. 2002] and recently developed Data-Adaptive Harmonic (DAH) decomposition method [Chekroun and Kondrashov, 2016]. In particular, new results by DAH-MSM modeling and prediction of Arctic Sea Ice, as well as decadal predictions of near-surface Earth temperatures will be presented.

On the Hilbert-Huang Transform Data Processing System Development

NASA Technical Reports Server (NTRS)

Kizhner, Semion; Flatley, Thomas P.; Huang, Norden E.; Cornwell, Evette; Smith, Darell

2003-01-01

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

Quantum annealing with all-to-all connected nonlinear oscillators

PubMed Central

Puri, Shruti; Andersen, Christian Kraglund; Grimsmo, Arne L.; Blais, Alexandre

2017-01-01

Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine. PMID:28593952

Antibunching and unconventional photon blockade with Gaussian squeezed states

NASA Astrophysics Data System (ADS)

Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.

2014-12-01

Photon antibunching is a quantum phenomenon typically observed in strongly nonlinear systems where photon blockade suppresses the probability of detecting two photons at the same time. Antibunching has also been reported with Gaussian states, where optimized amplitude squeezing yields classically forbidden values of the intensity correlation, g(2 )(0 ) <1 . As a consequence, observation of antibunching is not necessarily a signature of photon-photon interactions. To clarify the significance of the intensity correlations, we derive a sufficient condition for deducing whether a field is non-Gaussian based on a g(2 )(0 ) measurement. We then show that the Gaussian antibunching obtained with a degenerate parametric amplifier is close to the ideal case reached using dissipative squeezing protocols. We finally shed light on the so-called unconventional photon blockade effect predicted in a driven two-cavity setup with surprisingly weak Kerr nonlinearities, stressing that it is a particular realization of optimized Gaussian amplitude squeezing.

Expanding the role of reactive transport models in critical zone processes

USGS Publications Warehouse

Li, Li; Maher, Kate; Navarre-Sitchler, Alexis; Druhan, Jennifer; Meile, Christof; Lawrence, Corey; Moore, Joel; Perdrial, Julia; Sullivan, Pamela; Thompson, Aaron; Jin, Lixin; Bolton, Edward W.; Brantley, Susan L.; Dietrich, William E.; Mayer, K. Ulrich; Steefel, Carl; Valocchi, Albert J.; Zachara, John M.; Kocar, Benjamin D.; McIntosh, Jennifer; Tutolo, Benjamin M.; Kumar, Mukesh; Sonnenthal, Eric; Bao, Chen; Beisman, Joe

2017-01-01

Models test our understanding of processes and can reach beyond the spatial and temporal scales of measurements. Multi-component Reactive Transport Models (RTMs), initially developed more than three decades ago, have been used extensively to explore the interactions of geothermal, hydrologic, geochemical, and geobiological processes in subsurface systems. Driven by extensive data sets now available from intensive measurement efforts, there is a pressing need to couple RTMs with other community models to explore non-linear interactions among the atmosphere, hydrosphere, biosphere, and geosphere. Here we briefly review the history of RTM development, summarize the current state of RTM approaches, and identify new research directions, opportunities, and infrastructure needs to broaden the use of RTMs. In particular, we envision the expanded use of RTMs in advancing process understanding in the Critical Zone, the veneer of the Earth that extends from the top of vegetation to the bottom of groundwater. We argue that, although parsimonious models are essential at larger scales, process-based models offer tools to explore the highly nonlinear coupling that characterizes natural systems. We present seven testable hypotheses that emphasize the unique capabilities of process-based RTMs for (1) elucidating chemical weathering and its physical and biogeochemical drivers; (2) understanding the interactions among roots, micro-organisms, carbon, water, and minerals in the rhizosphere; (3) assessing the effects of heterogeneity across spatial and temporal scales; and (4) integrating the vast quantity of novel data, including “omics” data (genomics, transcriptomics, proteomics, metabolomics), elemental concentration and speciation data, and isotope data into our understanding of complex earth surface systems. With strong support from data-driven sciences, we are now in an exciting era where integration of RTM framework into other community models will facilitate process understanding across disciplines and across scales.

Real-Time Global Nonlinear Aerodynamic Modeling for Learn-To-Fly

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2016-01-01

Flight testing and modeling techniques were developed to accurately identify global nonlinear aerodynamic models for aircraft in real time. The techniques were developed and demonstrated during flight testing of a remotely-piloted subscale propeller-driven fixed-wing aircraft using flight test maneuvers designed to simulate a Learn-To-Fly scenario. Prediction testing was used to evaluate the quality of the global models identified in real time. The real-time global nonlinear aerodynamic modeling algorithm will be integrated and further tested with learning adaptive control and guidance for NASA Learn-To-Fly concept flight demonstrations.

The Alfvénic nature of energy transfer mediation in localized, strongly nonlinear Alfvén wavepacket collisions

NASA Astrophysics Data System (ADS)

Verniero, J. L.; Howes, G. G.

2018-02-01

In space and astrophysical plasmas, violent events or instabilities inject energy into turbulent motions at large scales. Nonlinear interactions among the turbulent fluctuations drive a cascade of energy to small perpendicular scales at which the energy is ultimately converted into plasma heat. Previous work with the incompressible magnetohydrodynamic (MHD) equations has shown that this turbulent energy cascade is driven by the nonlinear interaction between counterpropagating Alfvén waves - also known as Alfvén wave collisions. Direct numerical simulations of weakly collisional plasma turbulence enables deeper insight into the nature of the nonlinear interactions underlying the turbulent cascade of energy. In this paper, we directly compare four cases: both periodic and localized Alfvén wave collisions in the weakly and strongly nonlinear limits. Our results reveal that in the more realistic case of localized Alfvén wave collisions (rather than the periodic case), all nonlinearly generated fluctuations are Alfvén waves, which mediates nonlinear energy transfer to smaller perpendicular scales.

Data-driven Modelling for decision making under uncertainty

NASA Astrophysics Data System (ADS)

Angria S, Layla; Dwi Sari, Yunita; Zarlis, Muhammad; Tulus

2018-01-01

The rise of the issues with the uncertainty of decision making has become a very warm conversation in operation research. Many models have been presented, one of which is with data-driven modelling (DDM). The purpose of this paper is to extract and recognize patterns in data, and find the best model in decision-making problem under uncertainty by using data-driven modeling approach with linear programming, linear and nonlinear differential equation, bayesian approach. Model criteria tested to determine the smallest error, and it will be the best model that can be used.

Quantum refrigerators and the third law of thermodynamics.

PubMed

Levy, Amikam; Alicki, Robert; Kosloff, Ronnie

2012-06-01

The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process dT(t)/dt∼-T^{ζ} when approaching absolute zero, T→0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled two-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat-driven refrigerator (absorption refrigerator) is compared to a power-driven refrigerator. When optimized, both cases lead to the same exponent ζ, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined.

Internal transport barrier triggered by non-linear lower hybrid wave deposition under condition of beam-driven toroidal rotation

NASA Astrophysics Data System (ADS)

Gao, Q. D.; Budny, R. V.

2015-03-01

By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (Vϕ) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.

Linear and nonlinear properties of the ULF waves driven by ring-beam distribution functions

NASA Technical Reports Server (NTRS)

Killen, K.; Omidi, N.; Krauss-Varban, D.; Karimabadi, H.

1995-01-01

The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam velocity distributions in great detail. The effects of both proton and oxygen ring-beams are considered. The study of instabilities excited by a proton ring-beam is relevant to the region upstream of the Earth's bow shock, whereas the oxygen ring-beam corresponds to cometary ions picked up by the solar wind. Linear theory has shown that for a ring-beam, four instabilities are found, one on the nonresonant mode, one on the Alfven mode, and two along the magnetosonic/whistler branch. The relative growth rate of these instabilities is a sensitive function of parameters. Although one of the magnetosonic instabilities has maximum growth along the magnetic field, the other has maximum growth in oblique directions. We have studied the competition of these instabilities in the nonlinear regime using 2-D simulations. As in the linear limit, the nonlinear results are a function of beam density and distribution function. By performing the simulations as both initial value and driven systems, we have found that the outcome of the simulations can vary, suggesting that the latter type simulations is needed to address the observations. A general conclusion of the simulation results is that field-aligned beams do not result in the formation of shocklets, whereas ring-beam distributions can.

Melnikov's criteria, parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation.

PubMed

Kwuimy, C A Kitio; Nataraj, C; Litak, G

2011-12-01

We consider the problems of chaos and parametric control in nonlinear systems under an asymmetric potential subjected to a multiscale type excitation. The lower bound line for horseshoes chaos is analyzed using the Melnikov's criterion for a transition to permanent or transient nonperiodic motions, complement by the fractal or regular shape of the basin of attraction. Numerical simulations based on the basins of attraction, bifurcation diagrams, Poincaré sections, Lyapunov exponents, and phase portraits are used to show how stationary dissipative chaos occurs in the system. Our attention is focussed on the effects of the asymmetric potential term and the driven frequency. It is shown that the threshold amplitude ∣γ(c)∣ of the excitation decreases for small values of the driven frequency ω and increases for large values of ω. This threshold value decreases with the asymmetric parameter α and becomes constant for sufficiently large values of α. γ(c) has its maximum value for asymmetric load in comparison with the symmetric load. Finally, we apply the Melnikov theorem to the controlled system to explore the gain control parameter dependencies.

Ballistic induced pumping of hypersonic heat current in DNA nano wire

NASA Astrophysics Data System (ADS)

Behnia, Sohrab; Panahinia, Robabe

2016-12-01

Heat shuttling properties of DNA nano-wire driven by an external force against the spontaneous heat current direction in non-zero temperature bias (non averaged) have been studied. We examined the valid region of driving amplitude and frequency to have pumping state in terms of temperature bias and the system size. It was shown that DNA could act as a high efficiency thermal pump in the hypersonic region. Amplitude-dependent resonance frequencies of DNA indicating intrinsic base pair internal vibrations have been detected. Nonlinearity implies that by increasing the driven amplitude new vibration modes are detected. To verify the results, an analytical parallel investigation based on multifractal concept has been done. By using the geometric properties of the strange attractor of the system, the threshold value to transition to the pumping state for given external amplitude has been identified. It was shown that the system undergoes a phase transition in sliding point to the pumping state. Fractal dimension demonstrates that the ballistic transport is responsible for energy pumping in the system. In the forbidden band gap, DNA could transmit the energy by exceeding the threshold amplitude. Despite of success in energy pumping, in this framework, DNA could not act as a real cooler.

Model identification and vision-based H∞ position control of 6-DoF cable-driven parallel robots

NASA Astrophysics Data System (ADS)

Chellal, R.; Cuvillon, L.; Laroche, E.

2017-04-01

This paper presents methodologies for the identification and control of 6-degrees of freedom (6-DoF) cable-driven parallel robots (CDPRs). First a two-step identification methodology is proposed to accurately estimate the kinematic parameters independently and prior to the dynamic parameters of a physics-based model of CDPRs. Second, an original control scheme is developed, including a vision-based position controller tuned with the H∞ methodology and a cable tension distribution algorithm. The position is controlled in the operational space, making use of the end-effector pose measured by a motion-tracking system. A four-block H∞ design scheme with adjusted weighting filters ensures good trajectory tracking and disturbance rejection properties for the CDPR system, which is a nonlinear-coupled MIMO system with constrained states. The tension management algorithm generates control signals that maintain the cables under feasible tensions. The paper makes an extensive review of the available methods and presents an extension of one of them. The presented methodologies are evaluated by simulations and experimentally on a redundant 6-DoF INCA 6D CDPR with eight cables, equipped with a motion-tracking system.

Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators.

PubMed

Goto, Hayato; Lin, Zhirong; Nakamura, Yasunobu

2018-05-08

A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.

Nonlinear ARMA models for the D(st) index and their physical interpretation

NASA Technical Reports Server (NTRS)

Vassiliadis, D.; Klimas, A. J.; Baker, D. N.

1996-01-01

Time series models successfully reproduce or predict geomagnetic activity indices from solar wind parameters. A method is presented that converts a type of nonlinear filter, the nonlinear Autoregressive Moving Average (ARMA) model to the nonlinear damped oscillator physical model. The oscillator parameters, the growth and decay, the oscillation frequencies and the coupling strength to the input are derived from the filter coefficients. Mathematical methods are derived to obtain unique and consistent filter coefficients while keeping the prediction error low. These methods are applied to an oscillator model for the Dst geomagnetic index driven by the solar wind input. A data set is examined in two ways: the model parameters are calculated as averages over short time intervals, and a nonlinear ARMA model is calculated and the model parameters are derived as a function of the phase space.

Punchets: nonlinear transport in Hamiltonian pump-ratchet hybrids

NASA Astrophysics Data System (ADS)

Dittrich, Thomas; Medina Sánchez, Nicolás

2018-02-01

‘Punchets’ are hybrids between ratchets and pumps, combining a spatially periodic static potential, typically asymmetric under space inversion, with a local driving that breaks time-reversal invariance, and are intended to model metal or semiconductor surfaces irradiated by a collimated laser beam. Their crucial feature is irregular driven scattering between asymptotic regions supporting periodic (as opposed to free) motion. With all binary spatio-temporal symmetries broken, scattering in punchets typically generates directed currents. We here study the underlying nonlinear transport mechanisms, from chaotic scattering to the parameter dependence of the currents, in three types of Hamiltonian models, (i) with spatially periodic potentials where only in the driven scattering region, spatial and temporal symmetries are broken, and (ii), spatially asymmetric (ratchet) potentials with a driving that only breaks time-reversal invariance. As more realistic models of laser-irradiated surfaces, we consider (iii), a driving in the form of a running wave confined to a compact region by a static envelope. In this case, the induced current can even run against the direction of wave propagation, drastically evidencing its nonlinear nature. Quantizing punchets is indicated as a viable research perspective.

Generation of Raman lasers from nitrogen molecular ions driven by ultraintense laser fields

NASA Astrophysics Data System (ADS)

Yao, Jinping; Chu, Wei; Liu, Zhaoxiang; Xu, Bo; Chen, Jinming; Cheng, Ya

2018-03-01

Atmospheric lasing has aroused much interest in the past few years. The ‘air–laser’ opens promising potential for remote chemical sensing of trace gases with high sensitivity and specificity. At present, several approaches have been successfully implemented for generating highly coherent laser beams in atmospheric condition, including both amplified-spontaneous emission, and narrow-bandwidth stimulated emission in the forward direction in the presence of self-generated or externally injected seed pulses. Here, we report on generation of multiple-wavelength Raman lasers from nitrogen molecular ions ({{{N}}}2+), driven by intense mid-infrared laser fields. Intuitively, the approach appears problematic for the small nonlinear susceptibility of {{{N}}}2+ ions, whereas the efficiency of Raman laser can be significantly promoted in near-resonant condition. More surprisingly, a Raman laser consisting of a supercontinuum spanning from ∼310 to ∼392 nm has been observed resulting from a series near-resonant nonlinear processes including four-wave mixing, stimulated Raman scattering and cross phase modulation. To date, extreme nonlinear optics in molecular ions remains largely unexplored, which provides an alternative means for air–laser-based remote sensing applications.

Generalized Synchronization in AN Array of Nonlinear Dynamic Systems with Applications to Chaotic Cnn

NASA Astrophysics Data System (ADS)

Min, Lequan; Chen, Guanrong

This paper establishes some generalized synchronization (GS) theorems for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). These constructive theorems provide general representations of GS in CDADS and CCADS. Based on these theorems, one can design GS-driven CDADS and CCADS via appropriate (invertible) transformations. As applications, the results are applied to autonomous and nonautonomous coupled Chen cellular neural network (CNN) CDADS and CCADS, discrete bidirectional Lorenz CNN CDADS, nonautonomous bidirectional Chua CNN CCADS, and nonautonomously bidirectional Chen CNN CDADS and CCADS, respectively. Extensive numerical simulations show their complex dynamic behaviors. These theorems provide new means for understanding the GS phenomena of complex discrete and continuously differentiable networks.

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

NASA Astrophysics Data System (ADS)

Yang, Peng-fei; Fang, Yang-wang; Wu, You-li; Zhang, Dan-xu; Xu, Yang

2018-01-01

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein-Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.

Effect of nonlinear friction on the motion of an object on solid surface induced by external vibration

NASA Astrophysics Data System (ADS)

Gooh Pattader, Partho Sarathi

There are enumerable examples of natural processes which fall in the class of non-equilibrium stochastic dynamics. In the literature it is prescribed that such a process can be described completely using transition probability that satisfy the Fokker Planck equation. The analytical solutions of transition probability density function are difficult to obtain and are available for linear systems along with few first order nonlinear systems. We studied such nonlinear stochastic systems and tried to identify the important parameters associated with the dynamics and energy dissipative mechanism using statistical tools. We present experimental study of macroscopic systems driven away far from equilibrium with an applied bias and external mechanical noise. This includes sliding of small solid object, gliding of a liquid drop or a rolling of a rigid sphere. We demonstrated that the displacement statistics are non-Gaussian at short observation time, but they tend towards a Gaussian behavior at long time scale. We also found that, the drift velocity increases sub-linearly, but the diffusivity increases super-linearly with the strength of the noise. These observations reflect that the underlying non-linear friction controls the stochastic dynamics in each of these cases. We established a new statistical approach to determine the underlying friction law and identified the operating range of linear and nonlinear friction regime. In all these experiments source of the noise and the origin of the energy dissipation mechanism (i.e. friction) are decoupled. Naturally question arises whether the stochastic dynamics of these athermal systems are amenable to Einstein's Fluctuation dissipation theorem which is valid strictly for a closed thermodynamic system. We addressed these issues by comparing Einstein's ratio of Diffusivity and mobility which are measurable quantities in our experimental systems. As all our experimental systems exhibit substantial negative fluctuations of displacement that diminishes with observation time scale, we used another approach of integrated fluctuation theorem to identify athermal temperature of the system by characterizing a persistence time of negative fluctuations in terms of the measurable quantity. Specific experiments have also been designed to study the crossing of a small object over a physical barrier assisted by an external noise and a bias force. These results mimic the classical Arrhenius behavior from which another effective temperature may be deduced. All these studies confer that the nonlinear system does not possess any unique temperature. Detachment of a solid sphere as well as a liquid drop from a structured rubber surface during subcritical motion in presence of external noise was examined in the light of Arrhenius' activated rate equation. Drift velocity of small drops of water-glycerin solution behaves nonlinearly with viscosity which is reminiscence of Kramers' turn over theory of activated rate. In a designed experiment of barrier crossing of liquid drops we satisfactorily verified the Kramers' formalism of activated rate at the low friction limit.

Application of Petri Nets in Bone Remodeling

PubMed Central

Li, Lingxi; Yokota, Hiroki

2009-01-01

Understanding a mechanism of bone remodeling is a challenging task for both life scientists and model builders, since this highly interactive and nonlinear process can seldom be grasped by simple intuition. A set of ordinary differential equations (ODEs) have been built for simulating bone formation as well as bone resorption. Although solving ODEs numerically can provide useful predictions for dynamical behaviors in a continuous time frame, an actual bone remodeling process in living tissues is driven by discrete events of molecular and cellular interactions. Thus, an event-driven tool such as Petri nets (PNs), which may dynamically and graphically mimic individual molecular collisions or cellular interactions, seems to augment the existing ODE-based systems analysis. Here, we applied PNs to expand the ODE-based approach and examined discrete, dynamical behaviors of key regulatory molecules and bone cells. PNs have been used in many engineering areas, but their application to biological systems needs to be explored. Our PN model was based on 8 ODEs that described an osteoprotegerin linked molecular pathway consisting of 4 types of bone cells. The models allowed us to conduct both qualitative and quantitative evaluations and evaluate homeostatic equilibrium states. The results support that application of PN models assists understanding of an event-driven bone remodeling mechanism using PN-specific procedures such as places, transitions, and firings. PMID:19838338

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 complex dynamics. We found that complex dynamics occur even with a constant food supply maintained at the upstream boundary of the biofilm. Results will be presented along with a description of the model, including 3 coupled partial differential equations and examples of the localized and propagating nonlinear dynamics inherent in the system. Contrary to a common opinion that chaos in many mechanical systems is a type of instability, appearing when energy is added, we hypothesize, based on the results of our modeling, that chaos in biofilm dynamics and other microbial ecosystems is driven by a competitive decrease in the food supply (i.e., chemical energy). We also hypothesize that, somewhat paradoxically, this, in turn, may support a long-term system stability that could cause bioclogging in porous media.

Prediction of gravity-driven fingering in porous media

NASA Astrophysics Data System (ADS)

Beljadid, Abdelaziz; Cueto-Felgueroso, Luis; Juanes, Ruben

2017-11-01

Gravity-driven displacement of one fluid by another in porous media is often subject to a hydrodynamic instability, whereby fluid invasion takes the form of preferential flow paths-examples include secondary oil migration in reservoir rocks, and infiltration of rainfall water in dry soil. Here, we develop a continuum model of gravity-driven two-phase flow in porous media within the phase-field framework (Cueto-Felgueroso and Juanes, 2008). We employ pore-scale physics arguments to design the free energy of the system, which notably includes a nonlinear formulation of the high-order (square-gradient) term based on equilibrium considerations in the direction orthogonal to gravity. This nonlocal term plays the role of a macroscopic surface tension, which exhibits a strong link with capillary pressure. Our theoretical analysis shows that the proposed model enforces that fluid saturations are bounded between 0 and 1 by construction, therefore overcoming a serious limitation of previous models. Our numerical simulations show that the proposed model also resolves the pinning behavior at the base of the infiltration front, and the asymmetric behavior of the fingers at material interfaces observed experimentally.

Non-linearity of geocentre motion and its impact on the origin of the terrestrial reference frame

NASA Astrophysics Data System (ADS)

Dong, Danan; Qu, Weijing; Fang, Peng; Peng, Dongju

2014-08-01

The terrestrial reference frame is a cornerstone for modern geodesy and its applications for a wide range of Earth sciences. The underlying assumption for establishing a terrestrial reference frame is that the motion of the solid Earth's figure centre relative to the mass centre of the Earth system on a multidecadal timescale is linear. However, past international terrestrial reference frames (ITRFs) showed unexpected accelerated motion in their translation parameters. Based on this underlying assumption, the inconsistency of relative origin motions of the ITRFs has been attributed to data reduction imperfection. We investigated the impact of surface mass loading from atmosphere, ocean, snow, soil moisture, ice sheet, glacier and sea level from 1983 to 2008 on the geocentre variations. The resultant geocentre time-series display notable trend acceleration from 1998 onward, in particular in the z-component. This effect is primarily driven by the hydrological mass redistribution in the continents (soil moisture, snow, ice sheet and glacier). The acceleration is statistically significant at the 99 per cent confidence level as determined using the Mann-Kendall test, and it is highly correlated with the satellite laser ranging determined translation series. Our study, based on independent geophysical and hydrological models, demonstrates that, in addition to systematic errors from analysis procedures, the observed non-linearity of the Earth-system behaviour at interannual timescales is physically driven and is able to explain 42 per cent of the disparity between the origins of ITRF2000 and ITRF2005, as well as the high level of consistency between the ITRF2005 and ITRF2008 origins.

A Data-Driven Assessment of the Sensitivity of Global Ecosystems to Climate Anomalies

NASA Astrophysics Data System (ADS)

Miralles, D. G.; Papagiannopoulou, C.; Demuzere, M.; Decubber, S.; Waegeman, W.; Verhoest, N.; Dorigo, W.

2017-12-01

Vegetation is a central player in the climate system, constraining atmospheric conditions through a series of feedbacks. This fundamental role highlights the importance of understanding regional drivers of ecological sensitivity and the response of vegetation to climatic changes. While nutrient availability and short-term disturbances can be crucial for vegetation at various spatiotemporal scales, natural vegetation dynamics are overall driven by climate. At monthly scales, the interactions between vegetation and climate become complex: some vegetation types react preferentially to specific climatic changes, with different levels of intensity, resilience and lagged response. For our current Earth System Models (ESMs) being able to capture this complexity is crucial but extremely challenging. This adds uncertainty to our projections of future climate and the fate of global ecosystems. Here, following a Granger causality framework based on a non-linear random forest predictive model, we exploit the current wealth of satellite data records to uncover the main climatic drivers of monthly vegetation variability globally. Results based on three decades of satellite data indicate that water availability is the most dominant factor driving vegetation in over 60% of the vegetated land. This overall dependency of ecosystems on water availability is larger than previously reported, partly owed to the ability of our machine-learning framework to disentangle the co-linearites between climatic drivers, and to quantify non-linear impacts of climate on vegetation. Our observation-based results are then used to benchmark ESMs on their representation of vegetation sensitivity to climate and climatic extremes. Our findings indicate that the sensitivity of vegetation to climatic anomalies is ill-reproduced by some widely-used ESMs.

Benchmarking of Advanced Control Strategies for a Simulated Hydroelectric System

NASA Astrophysics Data System (ADS)

Finotti, S.; Simani, S.; Alvisi, S.; Venturini, M.

2017-01-01

This paper analyses and develops the design of advanced control strategies for a typical hydroelectric plant during unsteady conditions, performed in the Matlab and Simulink environments. The hydraulic system consists of a high water head and a long penstock with upstream and downstream surge tanks, and is equipped with a Francis turbine. The nonlinear characteristics of hydraulic turbine and the inelastic water hammer effects were considered to calculate and simulate the hydraulic transients. With reference to the control solutions addressed in this work, the proposed methodologies rely on data-driven and model-based approaches applied to the system under monitoring. Extensive simulations and comparisons serve to determine the best solution for the development of the most effective, robust and reliable control tool when applied to the considered hydraulic system.

Coupling induced logical stochastic resonance

NASA Astrophysics Data System (ADS)

Aravind, Manaoj; Murali, K.; Sinha, Sudeshna

2018-06-01

In this work we will demonstrate the following result: when we have two coupled bistable sub-systems, each driven separately by an external logic input signal, the coupled system yields outputs that can be mapped to specific logic gate operations in a robust manner, in an optimal window of noise. So, though the individual systems receive only one logic input each, due to the interplay of coupling, nonlinearity and noise, they cooperatively respond to give a logic output that is a function of both inputs. Thus the emergent collective response of the system, due to the inherent coupling, in the presence of a noise floor, maps consistently to that of logic outputs of the two inputs, a phenomenon we term coupling induced Logical Stochastic Resonance. Lastly, we demonstrate our idea in proof of principle circuit experiments.

A new design of robust H∞ sliding mode control for uncertain stochastic T-S fuzzy time-delay systems.

PubMed

Gao, Qing; Feng, Gang; Xi, Zhiyu; Wang, Yong; Qiu, Jianbin

2014-09-01

In this paper, a novel dynamic sliding mode control scheme is proposed for a class of uncertain stochastic nonlinear time-delay systems represented by Takagi-Sugeno fuzzy models. The key advantage of the proposed scheme is that two very restrictive assumptions in most existing sliding mode control approaches for stochastic fuzzy systems have been removed. It is shown that the closed-loop control system trajectories can be driven onto the sliding surface in finite time almost certainly. It is also shown that the stochastic stability of the resulting sliding motion can be guaranteed in terms of linear matrix inequalities; moreover, the sliding-mode controller can be obtained simultaneously. Simulation results illustrating the advantages and effectiveness of the proposed approaches are also provided.

Chaotic non-planar vibrations of the thin elastica. Part I: Experimental observation of planar instability

NASA Astrophysics Data System (ADS)

Cusumano, J. P.; Moon, F. C.

1995-01-01

In this two-part paper, the results of an investigation into the non-linear dynamics of a flexible cantilevered rod (the elastica) with a thin rectangular cross-section are presented. An experimental examination of the dynamics of the elastica over a broad parameter range forms the core of Part I. In Part II, the experimental work is related to a theoretical study of the mechanics of the elastica, and the study of a two-degree-of-freedom model obtained by modal projection. The experimental system used in this investigation is a rod with clamped-free boundary conditions, forced by sinusoidally displacing the clamped end. Planar periodic motions of the driven elastica are shown to lose stability at distinct resonant wedges, and the resulting motions are shown in general to be non-planar, chaotic, bending-torsion oscillations. Non-planar motions in all resonances exhibit energy cascading and dynamic two-well phenomena, and a family of asymmetric, bending-torsion non-linear modes is discovered. Correlation dimension calculations are used to estimate the number of active degrees of freedom in the system.

Lie-algebraic Approach to Dynamics of Closed Quantum Systems and Quantum-to-Classical Correspondence

NASA Astrophysics Data System (ADS)

Galitski, Victor

2012-02-01

I will briefly review our recent work on a Lie-algebraic approach to various non-equilibrium quantum-mechanical problems, which has been motivated by continuous experimental advances in the field of cold atoms. First, I will discuss non-equilibrium driven dynamics of a generic closed quantum system. It will be emphasized that mathematically a non-equilibrium Hamiltonian represents a trajectory in a Lie algebra, while the evolution operator is a trajectory in a Lie group generated by the underlying algebra via exponentiation. This turns out to be a constructive statement that establishes, in particular, the fact that classical and quantum unitary evolutions are two sides of the same coin determined uniquely by the same dynamic generators in the group. An equation for these generators - dubbed dual Schr"odinger-Bloch equation - will be derived and analyzed for a few of specific examples. This non-linear equation allows one to construct new exact non-linear solutions to quantum-dynamical systems. An experimentally-relevant example of a family of exact solutions to the many-body Landau-Zener problem will be presented. One practical application of the latter result includes dynamical means to optimize molecular production rate following a quench across the Feshbach resonance.

Characteristics of solitary waves in a relativistic degenerate ion beam driven magneto plasma

NASA Astrophysics Data System (ADS)

Deka, Manoj Kr.; Dev, Apul N.; Misra, Amar P.; Adhikary, Nirab C.

2018-01-01

The nonlinear propagation of a small amplitude ion acoustic solitary wave in a relativistic degenerate magneto plasma in the presence of an ion beam is investigated in detail. The nonlinear equations describing the evolution of a solitary wave in the presence of relativistic non-degenerate magnetized positive ions and ion beams including magnetized degenerate relativistic electrons are derived in terms of Zakharov-Kuznetsov (Z-K) equation for such plasma systems. The ion beams which are a ubiquitous ingredient in such plasma systems are found to have a decisive role in the propagation of a solitary wave in such a highly dense plasma system. The conditions of a wave, propagating with typical solitonic characteristics, are examined and discussed in detail under suitable conditions of different physical parameters. Both a subsonic and supersonic wave can propagate in such plasmas bearing different characteristics under different physical situations. A detailed analysis of waves propagating in subsonic and/or supersonic regime is carried out. The ion beam concentrations, magnetic field, as well as ion beam streaming velocity are found to play a momentous role on the control of the amplitude and width of small amplitude perturbation in both weakly (or non-relativistic) and relativistic plasmas.

Emergent structure-function relations in emphysema and asthma.

PubMed

Winkler, Tilo; Suki, Béla

2011-01-01

Structure-function relationships in the respiratory system are often a result of the emergence of self-organized patterns or behaviors that are characteristic of certain respiratory diseases. Proper description of such self-organized behavior requires network models that include nonlinear interactions among different parts of the system. This review focuses on 2 models that exhibit self-organized behavior: a network model of the lung parenchyma during the progression of emphysema that is driven by mechanical force-induced breakdown, and an integrative model of bronchoconstriction in asthma that describes interactions among airways within the bronchial tree. Both models suggest that the transition from normal to pathologic states is a nonlinear process that includes a tipping point beyond which interactions among the system components are reinforced by positive feedback, further promoting the progression of pathologic changes. In emphysema, the progressive destruction of tissue is irreversible, while in asthma, it is possible to recover from a severe bronchoconstriction. These concepts may have implications for pulmonary medicine. Specifically, we suggest that structure-function relationships emerging from network behavior across multiple scales should be taken into account when the efficacy of novel treatments or drug therapy is evaluated. Multiscale, computational, network models will play a major role in this endeavor.

Uncertainty Quantification of Non-linear Oscillation Triggering in a Multi-injector Liquid-propellant Rocket Combustion Chamber

NASA Astrophysics Data System (ADS)

Popov, Pavel; Sideris, Athanasios; Sirignano, William

2014-11-01

We examine the non-linear dynamics of the transverse modes of combustion-driven acoustic instability in a liquid-propellant rocket engine. Triggering can occur, whereby small perturbations from mean conditions decay, while larger disturbances grow to a limit-cycle of amplitude that may compare to the mean pressure. For a deterministic perturbation, the system is also deterministic, computed by coupled finite-volume solvers at low computational cost for a single realization. The randomness of the triggering disturbance is captured by treating the injector flow rates, local pressure disturbances, and sudden acceleration of the entire combustion chamber as random variables. The combustor chamber with its many sub-fields resulting from many injector ports may be viewed as a multi-scale complex system wherein the developing acoustic oscillation is the emergent structure. Numerical simulation of the resulting stochastic PDE system is performed using the polynomial chaos expansion method. The overall probability of unstable growth is assessed in different regions of the parameter space. We address, in particular, the seven-injector, rectangular Purdue University experimental combustion chamber. In addition to the novel geometry, new features include disturbances caused by engine acceleration and unsteady thruster nozzle flow.

Dynamic bifurcation and strange nonchaos in a two-frequency parametrically driven nonlinear oscillator

NASA Astrophysics Data System (ADS)

Premraj, D.; Suresh, K.; Palanivel, J.; Thamilmaran, K.

2017-09-01

A periodically forced series LCR circuit with Chua's diode as a nonlinear element exhibits slow passage through Hopf bifurcation. This slow passage leads to a delay in the Hopf bifurcation. The delay in this bifurcation is a unique quantity and it can be predicted using various numerical analysis. We find that when an additional periodic force is added to the system, the delay in bifurcation becomes chaotic which leads to an unpredictability in bifurcation delay. Further, we study the bifurcation of the periodic delay to chaotic delay in the slow passage effect through strange nonchaotic delay. We also report the occurrence of strange nonchaotic dynamics while varying the parameter of the additional force included in the system. We observe that the system exhibits a hitherto unknown dynamical transition to a strange nonchaotic attractor. With the help of Lyapunov exponent, we explain the new transition to strange nonchaotic attractor and its mechanism is studied by making use of rational approximation theory. The birth of SNA has also been confirmed numerically, using Poincaré maps, phase sensitivity exponent, the distribution of finite-time Lyapunov exponents and singular continuous spectrum analysis.

General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles

NASA Astrophysics Data System (ADS)

Navarrete-Benlloch, Carlos; Weiss, Talitha; Walter, Stefan; de Valcárcel, Germán J.

2017-09-01

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its accuracy far from critical points or situations where the nonlinearity reaches the strong coupling regime, has turned it into a widespread technique, being the first method of choice in most works on the subject. However, such a technique finds strong practical and conceptual complications when one tries to apply it to situations in which the classical long-time solution is time dependent, a most prominent example being spontaneous limit-cycle formation. Here, we introduce a linearization scheme adapted to such situations, using the driven Van der Pol oscillator as a test bed for the method, which allows us to compare it with full numerical simulations. On a conceptual level, the scheme relies on the connection between the emergence of limit cycles and the spontaneous breaking of the symmetry under temporal translations. On the practical side, the method keeps the simplicity and linear scaling with the size of the problem (number of modes) characteristic of standard linearization, making it applicable to large (many-body) systems.

Generation of squeezing in a driven many-body system

NASA Astrophysics Data System (ADS)

Hebbe Madhusudhana, Bharath; Boguslawski, Matthew; Anquez, Martin; Robbins, Bryce; Barrios, Maryrose; Hoang, Thai; Chapman, Michael

2016-05-01

In a spin-1 Bose-Einstein condensate, the non-linear spin-dependent collisional interactions can create entanglement and squeezing. Typically, the condensate is initialized at an unstable fixed point of the phase space, and subsequent free evolution under a time-independent Hamiltonian creates the squeezed state. Alternatively, it is possible to generate squeezing by driving the system localized at a stable fixed point. Here, we demonstrate that periodic modulation of the Hamiltonian can generate highly squeezed states. Our measurements show -5 dB of squeezing, limited by the detection, but calculations indicate that a theoretical potential of -20 dB of squeezing. We discuss the advantages of this method compared with the typical techniques.

Reactive transport modeling of the enhancement of density-driven CO 2 convective mixing in carbonate aquifers and its potential implication on geological carbon sequestration

DOE PAGES

Islam, Akand; Sun, Alexander Y.; Yang, Changbing

2016-04-20

We study the convection and mixing of CO 2 in a brine aquifer, where the spread of dissolved CO 2 is enhanced because of geochemical reactions with the host formations (calcite and dolomite), in addition to the extensively studied, buoyancy-driven mixing. The nonlinear convection is investigated under the assumptions of instantaneous chemical equilibrium, and that the dissipation of carbonate rocks solely depends on flow and transport and chemical speciation depends only on the equilibrium thermodynamics of the chemical system. The extent of convection is quantified in term of the CO 2 saturation volume of the storage formation. Our results suggestmore » that the density increase of resident species causes significant enhancement in CO 2 dissolution, although no significant porosity and permeability alterations are observed. Furthermore, early saturation of the reservoir can have negative impact on CO 2 sequestration.« less

Reactive Transport Modeling of the Enhancement of Density-Driven CO2 Convective Mixing in Carbonate Aquifers and its Potential Implication on Geological Carbon Sequestration.

PubMed

Islam, Akand; Sun, Alexander Y; Yang, Changbing

2016-04-20

We study the convection and mixing of CO2 in a brine aquifer, where the spread of dissolved CO2 is enhanced because of geochemical reactions with the host formations (calcite and dolomite), in addition to the extensively studied, buoyancy-driven mixing. The nonlinear convection is investigated under the assumptions of instantaneous chemical equilibrium, and that the dissipation of carbonate rocks solely depends on flow and transport and chemical speciation depends only on the equilibrium thermodynamics of the chemical system. The extent of convection is quantified in term of the CO2 saturation volume of the storage formation. Our results suggest that the density increase of resident species causes significant enhancement in CO2 dissolution, although no significant porosity and permeability alterations are observed. Early saturation of the reservoir can have negative impact on CO2 sequestration.

Drift wave turbulence simulations in LAPD

NASA Astrophysics Data System (ADS)

Popovich, P.; Umansky, M.; Carter, T. A.; Auerbach, D. W.; Friedman, B.; Schaffner, D.; Vincena, S.

2009-11-01

We present numerical simulations of turbulence in LAPD plasmas using the 3D electromagnetic code BOUT (BOUndary Turbulence). BOUT solves a system of fluid moment equations in a general toroidal equlibrium geometry near the plasma boundary. The underlying assumptions for the validity of the fluid model are well satisfied for drift waves in LAPD plasmas (typical plasma parameters ne˜1x10^12cm-3, Te˜10eV, and B ˜1kG), which makes BOUT a perfect tool for simulating LAPD. We have adapted BOUT for the cylindrical geometry of LAPD and have extended the model to include the background flows required for simulations of recent bias-driven rotation experiments. We have successfully verified the code for several linear instabilities, including resistive drift waves, Kelvin-Helmholtz and rotation-driven interchange. We will discuss first non-linear simulations and quasi-stationary solutions with self-consistent plasma flows and saturated density profiles.

Dynamic Performance of Subway Vehicle with Linear Induction Motor System

NASA Astrophysics Data System (ADS)

Wu, Pingbo; Luo, Ren; Hu, Yan; Zeng, Jing

The light rail vehicle with Linear Induction Motor (LIM) bogie, which is a new type of urban rail traffic tool, has the advantages of low costs, wide applicability, low noise, simple maintenance and better dynamic behavior. This kind of vehicle, supported and guided by the wheel and rail, is not driven by the wheel/rail adhesion force, but driven by the electromagnetic force between LIM and reaction plate. In this paper, three different types of suspensions and their characteristic are discussed with considering the interactions both between wheel and rail and between LIM and reaction plate. A nonlinear mathematical model of the vehicle with LIM bogie is set up by using the software SIMPACK, and the electromechanical model is also set up on Simulink roof. Then the running behavior of the LIM vehicle is simulated, and the influence of suspension on the vehicle dynamic performance is investigated.

Bloch-Siegert shift in an interacting Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Zhang, Jinyi; Eigen, Christoph; Lopes, Raphael; Garratt, Sam; Rousso, David; Smith, Robert P.; Hadzibabic, Zoran; Navon, Nir

2017-04-01

The Bloch-Siegert shift (BSS) is a paradigmatic frequency shift that arises from the nonlinear response of a two-level system (TLS) subjected to strong driving fields. When a TLS is driven by a linearly polarized field, the co-rotating-wave component leads to the famous Rabi oscillations. By contrast the co-rotating-wave component, whose role is usually neglected in a weak driving, leads to a frequency shift of the TLS resonance frequency. This phenomenon is encountered in various areas, from quantum optics to nuclear magnetic resonance.Here, we investigate the BSS in a box-trapped 87 Rb Bose-Einstein condensate (BEC) driven by a strong oscillating magnetic field gradient. By tuning the chemical potential of the gas, we investigate how the BSS evolves from the ideal shift of the two lowest energy levels of a single particle in a box to the unexplored shift of long-wavelength collective excitations of the interacting BEC.

Simultaneously driven linear and nonlinear spatial encoding fields in MRI.

PubMed

Gallichan, Daniel; Cocosco, Chris A; Dewdney, Andrew; Schultz, Gerrit; Welz, Anna; Hennig, Jürgen; Zaitsev, Maxim

2011-03-01

Spatial encoding in MRI is conventionally achieved by the application of switchable linear encoding fields. The general concept of the recently introduced PatLoc (Parallel Imaging Technique using Localized Gradients) encoding is to use nonlinear fields to achieve spatial encoding. Relaxing the requirement that the encoding fields must be linear may lead to improved gradient performance or reduced peripheral nerve stimulation. In this work, a custom-built insert coil capable of generating two independent quadratic encoding fields was driven with high-performance amplifiers within a clinical MR system. In combination with the three linear encoding fields, the combined hardware is capable of independently manipulating five spatial encoding fields. With the linear z-gradient used for slice-selection, there remain four separate channels to encode a 2D-image. To compare trajectories of such multidimensional encoding, the concept of a local k-space is developed. Through simulations, reconstructions using six gradient-encoding strategies were compared, including Cartesian encoding separately or simultaneously on both PatLoc and linear gradients as well as two versions of a radial-based in/out trajectory. Corresponding experiments confirmed that such multidimensional encoding is practically achievable and demonstrated that the new radial-based trajectory offers the PatLoc property of variable spatial resolution while maintaining finite resolution across the entire field-of-view. Copyright © 2010 Wiley-Liss, Inc.

Stochastic Multiscale Analysis and Design of Engine Disks

DTIC Science & Technology

2010-07-28

shown recently to fail when used with data-driven non-linear stochastic input models (KPCA, IsoMap, etc.). Need for scalable exascale computing algorithms Materials Process Design and Control Laboratory Cornell University

The development of neutrino-driven convection in core-collapse supernovae: 2D vs 3D

NASA Astrophysics Data System (ADS)

Kazeroni, R.; Krueger, B. K.; Guilet, J.; Foglizzo, T.

2017-12-01

A toy model is used to study the non-linear conditions for the development of neutrino-driven convection in the post-shock region of core-collapse supernovae. Our numerical simulations show that a buoyant non-linear perturbation is able to trigger self-sustained convection only in cases where convection is not linearly stabilized by advection. Several arguments proposed to interpret the impact of the dimensionality on global core-collapse supernova simulations are discussed in the light of our model. The influence of the numerical resolution is also addressed. In 3D a strong mixing to small scales induces an increase of the neutrino heating efficiency in a runaway process. This phenomenon is absent in 2D and this may indicate that the tridimensional nature of the hydrodynamics could foster explosions.

Flower-Like Squeezing in the Motion of a Laser-Driven Trapped Ion

NASA Astrophysics Data System (ADS)

Nguyen, Ba An; Truong, Minh Duc

We investigate the Nth order amplitude squeezing in the fan-state |ξ2k,f>F which is a linear superposition of the 2k-quantum nonlinear coherent states. Unlike in usual states where an ellipse is the symbol of squeezing, a 4k-winged flower results in the fan state. We first derive the analytical expression of squeezing for arbitrary k, N, f and then study in detail the case of a laser-driven trapped ion characterized by a specific form of the nonlinear function f. We show that the lowest order in which squeezing may appear and the number of directions along which the amplitude may be squeezed depend only on k whereas the precise directions of squeezing are determined also by the other physical parameters involved. Finally, we present a scheme to produce such fan-states.

New Instability Mode in A Driven Granular Gas: Athermal and Thermal Convection

NASA Astrophysics Data System (ADS)

Shukla, Priyanka; Alam, Meheboob

2017-11-01

For a thermally-driven granular gas confined between two plates under gravity, we report a new instability mode which is found to be active at very small values of the heat-loss parameter. We show that the origin of this new mode is tied to the ``thermal'' mode of the well-studied Rayleigh-Benard convection. This is dubbed purely elastic instability since it survives even for perfectly elastic collisions (en = 1). The distinction of this new instability mode from its dissipative/athermal counterpart is clarified for the first time. Furthermore, a weakly nonlinear analysis using Stuart-Landau equation has been carried out for both instability modes, and the underlying bifurcation scenario (supercritical/subcritical) from each mode is elucidated. The resulting linear and nonlinear patterns with respect to inelasticity and gravity are compared.

Nonlinear behavior of solar gravity modes driven by He-3 in the core. I - Bifurcation analysis

NASA Technical Reports Server (NTRS)

Merryfield, William J.; Gough, Douglas; Toomre, Juri

1990-01-01

The nonlinear development of solar gravity modes driven by He-3 burning in the solar core is investigated by means of an idealized dynamical model. Possible outcomes that have been suggested in the literature include the triggering of subcritical direct convection, leading to core mixing, and the saturation of the excitation processes, leading to sustained finite-amplitude oscillations. The present simple model suggests that the latter is the more likely. The limiting amplitude of the oscillations is estimated, ignoring possible resonances with other gravity modes, to be of order 10 km/s at the solar surface. Such oscillations would be easily observable. That large-amplitude gravity modes have not been observed suggests either that these modes are not unstable in the present era or that they are limited to much smaller amplitudes by resonant coupling.

Neuronal nonlinearity explains greater visual spatial resolution for darks than lights.

PubMed

Kremkow, Jens; Jin, Jianzhong; Komban, Stanley J; Wang, Yushi; Lashgari, Reza; Li, Xiaobing; Jansen, Michael; Zaidi, Qasim; Alonso, Jose-Manuel

2014-02-25

Astronomers and physicists noticed centuries ago that visual spatial resolution is higher for dark than light stimuli, but the neuronal mechanisms for this perceptual asymmetry remain unknown. Here we demonstrate that the asymmetry is caused by a neuronal nonlinearity in the early visual pathway. We show that neurons driven by darks (OFF neurons) increase their responses roughly linearly with luminance decrements, independent of the background luminance. However, neurons driven by lights (ON neurons) saturate their responses with small increases in luminance and need bright backgrounds to approach the linearity of OFF neurons. We show that, as a consequence of this difference in linearity, receptive fields are larger in ON than OFF thalamic neurons, and cortical neurons are more strongly driven by darks than lights at low spatial frequencies. This ON/OFF asymmetry in linearity could be demonstrated in the visual cortex of cats, monkeys, and humans and in the cat visual thalamus. Furthermore, in the cat visual thalamus, we show that the neuronal nonlinearity is present at the ON receptive field center of ON-center neurons and ON receptive field surround of OFF-center neurons, suggesting an origin at the level of the photoreceptor. These results demonstrate a fundamental difference in visual processing between ON and OFF channels and reveal a competitive advantage for OFF neurons over ON neurons at low spatial frequencies, which could be important during cortical development when retinal images are blurred by immature optics in infant eyes.

Nonlinear dynamics of nanoscale systems

NASA Astrophysics Data System (ADS)

Hodas, Nathan Oken

This work builds theoretical tools to better understand nanoscale systems, and it ex- plores experimental techniques to probe nanoscale dynamics using nonlinear optical microscopy. In both the theory and experiment, this work harnesses nonlinearity to explore new boundaries in the ongoing attempts to understand the amazing world that is much smaller than we can see. In particular, the first part of this work proves the upper-bounds on the number and quality of oscillations when the sys- tem in question is homogeneously driven and has discrete states, a common way of describing nanoscale motors and chemical systems, although it has application to networked systems in general. The consequences of this limit are explored in the context of chemical clocks and limit cycles. This leads to the analysis of sponta- neous oscillations in GFPmut2, where we postulate that the oscillations must be due to coordinated rearrangement of the beta-barrel. Next, we utilize nonlinear optics to probe the constituent structures of zebrafish muscle. By comparing experimental observations with computational models, we show how second harmonic generation differs from fluorescence for confocal imaging. We use the wavelength dependence of the second harmonic generation conversion efficiency to extract information about the microscopic organization of muscle fibers, using the coherent nature of second ix harmonic generation as an analytical probe. Finally, existing experiments have used a related technique, sum-frequency generation, to directly probe the dynamics of free OH bonds at the water-vapor boundary. Using molecular dynamic simulations of the water surface and by designating surface-sensitive free OH bonds on the water surface, many aspects of the sum-frequency generation measurements were calcu- lated and compared with those inferred from experiment. The method utilizes results available from independent IR and Raman experiments to obtain some of the needed quantities, rather than calculating them ab initio. The results provide insight into the microscopic dynamics at the air-water interface and have useful application in the field of on-water catalysis.

Nonlinear Landau damping in the ionosphere

NASA Technical Reports Server (NTRS)

Kiwamoto, Y.; Benson, R. F.

1978-01-01

A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.

The effect of sheared toroidal rotation on pressure driven magnetic islands in toroidal plasmas

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

Hegna, C. C.

2016-05-15

The impact of sheared toroidal rotation on the evolution of pressure driven magnetic islands in tokamak plasmas is investigated using a resistive magnetohydrodynamics model augmented by a neoclassical Ohm's law. Particular attention is paid to the asymptotic matching data as the Mercier indices are altered in the presence of sheared flow. Analysis of the nonlinear island Grad-Shafranov equation shows that sheared flows tend to amplify the stabilizing pressure/curvature contribution to pressure driven islands in toroidal tokamaks relative to the island bootstrap current contribution. As such, sheared toroidal rotation tends to reduce saturated magnetic island widths.

Theoretical and experimental research on machine tool servo system for ultra-precision position compensation on CNC lathe

NASA Astrophysics Data System (ADS)

Ma, Zhichao; Hu, Leilei; Zhao, Hongwei; Wu, Boda; Peng, Zhenxing; Zhou, Xiaoqin; Zhang, Hongguo; Zhu, Shuai; Xing, Lifeng; Hu, Huang

2010-08-01

The theories and techniques for improving machining accuracy via position control of diamond tool's tip and raising resolution of cutting depth on precise CNC lathes have been extremely focused on. A new piezo-driven ultra-precision machine tool servo system is designed and tested to improve manufacturing accuracy of workpiece. The mathematical model of machine tool servo system is established and the finite element analysis is carried out on parallel plate flexure hinges. The output position of diamond tool's tip driven by the machine tool servo system is tested via a contact capacitive displacement sensor. Proportional, integral, derivative (PID) feedback is also implemented to accommodate and compensate dynamical change owing cutting forces as well as the inherent non-linearity factors of the piezoelectric stack during cutting process. By closed loop feedback controlling strategy, the tracking error is limited to 0.8 μm. Experimental results have shown the proposed machine tool servo system could provide a tool positioning resolution of 12 nm, which is much accurate than the inherent CNC resolution magnitude. The stepped shaft of aluminum specimen with a step increment of cutting depth of 1 μm is tested, and the obtained contour illustrates the displacement command output from controller is accurately and real-time reflected on the machined part.

Quasiperiodicity and Frequency Locking in Electronic Conduction in Germanium.

NASA Astrophysics Data System (ADS)

Gwinn, Elisabeth Gray

1987-09-01

This thesis presents an experimental study of a driven spatio-temporal instability in high-field transport in cooled, p-type Ge. The instability is produced at liquid He temperatures by d.c. voltage bias above the threshold for breakdown by impurity impact ionization, and is associated experimentally with voltage-controlled negative differential conductivity. The instability is coupled to an external oscillator by applying a sinusoidal voltage bias across the Ge sample. The driven instability exhibits frequency locking, quasiperiodicity, and chaos as the frequency and amplitude of the sinusoidal bias are varied. An iterative map of the circle provides a simple model for such a coupled, dissipative nonlinear oscillator system. The transition from quasiperiodicity to chaos in this model system occurs in a universal way; for example, the circle map has a universal, self-similar power spectrum at the onset of chaos with the golden mean winding number. When normalized appropriately, the power spectrum at the onset of chaos in the driven instability in Ge displays the same structure, with good agreement between the amplitudes of the experimental and theoretical spectral peaks. The relevance of universal theory to experiment can also be tested with a spectrum of scaling indices f( alpha), which is used to compare the probability distribution for the circle map at the onset of chaos with the golden mean winding number to the distribution of probability on a Poincare section of the experimental attractor. The procedure used to find f(alpha ) for the driven transport instability overcomes the sensitivity of f(alpha) to noise and to deviation from the critical amplitude. The f( alpha) curve for the driven instability in Ge is found to be in good agreement with the universal circle map result.

Discovery of functional interactions among actin regulators by analysis of image fluctuations in an unperturbed motile cell system.

PubMed

Isogai, Tadamoto; Danuser, Gaudenz

2018-05-26

Cell migration is driven by propulsive forces derived from polymerizing actin that pushes and extends the plasma membrane. The underlying actin network is constantly undergoing adaptation to new mechano-chemical environments and intracellular conditions. As such, mechanisms that regulate actin dynamics inherently contain multiple feedback loops and redundant pathways. Given the highly adaptable nature of such a system, studies that use only perturbation experiments (e.g. knockdowns, overexpression, pharmacological activation/inhibition, etc.) are challenged by the nonlinearity and redundancy of the pathway. In these pathway configurations, perturbation experiments at best describe the function(s) of a molecular component in an adapting (e.g. acutely drug-treated) or fully adapted (e.g. permanent gene silenced) cell system, where the targeted component now resides in a non-native equilibrium. Here, we propose how quantitative live-cell imaging and analysis of constitutive fluctuations of molecular activities can overcome these limitations. We highlight emerging actin filament barbed-end biology as a prime example of a complex, nonlinear molecular process that requires a fluctuation analytic approach, especially in an unperturbed cellular system, to decipher functional interactions of barbed-end regulators, actin polymerization and membrane protrusion.This article is part of the theme issue 'Self-organization in cell biology'. © 2018 The Author(s).

Nonlinear damage identification of breathing cracks in Truss system

NASA Astrophysics Data System (ADS)

Zhao, Jie; DeSmidt, Hans

2014-03-01

The breathing cracks in truss system are detected by Frequency Response Function (FRF) based damage identification method. This method utilizes damage-induced changes of frequency response functions to estimate the severity and location of structural damage. This approach enables the possibility of arbitrary interrogation frequency and multiple inputs/outputs which greatly enrich the dataset for damage identification. The dynamical model of truss system is built using the finite element method and the crack model is based on fracture mechanics. Since the crack is driven by tensional and compressive forces of truss member, only one damage parameter is needed to represent the stiffness reduction of each truss member. Assuming that the crack constantly breathes with the exciting frequency, the linear damage detection algorithm is developed in frequency/time domain using Least Square and Newton Raphson methods. Then, the dynamic response of the truss system with breathing cracks is simulated in the time domain and meanwhile the crack breathing status for each member is determined by the feedback from real-time displacements of member's nodes. Harmonic Fourier Coefficients (HFCs) of dynamical response are computed by processing the data through convolution and moving average filters. Finally, the results show the effectiveness of linear damage detection algorithm in identifying the nonlinear breathing cracks using different combinations of HFCs and sensors.

Uncertainty Quantification of Nonlinear Electrokinetic Response in a Microchannel-Membrane Junction

NASA Astrophysics Data System (ADS)

Alizadeh, Shima; Iaccarino, Gianluca; Mani, Ali

2015-11-01

We have conducted uncertainty quantification (UQ) for electrokinetic transport of ionic species through a hybrid microfluidic system using different probabilistic techniques. The system of interest is an H-configuration consisting of two parallel microchannels that are connected via a nafion junction. This system is commonly used for ion preconcentration and stacking by utilizing a nonlinear response at the channel-nafion junction that leads to deionization shocks. In this work, the nafion medium is modeled as many parallel nano-pores where, the nano-pore diameter, nafion porosity, and surface charge density are independent random variables. We evaluated the resulting uncertainty on the ion concentration fields as well as the deionization shock location. The UQ methods predicted consistent statistics for the outputs and the results revealed that the shock location is weakly sensitive to the nano-pore surface charge and primarily driven by nano-pore diameters. The present study can inform the design of electrokinetic networks with increased robustness to natural manufacturing variability. Applications include water desalination and lab-on-a-chip systems. Shima is a graduate student in the department of Mechanical Engineering at Stanford University. She received her Master's degree from Stanford in 2011. Her research interests include Electrokinetics in porous structures and high performance computing.

Nonlinearly driven harmonics of Alfvén modes

NASA Astrophysics Data System (ADS)

Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.

2014-01-01

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma

NASA Astrophysics Data System (ADS)

Bénisti, Didier

2018-01-01

In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave (EPW) which is assumed to grow from the noise level, and to keep growing at least up to the amplitude when linear theory in no longer valid (while the wave evolution in the nonlinear regime may be arbitrary). The ions are considered as a neutralizing fluid, while the electron response to the wave is derived by matching two different techniques. We make use of a perturbation analysis similar to that introduced to prove the Kolmogorov-Arnold-Moser theorem, up to amplitudes large enough for neo-adiabatic results to be valid. Our theory is applied to the growth and saturation of the beam-plasma instability, and to the three-dimensional propagation of a driven EPW in a non-uniform and non-stationary plasma. For the latter example, we lay a special emphasis on nonlinear collisionless dissipation. We provide an explicit theoretical expression for the nonlinear Landau-like damping rate which, in some instances, is amenable to a simple analytic formula. We also insist on the irreversible evolution of the electron distribution function, which is nonlocal in the wave amplitude and phase velocity. This makes trapping an effective means of dissipation for the electrostatic energy, and also makes the wave dispersion relation nonlocal. Our theory is generalized to allow for stimulated Raman scattering, which we address up to saturation by accounting for plasma inhomogeneity and non-stationarity, nonlinear kinetic effects, and interspeckle coupling.

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Mamatsashvili, G.; Stefani, F.; Guseva, A.; Avila, M.

2018-01-01

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

A three-dimensional dynamical model for channeled lava flow with nonlinear rheology

NASA Astrophysics Data System (ADS)

Filippucci, Marilena; Tallarico, Andrea; Dragoni, Michele

2010-05-01

Recent laboratory studies on the rheology of lava samples from different volcanic areas have highlighted that the apparent viscosity depends on a power of the strain rate. Several authors agree in attributing this dependence to the crystal content of the sample and to temperature. Starting from these results, in this paper we studied the effect of a power law rheology on a gravity-driven lava flow. The equation of motion is nonlinear in the diffusion term, and an analytical solution does not seem to be possible. The finite-volume method has been applied to solve numerically the equation governing the fully developed laminar flow of a power law non-Newtonian fluid in an inclined rectangular channel. The convergence, the stability, and the order of approximation were tested for the Newtonian rheology case, comparing the numerical solution with the available analytical solution. Results indicate that the assumption on the rheology, whether linear or nonlinear, strongly affects the velocity and/or the thickness of the lava channel both for channels with fixed geometry and for channels with constant flow rate. Results on channels with fixed geometry are confirmed by some simulations for real lava channels. Finally, the study of the Reynolds number indicates that gravity-driven lava channel flows are always in laminar regime, except for strongly nonlinear pseudoplastic fluids with low fluid consistency and at high slopes.

Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification

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

Bierwage, Andreas; Shinohara, Kouji

2016-04-15

The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in realistic geometry for a JT-60U tokamak scenario. In Paper I, which was reported in the companion paper, the recently developed orbit-based resonance analysis method was used to track the resonant frequency of fast ions during their nonlinear evolution subject to large magnetic and electric drifts. Here, that method is applied to map the wave-particle power transfer from the canonical guiding center phase space into the frequency-radius plane, where it can be directly compared with the evolution of the fluctuation spectramore » of fast-ion-driven modes. Using this technique, we study the nonlinear dynamics of strongly driven shear Alfvén modes with low toroidal mode numbers n = 1 and n = 3. In the n = 3 case, both chirping and convective amplification can be attributed to the mode following the resonant frequency of the radially displaced particles, i.e., the usual one-dimensional phase locking process. In the n = 1 case, a new chirping mechanism is found, which involves multiple dimensions, namely, wave-particle trapping in the radial direction and phase mixing across velocity coordinates.« less

Non-linear vibrational response of Ge and SiC membranes

NASA Astrophysics Data System (ADS)

Zhou, L. Q.; Colston, G.; Pearce, M. J.; Prince, R. G.; Myronov, M.; Leadley, D. R.; Trushkevych, O.; Edwards, R. S.

2017-07-01

Characterisation of membranes produced for use as micro-electro-mechanical systems using vibrational techniques can give a measure of their behaviour and suitability for operation in different environments. Two membranes are studied here: germanium (Ge) and cubic silicon carbide (3C-SiC) on a silicon (Si) substrate. When driven at higher displacements, the membranes exhibit self-protecting behaviour. The resonant vibration amplitude is limited to a maximum value of around 10 nm, through dissipation of energy via higher harmonic vibrations. This is observed for both materials, despite their different Young's moduli and defect densities.

Human sleep and circadian rhythms: a simple model based on two coupled oscillators.

PubMed

Strogatz, S H

1987-01-01

We propose a model of the human circadian system. The sleep-wake and body temperature rhythms are assumed to be driven by a pair of coupled nonlinear oscillators described by phase variables alone. The novel aspect of the model is that its equations may be solved analytically. Computer simulations are used to test the model against sleep-wake data pooled from 15 studies of subjects living for weeks in unscheduled, time-free environments. On these tests the model performs about as well as the existing models, although its mathematical structure is far simpler.

Chaotic and Bifurcating Nonlinear Systems Driven by Noise with Applications to Laser Dynamics

DTIC Science & Technology

1988-12-30

W. o. leich and M. 0. Scully, Phys. Rev. A . 37, 3010 (1988) and ibid, 1261 (1988), and references therein. 14. A . K. Dhara and S. V . G. Menon, J...Fronzoni, F. Moss, R. Mannella and P. V . E. McClintock. Phys. Rev. A 36. 834 (1987) 35. L. Fronzoni, F. Moss and P. V . E. McClintock, Phys. Rev. A . 36...1492 (1987). 36. V . Altares and G. Nicolis, Phys. Rev. A 37. 3630 (1988) 37. R. Lefever and JI Win. Turner. Phys. Rev. Lett. 56, 1631 (1986) 38. K

Noise-Driven Manifestation of Learning in Mature Neural Networks

NASA Astrophysics Data System (ADS)

Monterola, Christopher; Saloma, Caesar

2002-10-01

We show that the generalization capability of a mature thresholding neural network to process above-threshold disturbances in a noise-free environment is extended to subthreshold disturbances by ambient noise without retraining. The ability to benefit from noise is intrinsic and does not have to be learned separately. Nonlinear dependence of sensitivity with noise strength is significantly narrower than in individual threshold systems. Noise has a minimal effect on network performance for above-threshold signals. We resolve two seemingly contradictory responses of trained networks to noise-their ability to benefit from its presence and their robustness against noisy strong disturbances.

Comparison of Classifiers for Decoding Sensory and Cognitive Information from Prefrontal Neuronal Populations

PubMed Central

Astrand, Elaine; Enel, Pierre; Ibos, Guilhem; Dominey, Peter Ford; Baraduc, Pierre; Ben Hamed, Suliann

2014-01-01

Decoding neuronal information is important in neuroscience, both as a basic means to understand how neuronal activity is related to cerebral function and as a processing stage in driving neuroprosthetic effectors. Here, we compare the readout performance of six commonly used classifiers at decoding two different variables encoded by the spiking activity of the non-human primate frontal eye fields (FEF): the spatial position of a visual cue, and the instructed orientation of the animal's attention. While the first variable is exogenously driven by the environment, the second variable corresponds to the interpretation of the instruction conveyed by the cue; it is endogenously driven and corresponds to the output of internal cognitive operations performed on the visual attributes of the cue. These two variables were decoded using either a regularized optimal linear estimator in its explicit formulation, an optimal linear artificial neural network estimator, a non-linear artificial neural network estimator, a non-linear naïve Bayesian estimator, a non-linear Reservoir recurrent network classifier or a non-linear Support Vector Machine classifier. Our results suggest that endogenous information such as the orientation of attention can be decoded from the FEF with the same accuracy as exogenous visual information. All classifiers did not behave equally in the face of population size and heterogeneity, the available training and testing trials, the subject's behavior and the temporal structure of the variable of interest. In most situations, the regularized optimal linear estimator and the non-linear Support Vector Machine classifiers outperformed the other tested decoders. PMID:24466019

Internal transport barrier triggered by non-linear lower hybrid wave deposition under condition of beam-driven toroidal rotation

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

Gao, Q. D., E-mail: qgao@swip.ac.cn; Budny, R. V.

2015-03-15

By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (T{sub i,e}) and toroidal velocity (V{sub ϕ}) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LHmore » driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.« less

Advances in Statistical and Deterministic Modeling of Wind-Driven Seas

DTIC Science & Technology

2011-09-30

Zakharov. Scales of nonlinear relaxation and balance of wind- driven seas. Geophysical Research Abstracts Vol. 13, EGU2011-2042, 2011. EGU General ...Dyachenko A. “On canonical equation for water waves” at General Assembly 2011 of the European Geosciences Union in Vienna, Austria, 03 – 08 April...scattering and equilibrium ranges in wind- generated waves with application to spectrometry, J. Geoph. Res., 92, 49715029, 1987. [3] Hsiao S.V. and

Adaptive NN Control Using Integral Barrier Lyapunov Functionals for Uncertain Nonlinear Block-Triangular Constraint Systems.

PubMed

Liu, Yan-Jun; Tong, Shaocheng; Chen, C L Philip; Li, Dong-Juan

2017-11-01

A neural network (NN) adaptive control design problem is addressed for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. The considered systems contain uncertainty dynamics and their states are enforced to subject to bounded constraints as well as the couplings among various inputs and outputs are inserted in each subsystem. To stabilize this class of systems, a novel adaptive control strategy is constructively framed by using the backstepping design technique and NNs. The novel integral barrier Lyapunov functionals (BLFs) are employed to overcome the violation of the full state constraints. The proposed strategy can not only guarantee the boundedness of the closed-loop system and the outputs are driven to follow the reference signals, but also can ensure all the states to remain in the predefined compact sets. Moreover, the transformed constraints on the errors are used in the previous BLF, and accordingly it is required to determine clearly the bounds of the virtual controllers. Thus, it can relax the conservative limitations in the traditional BLF-based controls for the full state constraints. This conservatism can be solved in this paper and it is for the first time to control this class of MIMO systems with the full state constraints. The performance of the proposed control strategy can be verified through a simulation example.

Bridging Media with the Help of Players

NASA Astrophysics Data System (ADS)

Nitsche, Michael; Drake, Matthew; Murray, Janet

We suggest harvesting the power of multiplayer design to bridge content across different media platforms and develop player-driven cross-media experiences. This paper first argues to partially replace complex AI systems with multiplayer design strategies to provide the necessary level of flexibility in the content generation for cross-media applications. The second part describes one example project - the Next Generation Play (NGP) project - that illustrates one practical approach of such a player-driven cross-media content generation. NGP allows players to collect virtual items while watching a TV show. These items are re-used in a multiplayer casual game that automatically generates new game worlds based on the various collections of active players joining a game session. While the TV experience is designed for the single big screen, the game executes on multiple mobile phones. Design and technical implementation of the prototype are explained in more detail to clarify how players carry elements of television narratives into a non-linear handheld gaming experience. The system describes a practical way to create casual game adaptations based on players' personal preferences in a multi-user environment.

Characterization of friction in the 3.6m Devasthal optical telescope

NASA Astrophysics Data System (ADS)

Kumar, T. S.; Bastin, Christian; Kumar, Brijesh

2016-07-01

In this paper, we present the work on characterization of friction in the 3.6 m Devasthal optical telescope axes. The telescope azimuth axis is supported on a hydrostatic bearing while the altitude and rotator axes are supported on hydrodynamic bearings. Both altitude and azimuth axes are driven directly by high power BLDC motors and the rotator is driven by BLDC motor via a gearbox. This system is designed by AMOS, Belgium and tuned to achieve a tracking accuracy better than 0.1 arcsec RMS. Friction poses control related problems at such low speeds hence it is important to periodically characterize the behaviour at each axes. Compensation is necessary if the friction behaviour changes over the time and starts dominating the overall system response. For identifying friction each axis of telescope is rotated at different constant speeds and speed versus torque maps are generated. The LuGre model for friction is employed and nonlinear optimization is performed to identify the four static parameters of friction. The behaviour of friction for each axis is presented and the results are discussed.

Enhanced noise at high bias in atomic-scale Au break junctions

PubMed Central

Chen, Ruoyu; Wheeler, Patrick J.; Di Ventra, M.; Natelson, D.

2014-01-01

Heating in nanoscale systems driven out of equilibrium is of fundamental importance, has ramifications for technological applications, and is a challenge to characterize experimentally. Prior experiments using nanoscale junctions have largely focused on heating of ionic degrees of freedom, while heating of the electrons has been mostly neglected. We report measurements in atomic-scale Au break junctions, in which the bias-driven component of the current noise is used as a probe of the electronic distribution. At low biases (<150 mV) the noise is consistent with expectations of shot noise at a fixed electronic temperature. At higher biases, a nonlinear dependence of the noise power is observed. We consider candidate mechanisms for this increase, including flicker noise (due to ionic motion), heating of the bulk electrodes, nonequilibrium electron-phonon effects, and local heating of the electronic distribution impinging on the ballistic junction. We find that flicker noise and bulk heating are quantitatively unlikely to explain the observations. We discuss the implications of these observations for other nanoscale systems, and experimental tests to distinguish vibrational and electron interaction mechanisms for the enhanced noise. PMID:24573177

Multimodal nonlinear nanophotonics (Conference Presentation)

NASA Astrophysics Data System (ADS)

Kivshar, Yuri S.

2017-05-01

Nonlinear nanophotonics is a rapidly developing field of research with many potential applications for the design of nonlinear nanoantennas, light sources, nanolasers, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for the subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. To engineer nonlinear scattering from resonant nanoscale elements, both modal and multipolar control of the nonlinear response are widely exploited for enhancing the near-field interaction and optimizing the radiation directionality. Motivated by the recent progress of all-dielectric nanophotonics, where the electric and magnetic multipolar contributions may become comparable, here we review the advances in the recently emerged field of multipolar nonlinear nanophotonics, starting from earlier relevant studies of metallic and metal-dielectric structures supporting localized plasmonic resonances to then discussing the latest results for all-dielectric nanostructures driven by Mie-type multipolar resonances and optically induced magnetic response. These recent developments suggest intriguing opportunities for a design of nonlinear subwavelength light sources with reconfigurable radiation characteristics and engineering large effective optical nonlinearities at the nanoscale, which could have important implications for novel nonlinear photonic devices operating beyond the diffraction limit.

Identification of minimal parameters for optimal suppression of chaos in dissipative driven systems.

PubMed

Martínez, Pedro J; Euzzor, Stefano; Gallas, Jason A C; Meucci, Riccardo; Chacón, Ricardo

2017-12-21

Taming chaos arising from dissipative non-autonomous nonlinear systems by applying additional harmonic excitations is a reliable and widely used procedure nowadays. But the suppressory effectiveness of generic non-harmonic periodic excitations continues to be a significant challenge both to our theoretical understanding and in practical applications. Here we show how the effectiveness of generic suppressory excitations is optimally enhanced when the impulse transmitted by them (time integral over two consecutive zeros) is judiciously controlled in a not obvious way. Specifically, the effective amplitude of the suppressory excitation is minimal when the impulse transmitted is maximum. Also, by lowering the impulse transmitted one obtains larger regularization areas in the initial phase difference-amplitude control plane, the price to be paid being the requirement of larger amplitudes. These two remarkable features, which constitute our definition of optimum control, are demonstrated experimentally by means of an analog version of a paradigmatic model, and confirmed numerically by simulations of such a damped driven system including the presence of noise. Our theoretical analysis shows that the controlling effect of varying the impulse is due to a subsequent variation of the energy transmitted by the suppressory excitation.

Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach

NASA Astrophysics Data System (ADS)

Neicu, Toni

2002-09-01

An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were observed in a strongly nonlinear, dissipative granular system of vertically vibrated rods. Above a critical packing fraction, moving domains of nearly vertical rods were seen to coexist with horizontal rods. The vertical domains coarsen to form several large vortices, which were driven by the anisotropy and inclination of the rods.

A data-driven prediction method for fast-slow systems

NASA Astrophysics Data System (ADS)

Groth, Andreas; Chekroun, Mickael; Kondrashov, Dmitri; Ghil, Michael

2016-04-01

In this work, we present a prediction method for processes that exhibit a mixture of variability on low and fast scales. The method relies on combining empirical model reduction (EMR) with singular spectrum analysis (SSA). EMR is a data-driven methodology for constructing stochastic low-dimensional models that account for nonlinearity and serial correlation in the estimated noise, while SSA provides a decomposition of the complex dynamics into low-order components that capture spatio-temporal behavior on different time scales. Our study focuses on the data-driven modeling of partial observations from dynamical systems that exhibit power spectra with broad peaks. The main result in this talk is that the combination of SSA pre-filtering with EMR modeling improves, under certain circumstances, the modeling and prediction skill of such a system, as compared to a standard EMR prediction based on raw data. Specifically, it is the separation into "fast" and "slow" temporal scales by the SSA pre-filtering that achieves the improvement. We show, in particular that the resulting EMR-SSA emulators help predict intermittent behavior such as rapid transitions between specific regions of the system's phase space. This capability of the EMR-SSA prediction will be demonstrated on two low-dimensional models: the Rössler system and a Lotka-Volterra model for interspecies competition. In either case, the chaotic dynamics is produced through a Shilnikov-type mechanism and we argue that the latter seems to be an important ingredient for the good prediction skills of EMR-SSA emulators. Shilnikov-type behavior has been shown to arise in various complex geophysical fluid models, such as baroclinic quasi-geostrophic flows in the mid-latitude atmosphere and wind-driven double-gyre ocean circulation models. This pervasiveness of the Shilnikow mechanism of fast-slow transition opens interesting perspectives for the extension of the proposed EMR-SSA approach to more realistic situations.

Model-free adaptive speed control on travelling wave ultrasonic motor

NASA Astrophysics Data System (ADS)

Di, Sisi; Li, Huafeng

2018-01-01

This paper introduced a new data-driven control (DDC) method for the speed control of ultrasonic motor (USM). The model-free adaptive control (MFAC) strategy was presented in terms of its principles, algorithms, and parameter selection. To verify the efficiency of the proposed method, a speed-frequency-time model, which contained all the measurable nonlinearity and uncertainties based on experimental data was established for simulation to mimic the USM operation system. Furthermore, the model was identified using particle swarm optimization (PSO) method. Then, the control of the simulated system using MFAC was evaluated under different expectations in terms of overshoot, rise time and steady-state error. Finally, the MFAC results were compared with that of proportion iteration differentiation (PID) to demonstrate its advantages in controlling general random system.

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

PubMed

Werblin, Frank S

2010-03-01

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

SHEAR-DRIVEN DYNAMO WAVES IN THE FULLY NONLINEAR REGIME

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

Pongkitiwanichakul, P.; Nigro, G.; Cattaneo, F.

2016-07-01

Large-scale dynamo action is well understood when the magnetic Reynolds number ( Rm ) is small, but becomes problematic in the astrophysically relevant large Rm limit since the fluctuations may control the operation of the dynamo, obscuring the large-scale behavior. Recent works by Tobias and Cattaneo demonstrated numerically the existence of large-scale dynamo action in the form of dynamo waves driven by strongly helical turbulence and shear. Their calculations were carried out in the kinematic regime in which the back-reaction of the Lorentz force on the flow is neglected. Here, we have undertaken a systematic extension of their work tomore » the fully nonlinear regime. Helical turbulence and large-scale shear are produced self-consistently by prescribing body forces that, in the kinematic regime, drive flows that resemble the original velocity used by Tobias and Cattaneo. We have found four different solution types in the nonlinear regime for various ratios of the fluctuating velocity to the shear and Reynolds numbers. Some of the solutions are in the form of propagating waves. Some solutions show large-scale helical magnetic structure. Both waves and structures are permanent only when the kinetic helicity is non-zero on average.« less

Knowledge Driven Image Mining with Mixture Density Mercer Kernels

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Oza, Nikunj

2004-01-01

This paper presents a new methodology for automatic knowledge driven image mining based on the theory of Mercer Kernels; which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. In that high dimensional feature space, linear clustering, prediction, and classification algorithms can be applied and the results can be mapped back down to the original image space. Thus, highly nonlinear structure in the image can be recovered through the use of well-known linear mathematics in the feature space. This process has a number of advantages over traditional methods in that it allows for nonlinear interactions to be modelled with only a marginal increase in computational costs. In this paper, we present the theory of Mercer Kernels, describe its use in image mining, discuss a new method to generate Mercer Kernels directly from data, and compare the results with existing algorithms on data from the MODIS (Moderate Resolution Spectral Radiometer) instrument taken over the Arctic region. We also discuss the potential application of these methods on the Intelligent Archive, a NASA initiative for developing a tagged image data warehouse for the Earth Sciences.

Knowledge Driven Image Mining with Mixture Density Mercer Kernals

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Oza, Nikunj

2004-01-01

This paper presents a new methodology for automatic knowledge driven image mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. In that high dimensional feature space, linear clustering, prediction, and classification algorithms can be applied and the results can be mapped back down to the original image space. Thus, highly nonlinear structure in the image can be recovered through the use of well-known linear mathematics in the feature space. This process has a number of advantages over traditional methods in that it allows for nonlinear interactions to be modelled with only a marginal increase in computational costs. In this paper we present the theory of Mercer Kernels; describe its use in image mining, discuss a new method to generate Mercer Kernels directly from data, and compare the results with existing algorithms on data from the MODIS (Moderate Resolution Spectral Radiometer) instrument taken over the Arctic region. We also discuss the potential application of these methods on the Intelligent Archive, a NASA initiative for developing a tagged image data warehouse for the Earth Sciences.

Nonlinear optimal filter technique for analyzing energy depositions in TES sensors driven into saturation

DOE PAGES

Shank, B.; Yen, J. J.; Cabrera, B.; ...

2014-11-04

We present a detailed thermal and electrical model of superconducting transition edge sensors (TESs) connected to quasiparticle (qp) traps, such as the W TESs connected to Al qp traps used for CDMS (Cryogenic Dark Matter Search) Ge and Si detectors. We show that this improved model, together with a straightforward time-domain optimal filter, can be used to analyze pulses well into the nonlinear saturation region and reconstruct absorbed energies with optimal energy resolution.

Nonlinear response of a harmonic diatomic molecule: Algebraic nonperturbative calculation

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

Recamier, Jose; Mochan, W. Luis; Maytorena, Jesus A.

2005-08-15

Even harmonic molecules display a nonlinear behavior when driven by an inhomogeneous field. We calculate the response of single harmonic molecules to a monochromatic time and space dependent electric field E(r,t) of frequency {omega} employing exact algebraic methods. We evaluate the responses at the fundamental frequency {omega} and at successive harmonics 2{omega}, 3{omega}, etc., as a function of the intensity and of the frequency of the field and compare the results with those of first and second order perturbation theory.

Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment

NASA Astrophysics Data System (ADS)

Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

2018-04-01

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment.

PubMed

Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

2018-04-27

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Suppressing electron turbulence and triggering internal transport barriers with reversed magnetic shear in the National Spherical Torus Experimenta)

NASA Astrophysics Data System (ADS)

Peterson, J. L.; Bell, R.; Candy, J.; Guttenfelder, W.; Hammett, G. W.; Kaye, S. M.; LeBlanc, B.; Mikkelsen, D. R.; Smith, D. R.; Yuh, H. Y.

2012-05-01

The National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] can achieve high electron plasma confinement regimes that are super-critically unstable to the electron temperature gradient driven (ETG) instability. These plasmas, dubbed electron internal transport barriers (e-ITBs), occur when the magnetic shear becomes strongly negative. Using the gyrokinetic code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)], the first nonlinear ETG simulations of NSTX e-ITB plasmas reinforce this observation. Local simulations identify a strongly upshifted nonlinear critical gradient for thermal transport that depends on magnetic shear. Global simulations show e-ITB formation can occur when the magnetic shear becomes strongly negative. While the ETG-driven thermal flux at the outer edge of the barrier is large enough to be experimentally relevant, the turbulence cannot propagate past the barrier into the plasma interior.

Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo

NASA Astrophysics Data System (ADS)

Hide, R.

In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions. New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenching by nonlineax effects of current fluctuations in a self-exciting homopolar dynamo with its single Faraday disk driven into rotation with angular speed y(τ) (where τ denotes time) by a steady applied couple. The armature of an electric motor connected in series with the coil of the dynamo is driven into rotation' with angular speed z(τ) by a torque xf (x) due to Lorentz forces associated with the electric current x(τ) in the system (just as certain parts of the spectrum of eddies within the liquid outer core are generated largely by Lorentz forces associated with currents generated by the self-exciting magnetohydrodynamic (MHD) geodynamo). The discovery is based on bifurcation analysis supported by computational studies of the following (mathematically novel) autonomous set of nonlinear ordinary differential equations: dx/dt = x(y - 1) - βzf(x), dy/dt = α(1 - x²) - κy, dz/dt = xf (x) -λz, where f (x) = 1 - ɛ + ɛσx, in cases when the dimensionless parameters (α, β, κ, λ, σ) are all positive and 0 ≤ ɛ ≤ 1. Within those regions of (α, β, κ, λ, σ) parameter space where the applied couple, as measured by α, is strong enough for persistent dynamo action (i.e. x ≠ 0) to occur at all, there are in general extensive regions where x(τ) exhibits large amplitude regular or irregular (chaotic) fluctuations. But these fluctuating régimes shrink in size as increases from zero, and they disappear altogether when ɛ = 1, leaving only steady régimes of dynamo action.

Nonlinear Interactions between Climate and Atmospheric Carbon Dioxide Drivers of Terrestrial and Marine Carbon Cycle Changes

NASA Astrophysics Data System (ADS)

Hoffman, F. M.; Randerson, J. T.; Moore, J. K.; Goulden, M.; Fu, W.; Koven, C.; Swann, A. L. S.; Mahowald, N. M.; Lindsay, K. T.; Munoz, E.

2017-12-01

Quantifying interactions between global biogeochemical cycles and the Earth system is important for predicting future atmospheric composition and informing energy policy. We applied a feedback analysis framework to three sets of Historical (1850-2005), Representative Concentration Pathway 8.5 (2006-2100), and its extension (2101-2300) simulations from the Community Earth System Model version 1.0 (CESM1(BGC)) to quantify drivers of terrestrial and ocean responses of carbon uptake. In the biogeochemically coupled simulation (BGC), the effects of CO2 fertilization and nitrogen deposition influenced marine and terrestrial carbon cycling. In the radiatively coupled simulation (RAD), the effects of rising temperature and circulation changes due to radiative forcing from CO2, other greenhouse gases, and aerosols were the sole drivers of carbon cycle changes. In the third, fully coupled simulation (FC), both the biogeochemical and radiative coupling effects acted simultaneously. We found that climate-carbon sensitivities derived from RAD simulations produced a net ocean carbon storage climate sensitivity that was weaker and a net land carbon storage climate sensitivity that was stronger than those diagnosed from the FC and BGC simulations. For the ocean, this nonlinearity was associated with warming-induced weakening of ocean circulation and mixing that limited exchange of dissolved inorganic carbon between surface and deeper water masses. For the land, this nonlinearity was associated with strong gains in gross primary production in the FC simulation, driven by enhancements in the hydrological cycle and increased nutrient availability. We developed and applied a nonlinearity metric to rank model responses and driver variables. The climate-carbon cycle feedback gain at 2300 was 42% higher when estimated from climate-carbon sensitivities derived from the difference between FC and BGC than when derived from RAD. We re-analyzed other CMIP5 model results to quantify the effects of such nonlinearities on their projected climate-carbon cycle feedback gains.

Electrostatic trapping as a key to the dynamics of plasmas, fluids and other collective systems [review article

NASA Astrophysics Data System (ADS)

Luque, A.; Schamel, H.

2005-08-01

This review article focusses on the phenomenon of collective particle trapping in dilute plasmas and related fluid-like systems. A coherent electrostatic wave or fluctuation, being excited by some mechanism in a plasma, is able to trap collectively charged particles in its potential trough(s) with the ultimate feedback of stabilizing and manipulating the original cause of growth. This phenomenon is well-known from particle simulations of a current-driven two-stream instability and its subsequent quenching by particle trapping. But also the nonlinear Landau damping process resulting in a BGK-like (Bernstein, Green, Kruskal) trapped particle mode sets an example. However, as shown in this report, already a slightly driven plasma has many possibilities of generating trapped particle modes-the mentioned cases representing only two examples-through which it generally becomes nonlinearly unstable. A direct consequence of this feedback of particle trapping is that the macroscopic (dielectric) properties of such a structured plasma may have changed fundamentally such that the relationship to what is known from linear wave theory is lost. We, hence, have to deal with a nonlinear kinetic description which, in case of a collisionless, electrostatic plasma, is the Vlasov-Poisson description. The present report is devoted to a large extent to a 1D Vlasov-Poisson system but also consequences for other physical systems will be derived and mentioned. These and other findings will be developed in some detail culminating in a new paradigm for plasma stability which says: a current-carrying plasma is nonlinearly unstable in a much wider region of parameter space than predicted by linear wave theory with the consequence that the associated turbulence and anomalous transport are triggered much easier than suggested by standard linear wave analysis. Responsible for this new scenario are localized trapped particle modes-more specifically electron and ion holes of zero or negative energy-which are found to be excited well below the threshold of linear instability. In other words, a current-driven plasma shows a much larger sensibility to fluctuations than thought before and described in textbooks. The analysis presented reveals that a plasma, becoming structured by the generation of such modes, resides in a lower free energy state than the one without structures, being therefore in a preferred state that acts as an attractor in the system. Holes having this property will be briefly called negative energy holes (NEHs). For example, zero or negative energy ion holes are found to exist for any drift velocity between electrons and ions and for any temperature ratio. Two independent codes, a Vlasov-code and a PIC-(particle in cell)code, are used to approve this new scenario of instability. Moreover, by adding a Fokker-Planck collision term to the Vlasov-code, holes are shown to resist weak collisions, turn out to be robust and not only found in purely collisionless plasmas and cause an increase of resistivity. A natural outcome of this scenario, therefore, is that whenever free (kinetic) energy is available, holes (and double layers) are necessarily excited, penetrating intermittently the plasma. Satellite measurements, yielding holes and double layers as the most omnipresent structures found in space, provide a typical example. Having investigated classical plasmas this way, we show that many of these innovations can be transferred to other systems, as well. First, we perform a quantum-correction to electron holes by using the Wigner-Moyal description of quantum mechanics in phase-space. As a result we get a weakening of the hole for which tunneling of particles across the separatrix of the unperturbed, deterministic classical hole equilibrium is responsible. The formalism is then used to find a link between hole structures in classical plasmas and envelope solitons in nonlinear optical media. This gives rise to a new approximation method for wave envelope solutions of the nonlinear Schrödinger equation, which utilizes quasi-particle trapping and may be valuable in cases of nonlinearties for which a direct solution is missing. Another important application are particle beams in circular accelerators and storage rings. We prove analytically the existence of localized and periodic structures in coasting beams, as have been found experimentally for instance at Fermilab and at CERN, which are quite analogous to holes in classical plasmas. We also present an improved criterion for focusing. For bunched beams we describe and apply an iterative numerical procedure to find solitary hump and hole structures superimposed on the particle bunch, the former of which having been found recently in the Relativistic Hadron-Ion Collider (RHIC) at Brookhaven. Finally, we stress the mathematical equivalence between the 1D Vlasov-Poisson system and the equations describing a 2D incompressible, ideal fluid or the perpendicular dynamics of a strongly magnetized plasma in fluid or MHD approximation and other more complex fluids, such as rotating fluids, inhomogeneous plasmas, etc. This implies that tiny fluid elements trapped in coherent patches of shear flow motion, such as in secondary (tertiary) states that govern the transition to turbulence in ordinary hydrodynamics, do play a similar role than trapped particles in electrostatic waves, violating any linear wave ansatz. Or, said in different words, whenever a continues spectrum arises in a linearized fluid-like system associated with singular perturbations and a resonance between (quasi-)particles and the field, one has to consider this as a hint that the neglect of nonlinearity is not justified and that nonlinear wave solutions have to be taken into account in describing the evolution of the system correctly. This statement holds true already at an infinitesimal energy level of the coherent perturbations. Nonlinearity, and with it trapping structures, turns out to be a necessary requisite in all stages of the dynamical evolution not only at finite wave amplitudes, as commonly believed. In conclusion, in this report we emphasize the importance of collective trapping in (nearly) ideal plasmas and related systems bringing in at any level of wave activity a fundamental nonlinearity which is missed in standard linear wave theories as described in textbooks. The associated trapped particle modes challenge standard flow theories playing a key role in the interpretation of turbulence and anomalous transport.

An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1988-01-01

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

Enhanced Third-Order Optical Nonlinearity Driven by Surface-Plasmon Field Gradients.

PubMed

Kravtsov, Vasily; AlMutairi, Sultan; Ulbricht, Ronald; Kutayiah, A Ryan; Belyanin, Alexey; Raschke, Markus B

2018-05-18

Efficient nonlinear optical frequency mixing in small volumes is key for future on-chip photonic devices. However, the generally low conversion efficiency severely limits miniaturization to nanoscale dimensions. Here we demonstrate that gradient-field effects can provide for an efficient, conventionally dipole-forbidden nonlinear response. We show that a longitudinal nonlinear source current can dominate the third-order optical nonlinearity of the free electron response in gold in the technologically important near-IR frequency range where the nonlinearities due to other mechanisms are particularly small. Using adiabatic nanofocusing to spatially confine the excitation fields, from measurements of the 2ω_{1}-ω_{2} four-wave mixing response as a function of detuning ω_{1}-ω_{2}, we find up to 10^{-5} conversion efficiency with a gradient-field contribution to χ_{Au}^{(3)} of up to 10^{-19}  m^{2}/V^{2}. The results are in good agreement with the theory based on plasma hydrodynamics and underlying electron dynamics. The associated increase in the nonlinear conversion efficiency with a decreasing sample size, which can even overcompensate the volume decrease, offers a new approach for enhanced nonlinear nano-optics. This will enable more efficient nonlinear optical devices and the extension of coherent multidimensional spectroscopies to the nanoscale.

Enhanced Third-Order Optical Nonlinearity Driven by Surface-Plasmon Field Gradients

NASA Astrophysics Data System (ADS)

Kravtsov, Vasily; AlMutairi, Sultan; Ulbricht, Ronald; Kutayiah, A. Ryan; Belyanin, Alexey; Raschke, Markus B.

2018-05-01

Efficient nonlinear optical frequency mixing in small volumes is key for future on-chip photonic devices. However, the generally low conversion efficiency severely limits miniaturization to nanoscale dimensions. Here we demonstrate that gradient-field effects can provide for an efficient, conventionally dipole-forbidden nonlinear response. We show that a longitudinal nonlinear source current can dominate the third-order optical nonlinearity of the free electron response in gold in the technologically important near-IR frequency range where the nonlinearities due to other mechanisms are particularly small. Using adiabatic nanofocusing to spatially confine the excitation fields, from measurements of the 2 ω1-ω2 four-wave mixing response as a function of detuning ω1-ω2, we find up to 10-5 conversion efficiency with a gradient-field contribution to χAu(3 ) of up to 10-19 m2/V2 . The results are in good agreement with the theory based on plasma hydrodynamics and underlying electron dynamics. The associated increase in the nonlinear conversion efficiency with a decreasing sample size, which can even overcompensate the volume decrease, offers a new approach for enhanced nonlinear nano-optics. This will enable more efficient nonlinear optical devices and the extension of coherent multidimensional spectroscopies to the nanoscale.

Glassy phases and driven response of the phase-field-crystal model with random pinning.

PubMed

Granato, E; Ramos, J A P; Achim, C V; Lehikoinen, J; Ying, S C; Ala-Nissila, T; Elder, K R

2011-09-01

We study the structural correlations and the nonlinear response to a driving force of a two-dimensional phase-field-crystal model with random pinning. The model provides an effective continuous description of lattice systems in the presence of disordered external pinning centers, allowing for both elastic and plastic deformations. We find that the phase-field crystal with disorder assumes an amorphous glassy ground state, with only short-ranged positional and orientational correlations, even in the limit of weak disorder. Under increasing driving force, the pinned amorphous-glass phase evolves into a moving plastic-flow phase and then, finally, a moving smectic phase. The transverse response of the moving smectic phase shows a vanishing transverse critical force for increasing system sizes.

Noise-driven neuromorphic tuned amplifier.

PubMed

Fanelli, Duccio; Ginelli, Francesco; Livi, Roberto; Zagli, Niccoló; Zankoc, Clement

2017-12-01

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.

Measurement of Richtmyer–Meshkov mode coupling under steady shock conditions and at high energy density

DOE PAGES

Di Stefano, Carlos A.; Malamud, G.; Kuranz, C. C.; ...

2015-10-19

Here, we present experiments observing Richtmyer–Meshkov mode coupling and bubble competition in a system arising from well-characterized initial conditions and driven by a strong (Mach ~ 8) shock. These measurements and the analysis method developed to interpret them provide an important step toward the possibility of observing self-similarity under such conditions, as well as a general platform for performing and analyzing hydrodynamic instability experiments. A key feature of these experiments is that the shock is sustained sufficiently long that this nonlinear behavior occurs without decay of the shock velocity or other hydrodynamic properties of the system, which facilitates analysis andmore » allows the results to be used in the study of analytic models.« less

Information processing using a single dynamical node as complex system

PubMed Central

Appeltant, L.; Soriano, M.C.; Van der Sande, G.; Danckaert, J.; Massar, S.; Dambre, J.; Schrauwen, B.; Mirasso, C.R.; Fischer, I.

2011-01-01

Novel methods for information processing are highly desired in our information-driven society. Inspired by the brain's ability to process information, the recently introduced paradigm known as 'reservoir computing' shows that complex networks can efficiently perform computation. Here we introduce a novel architecture that reduces the usually required large number of elements to a single nonlinear node with delayed feedback. Through an electronic implementation, we experimentally and numerically demonstrate excellent performance in a speech recognition benchmark. Complementary numerical studies also show excellent performance for a time series prediction benchmark. These results prove that delay-dynamical systems, even in their simplest manifestation, can perform efficient information processing. This finding paves the way to feasible and resource-efficient technological implementations of reservoir computing. PMID:21915110

Quantum-limited amplification with a nonlinear cavity detector

NASA Astrophysics Data System (ADS)

Laflamme, C.; Clerk, A. A.

2011-03-01

We consider the quantum measurement properties of a driven cavity with a Kerr-type nonlinearity that is used to amplify a dispersively coupled input signal. Focusing on an operating regime that is near a bifurcation point, we derive simple asymptotic expressions describing the cavity’s noise and response. We show that the cavity’s backaction and imprecision noise allow for quantum-limited linear amplification and position detection only if one is able to utilize the sizable correlations between these quantities. This is possible when one amplifies a nonresonant signal but is not possible in quantum nondemolition qubit detection. We also consider the possibility of using the nonlinear cavity’s backaction for cooling a mechanical mode.

On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.

PubMed

Faizullah, Faiz

2016-01-01

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

NASA Astrophysics Data System (ADS)

Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

2002-05-01

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

Hot money and China's stock market volatility: Further evidence using the GARCH-MIDAS model

NASA Astrophysics Data System (ADS)

Wei, Yu; Yu, Qianwen; Liu, Jing; Cao, Yang

2018-02-01

This paper investigates the influence of hot money on the return and volatility of the Chinese stock market using a nonlinear Granger causality test and a new GARCH-class model based on mixed data sampling regression (GARCH-MIDAS). The empirical results suggest that no linear or nonlinear causality exists between the growth rate of hot money and the Chinese stock market return, implying that the Chinese stock market is not driven by hot money and vice versa. However, hot money has a significant positive impact on the long-term volatility of the Chinese stock market. Furthermore, the dependence between the long-term volatility caused by hot money and the total volatility of the Chinese stock market is time-variant, indicating that huge volatilities in the stock market are not always triggered by international speculation capital flow and that Chinese authorities should further focus on more systemic reforms in the trading rules and on effectively regulating the stock market.

A symbiotic approach to fluid equations and non-linear flux-driven simulations of plasma dynamics

NASA Astrophysics Data System (ADS)

Halpern, Federico

2017-10-01

The fluid framework is ubiquitous in studies of plasma transport and stability. Typical forms of the fluid equations are motivated by analytical work dating several decades ago, before computer simulations were indispensable, and can be, therefore, not optimal for numerical computation. We demonstrate a new first-principles approach to obtaining manifestly consistent, skew-symmetric fluid models, ensuring internal consistency and conservation properties even in discrete form. Mass, kinetic, and internal energy become quadratic (and always positive) invariants of the system. The model lends itself to a robust, straightforward discretization scheme with inherent non-linear stability. A simpler, drift-ordered form of the equations is obtained, and first results of their numerical implementation as a binary framework for bulk-fluid global plasma simulations are demonstrated. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award No. DE-FG02-95ER54309.

Physics-based Control-oriented Modeling of the Current Profile Evolution in NSTX-Upgrade

NASA Astrophysics Data System (ADS)

Ilhan, Zeki; Barton, Justin; Shi, Wenyu; Schuster, Eugenio; Gates, David; Gerhardt, Stefan; Kolemen, Egemen; Menard, Jonathan

2013-10-01

The operational goals for the NSTX-Upgrade device include non-inductive sustainment of high- β plasmas, realization of the high performance equilibrium scenarios with neutral beam heating, and achievement of longer pulse durations. Active feedback control of the current profile is proposed to enable these goals. Motivated by the coupled, nonlinear, multivariable, distributed-parameter plasma dynamics, the first step towards feedback control design is the development of a physics-based, control-oriented model for the current profile evolution in response to non-inductive current drives and heating systems. For this purpose, the nonlinear magnetic-diffusion equation is coupled with empirical models for the electron density, electron temperature, and non-inductive current drives (neutral beams). The resulting first-principles-driven, control-oriented model is tailored for NSTX-U based on the PTRANSP predictions. Main objectives and possible challenges associated with the use of the developed model for control design are discussed. This work was supported by PPPL.

Gyrokinetic GDC turbulence simulations: confirming a new instability regime in LAPD plasmas

NASA Astrophysics Data System (ADS)

Pueschel, M. J.; Rossi, G.; Told, D.; Terry, P. W.; Jenko, F.; Carter, T. A.

2016-10-01

Recent high-beta experiments at the LArge Plasma Device have found significant parallel magnetic fluctuations in the region of large pressure gradients. Linear gyrokinetic simulations show the dominant instability at these radii to be the gradient-driven drift coupling (GDC) mode, a non-textbook mode driven by pressure gradients and destabilized by the coupling of ExB and grad-B∥ drifts. Unlike in previous studies, the large parallel extent of the device allows for finite-kz versions of this instability in addition to kz = 0 . The locations of maximum linear growth match very well with experimentally observed peaks of B∥ fluctuations. Local nonlinear simulations reproduce many features of the observations fairly well, with the exception of Bperp fluctuations, for which experimental profiles suggest a source unrelated to pressure gradients. In toto, the results presented here show that turbulence and transport in these experiments are driven by the GDC instability, that important characteristics of the linear instability carry over to nonlinear simulations, and - in the context of validation - that the gyrokinetic framework performs surprisingly well far outside its typical area of application, increasing confidence in its predictive abilities. Supported by U.S. DOE.

Simulations on Monitoring and Evaluation of Plasticity-Driven Material Damage Based on Second Harmonic of S0 Mode Lamb Waves in Metallic Plates

PubMed Central

Sun, Xiaoqiang; Liu, Xuyang; Liu, Yaolu; Hu, Ning; Zhao, Youxuan; Ding, Xiangyan; Qin, Shiwei; Zhang, Jianyu; Zhang, Jun; Liu, Feng; Fu, Shaoyun

2017-01-01

In this study, a numerical approach—the discontinuous Meshless Local Petrov-Galerkin-Eshelby Method (MLPGEM)—was adopted to simulate and measure material plasticity in an Al 7075-T651 plate. The plate was modeled in two dimensions by assemblies of small particles that interact with each other through bonding stiffness. The material plasticity of the model loaded to produce different levels of strain is evaluated with the Lamb waves of S0 mode. A tone burst at the center frequency of 200 kHz was used as excitation. Second-order nonlinear wave was extracted from the spectrogram of a signal receiving point. Tensile-driven plastic deformation and cumulative second harmonic generation of S0 mode were observed in the simulation. Simulated measurement of the acoustic nonlinearity increased monotonically with the level of tensile-driven plastic strain captured by MLPGEM, whereas achieving this state by other numerical methods is comparatively more difficult. This result indicates that the second harmonics of S0 mode can be employed to monitor and evaluate the material or structural early-stage damage induced by plasticity. PMID:28773188

Self-Organization of Metal Nanoparticles in Light: Electrodynamics-Molecular Dynamics Simulations and Optical Binding Experiments.

PubMed

McCormack, Patrick; Han, Fei; Yan, Zijie

2018-02-01

Light-driven self-organization of metal nanoparticles (NPs) can lead to unique optical matter systems, yet simulation of such self-organization (i.e., optical binding) is a complex computational problem that increases nonlinearly with system size. Here we show that a combined electrodynamics-molecular dynamics simulation technique can simulate the trajectories and predict stable configurations of silver NPs in optical fields. The simulated dynamic equilibrium of a two-NP system matches the probability density of oscillations for two optically bound NPs obtained experimentally. The predicted stable configurations for up to eight NPs are further compared to experimental observations of silver NP clusters formed by optical binding in a Bessel beam. All configurations are confirmed to form in real systems, including pentagonal clusters with five-fold symmetry. Our combined simulations and experiments have revealed a diverse optical matter system formed by anisotropic optical binding interactions, providing a new strategy to discover artificial materials.

Microresonators for Nonlinear Quantum Optics

NASA Astrophysics Data System (ADS)

Vernon, Zachary

In this thesis I study in detail the quantum dynamics of several nonlinear optical processes in microresonator systems. A Heisenberg-picture input-output formalism is developed from first principles that includes the effects of scattering losses and independent quality factors and coupling ratios for different resonances. The task of calculating the device output is then reduced to solving a set of driven, damped, ordinary differential equations for the resonator mode operators alone. This theoretical framework is used to study photon pair generation via spontaneous four-wave mixing in the weakly pumped regime, on which the effects of scattering losses are appraised. A more strongly driven regime is studied for continuous wave pumps, demonstrating when self- and cross-phase modulation and multi-photon pair generation become important, and their effects on the spectral and power scaling properties of the system are examined; A detuning strategy is presented that compensates for some of these effects. The results of the weak-pump regime are applied to study microresonator-based heralded single photon sources. The impact of scattering losses is studied, revealing that typical systems suffer from low heralding efficiency due to these losses. A technique to improve heralding efficiency is presented through over-coupling the resonator-channel system, and a resultant trade-off between heralding rate and heralding efficiency is uncovered. Limitations to the spectral purity of the heralded single photon output for conventional microresonator systems are also analysed, and a more sophisticated coupling scheme presented to overcome the upper bound for spectral purity of 93% that exists in typical systems, permitting the generation of single photons with spectral purity arbitrarily close to 100% without spectral filtering or sophisticated phase-matching techniques. The theory of quantum frequency conversion in microresonators using four-wave mixing is then developed in detail, and the spectral conversion probability and conversion efficiency studied. Efficiencies exceeding 90% using less than 100 mW of pump power are predicted to be achievable with current technology. A dressed mode picture is developed to better understand the conversion dynamics. Rabi-like spectral splitting and temporal oscillations of the intraresonator mean photon number are predicted, exhibiting a novel regime of strongly coupled photonic modes.

Nuclear Methods for Transmutation of Nuclear Waste: Problems, Perspextives, Cooperative Research - Proceedings of the International Workshop

NASA Astrophysics Data System (ADS)

Khankhasayev, Zhanat B.; Kurmanov, Hans; Plendl, Mikhail Kh.

1996-12-01

The Table of Contents for the full book PDF is as follows: * Preface * I. Review of Current Status of Nuclear Transmutation Projects * Accelerator-Driven Systems — Survey of the Research Programs in the World * The Los Alamos Accelerator-Driven Transmutation of Nuclear Waste Concept * Nuclear Waste Transmutation Program in the Czech Republic * Tentative Results of the ISTC Supported Study of the ADTT Plutonium Disposition * Recent Neutron Physics Investigations for the Back End of the Nuclear Fuel Cycle * Optimisation of Accelerator Systems for Transmutation of Nuclear Waste * Proton Linac of the Moscow Meson Factory for the ADTT Experiments * II. Computer Modeling of Nuclear Waste Transmutation Methods and Systems * Transmutation of Minor Actinides in Different Nuclear Facilities * Monte Carlo Modeling of Electro-nuclear Processes with Nonlinear Effects * Simulation of Hybrid Systems with a GEANT Based Program * Computer Study of 90Sr and 137Cs Transmutation by Proton Beam * Methods and Computer Codes for Burn-Up and Fast Transients Calculations in Subcritical Systems with External Sources * New Model of Calculation of Fission Product Yields for the ADTT Problem * Monte Carlo Simulation of Accelerator-Reactor Systems * III. Data Basis for Transmutation of Actinides and Fission Products * Nuclear Data in the Accelerator Driven Transmutation Problem * Nuclear Data to Study Radiation Damage, Activation, and Transmutation of Materials Irradiated by Particles of Intermediate and High Energies * Radium Institute Investigations on the Intermediate Energy Nuclear Data on Hybrid Nuclear Technologies * Nuclear Data Requirements in Intermediate Energy Range for Improvement of Calculations of ADTT Target Processes * IV. Experimental Studies and Projects * ADTT Experiments at the Los Alamos Neutron Science Center * Neutron Multiplicity Distributions for GeV Proton Induced Spallation Reactions on Thin and Thick Targets of Pb and U * Solid State Nuclear Track Detector and Radiochemical Studies on the Transmutation of Nuclei Using Relativistic Heavy Ions * Experimental and Theoretical Study of Radionuclide Production on the Electronuclear Plant Target and Construction Materials Irradiated by 1.5 GeV and 130 MeV Protons * Neutronics and Power Deposition Parameters of the Targets Proposed in the ISTC Project 17 * Multicycle Irradiation of Plutonium in Solid Fuel Heavy-Water Blanket of ADS * Compound Neutron Valve of Accelerator-Driven System Sectioned Blanket * Subcritical Channel-Type Reactor for Weapon Plutonium Utilization * Accelerator Driven Molten-Fluoride Reactor with Modular Heat Exchangers on PB-BI Eutectic * A New Conception of High Power Ion Linac for ADTT * Pions and Accelerator-Driven Transmutation of Nuclear Waste? * V. Problems and Perspectives * Accelerator-Driven Transmutation Technologies for Resolution of Long-Term Nuclear Waste Concerns * Closing the Nuclear Fuel-Cycle and Moving Toward a Sustainable Energy Development * Workshop Summary * List of Participants

An afterword. HUMANING … (Anti-)DOPING; looking at "doping" sideways.

PubMed

Einstein, Stan

2014-07-01

This trek and quest explores a range of man-made anomalies and challenges which are rarely considered by their stakeholders in the complex, dynamic, nonlinear, multi-dimensionalities of both "doping" and antidoping, closure-driven certitudes.

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

Vaezi, P.; Holland, C.; Thakur, S. C.

The Controlled Shear Decorrelation Experiment (CSDX) linear plasma device provides a unique platform for investigating the underlying physics of self-regulating drift-wave turbulence/zonal flow dynamics. A minimal model of 3D drift-reduced nonlocal cold ion fluid equations which evolves density, vorticity, and electron temperature fluctuations, with proper sheath boundary conditions, is used to simulate dynamics of the turbulence in CSDX and its response to changes in parallel boundary conditions. These simulations are then carried out using the BOUndary Turbulence (BOUT++) framework and use equilibrium electron density and temperature profiles taken from experimental measurements. The results show that density gradient-driven drift-waves are themore » dominant instability in CSDX. However, the choice of insulating or conducting endplate boundary conditions affects the linear growth rates and energy balance of the system due to the absence or addition of Kelvin-Helmholtz modes generated by the sheath-driven equilibrium E × B shear and sheath-driven temperature gradient instability. Moreover, nonlinear simulation results show that the boundary conditions impact the turbulence structure and zonal flow formation, resulting in less broadband (more quasi-coherent) turbulence and weaker zonal flow in conducting boundary condition case. These results are qualitatively consistent with earlier experimental observations.« less

Geometric effects on bilayer convection in cylindrical containers

NASA Astrophysics Data System (ADS)

Johnson, Duane Thomas

The study of convection in two immiscible fluid layers is of interest for reasons both theoretical as well as applied. Recently, bilayer convection has been used as a model of convection in the earth's mantle. It is also an interesting system to use in the study of pattern formation. Bilayer convection also occurs in a process known as liquid encapsulated crystal growth, which is used to grow compound semiconductors. It is the last application which motivates this study. To analyze bilayer convection, theoretical models, numerical calculations and experiments were used. One theoretical model involves the derivation of the Navier- Stokes and energy equation for two immiscible fluid layers, using the Boussinesq approximation. A weakly nonlinear analysis was also performed to study the behavior of the system slightly beyond the onset of convection. Numerical calculations were necessary to solve both models. The experiments involved a single liquid layer of silicone oil, superposed by a layer of air. The radius and height of each fluid layer were changed to observe different flow patterns at the onset of convection. From the experiments and theory, two major discoveries were made as well as several interesting observations. The first discovery is the existence of codimension-two points-particular aspect ratios where two flow patterns coexist-in cylindrical containers. At these points, dynamic switching between different flow patterns was observed. The second discovery was the effect of air convection on the flow pattern in silicone oil. Historically, air has been considered a passive medium that has no effect on the lower fluid. However, experiments were done to show that for large air heights, convection in the air can cause radial temperature gradients at the liquid interface. These temperature gradients then cause surface tension gradient-driven flows. It was also shown that changing the radius of the container can change the driving force of convection from a surface tension gradient-driven to buoyancy-driven and back again. Finally, the weakly nonlinear analysis was able to give a qualitative description of codimension-two points as well as the change in flow patterns due to the convecting air layer.

Transition to subcritical turbulence in a tokamak plasma

NASA Astrophysics Data System (ADS)

van Wyk, F.; Highcock, E. G.; Schekochihin, A. A.; Roach, C. M.; Field, A. R.; Dorland, W.

2016-12-01

Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.

Subharmonics, chaos and beyond

NASA Astrophysics Data System (ADS)

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

2012-05-01

While studying finite amplitude ultrasonic wave resonance in a one dimensional liquid-filled cavity formed by a narrow band transducer and a plane reflector, subharmonics of the driver's frequency were observed (1,2) in addition to the expected harmonic structure. Subsequently, it was realized that the system was one of the many examples of parametric resonance in which the observed subharmonics are parametrically generated. The generation mechanism also requires a sufficiently high threshold value of the driving amplitude so that the system becomes increasingly nonlinear in response. The nonlinear features were recently investigated and are the focus of this paper. An ultrasonic interferometer with optical precision was built. The transducers were compressional, undamped quartz and Lithium Niobate crystals ranging from 1-10 MHz, driven by a high power amplifier. Both an optical diffraction system and a receiver transducer attached to an aligned reflector were used to observe the generated frequency components in the cavity. There are at least 5 regions of excitation that were identified. It is shown that from a region of oscillation stability into an unstable region leads to a cascade of bifurcations (subharmonics) culminating in chaotic oscillations. A further increase in the amplitude results in a reversion of the chaos into a second region of stability. A first-principle based explanation of the experimental findings is presented.

Designing gradient coils with reduced hot spot temperatures.

PubMed

While, Peter T; Forbes, Larry K; Crozier, Stuart

2010-03-01

Gradient coil temperature is an important concern in the design and construction of MRI scanners. Closely spaced gradient coil windings cause temperature hot spots within the system as a result of Ohmic heating associated with large current being driven through resistive material, and can strongly affect the performance of the coils. In this paper, a model is presented for predicting the spatial temperature distribution of a gradient coil, including the location and extent of temperature hot spots. Subsequently, a method is described for designing gradient coils with improved temperature distributions and reduced hot spot temperatures. Maximum temperature represents a non-linear constraint and a relaxed fixed point iteration routine is proposed to adjust coil windings iteratively to minimise this coil feature. Several examples are considered that assume different thermal material properties and cooling mechanisms for the gradient system. Coil winding solutions are obtained for all cases considered that display a considerable drop in hot spot temperature (>20%) when compared to standard minimum power gradient coils with equivalent gradient homogeneity, efficiency and inductance. The method is semi-analytical in nature and can be adapted easily to consider other non-linear constraints in the design of gradient coils or similar systems. Crown Copyright (c) 2009. Published by Elsevier Inc. All rights reserved.

Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow

NASA Astrophysics Data System (ADS)

Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.

2018-01-01

The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.

A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

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

Taverniers, Søren; Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu

2017-02-01

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement ofmore » path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.« less

Data-driven model reference control of MIMO vertical tank systems with model-free VRFT and Q-Learning.

PubMed

Radac, Mircea-Bogdan; Precup, Radu-Emil; Roman, Raul-Cristian

2018-02-01

This paper proposes a combined Virtual Reference Feedback Tuning-Q-learning model-free control approach, which tunes nonlinear static state feedback controllers to achieve output model reference tracking in an optimal control framework. The novel iterative Batch Fitted Q-learning strategy uses two neural networks to represent the value function (critic) and the controller (actor), and it is referred to as a mixed Virtual Reference Feedback Tuning-Batch Fitted Q-learning approach. Learning convergence of the Q-learning schemes generally depends, among other settings, on the efficient exploration of the state-action space. Handcrafting test signals for efficient exploration is difficult even for input-output stable unknown processes. Virtual Reference Feedback Tuning can ensure an initial stabilizing controller to be learned from few input-output data and it can be next used to collect substantially more input-state data in a controlled mode, in a constrained environment, by compensating the process dynamics. This data is used to learn significantly superior nonlinear state feedback neural networks controllers for model reference tracking, using the proposed Batch Fitted Q-learning iterative tuning strategy, motivating the original combination of the two techniques. The mixed Virtual Reference Feedback Tuning-Batch Fitted Q-learning approach is experimentally validated for water level control of a multi input-multi output nonlinear constrained coupled two-tank system. Discussions on the observed control behavior are offered. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Keeping it Together: Advanced algorithms and software for magma dynamics (and other coupled multi-physics problems)

NASA Astrophysics Data System (ADS)

Spiegelman, M.; Wilson, C. R.

2011-12-01

A quantitative theory of magma production and transport is essential for understanding the dynamics of magmatic plate boundaries, intra-plate volcanism and the geochemical evolution of the planet. It also provides one of the most challenging computational problems in solid Earth science, as it requires consistent coupling of fluid and solid mechanics together with the thermodynamics of melting and reactive flows. Considerable work on these problems over the past two decades shows that small changes in assumptions of coupling (e.g. the relationship between melt fraction and solid rheology), can have profound changes on the behavior of these systems which in turn affects critical computational choices such as discretizations, solvers and preconditioners. To make progress in exploring and understanding this physically rich system requires a computational framework that allows more flexible, high-level description of multi-physics problems as well as increased flexibility in composing efficient algorithms for solution of the full non-linear coupled system. Fortunately, recent advances in available computational libraries and algorithms provide a platform for implementing such a framework. We present results from a new model building system that leverages functionality from both the FEniCS project (www.fenicsproject.org) and PETSc libraries (www.mcs.anl.gov/petsc) along with a model independent options system and gui, Spud (amcg.ese.ic.ac.uk/Spud). Key features from FEniCS include fully unstructured FEM with a wide range of elements; a high-level language (ufl) and code generation compiler (FFC) for describing the weak forms of residuals and automatic differentiation for calculation of exact and approximate jacobians. The overall strategy is to monitor/calculate residuals and jacobians for the entire non-linear system of equations within a global non-linear solve based on PETSc's SNES routines. PETSc already provides a wide range of solvers and preconditioners, from parallel sparse direct to algebraic multigrid, that can be chosen at runtime. In particular, we make extensive use of PETSc's FieldSplit block preconditioners that allow us to use optimal solvers for subproblems (such as Stokes, or advection/diffusion of temperature) as preconditioners for the full problem. Thus these routines let us reuse effective solving recipes/splittings from previous experience while monitoring the convergence of the global problem. These techniques often yield quadratic (Newton like) convergence for the work of standard Picard schemes. We will illustrate this new framework with examples from the Magma Dynamic Demonstration suite (MADDs) of well understood magma dynamics benchmark problems including stokes flow in ridge geometries, magmatic solitary waves and shear-driven melt bands. While development of this system has been driven by magma dynamics, this framework is much more general and can be used for a wide range of PDE based multi-physics models.

Numerical study of bandwidth effect on stimulated Raman backscattering in nonlinear regime

NASA Astrophysics Data System (ADS)

Zhou, H. Y.; Xiao, C. Z.; Zou, D. B.; Li, X. Z.; Yin, Y.; Shao, F. Q.; Zhuo, H. B.

2018-06-01

Nonlinear behaviors of stimulated Raman scattering driven by finite bandwidth pumps are studied by one dimensional particle-in-cell simulations. The broad spectral feature of plasma waves and backscattered light reveals the different coupling and growth mechanisms, which lead to the suppression effect before the deep nonlinear stage. It causes nonperiodic plasma wave packets and reduces packet and etching velocities. Based on the negative frequency shift and electron energy distribution, the long-time evolution of instability can be divided into two stages by the relaxation time. It is a critical time after which the alleviation effects of nonlinear frequency shift and hot electrons are replaced by enhancement. Thus, the broadband pump suppresses instability at early time. However, it aggravates in the deep nonlinear stage by lifting the saturation level due to the coupling of the incident pump with each frequency shifted plasma wave. Our simulation results show that the nonlinear effects are valid in a bandwidth range from 2.25% to 3.0%, and the physics are similar within a nearby parameter space.

Poloidal rotation driven by nonlinear momentum transport in strong electrostatic turbulence

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

Wang, Lu; Wen, Tiliang; Diamond, P. H.

2016-08-11

Virtually, all existing theoretical works on turbulent poloidal momentum transport are based on quasilinear theory. Nonlinear poloidal momentum flux—more » $$\\langle {{\\tilde{v}}_{r}}\\tilde{n}{{\\tilde{v}}_{\\theta}}\\rangle $$ is universally neglected. However, in the strong turbulence regime where relative fluctuation amplitude is no longer small, quasilinear theory is invalid. This is true at the all-important plasma edge. In this work, nonlinear poloidal momentum flux $$\\langle {{\\tilde{v}}_{r}}\\tilde{n}{{\\tilde{v}}_{\\theta}}\\rangle $$ in strong electrostatic turbulence is calculated using the Hasegawa–Mima equation, and is compared with quasilinear poloidal Reynolds stress. A novel property is that symmetry breaking in fluctuation spectrum is not necessary for a nonlinear poloidal momentum flux. This is fundamentally different from the quasilinear Reynold stress. Furthermore, the comparison implies that the poloidal rotation drive from the radial gradient of nonlinear momentum flux is comparable to that from the quasilinear Reynolds force. Nonlinear poloidal momentum transport in strong electrostatic turbulence is thus not negligible for poloidal rotation drive, and so may be significant to transport barrier formation.« less

Nonlinear Dynamic Modeling of Neuron Action Potential Threshold During Synaptically Driven Broadband Intracellular Activity

PubMed Central

Roach, Shane M.; Song, Dong; Berger, Theodore W.

2012-01-01

Activity-dependent variation of neuronal thresholds for action potential (AP) generation is one of the key determinants of spike-train temporal-pattern transformations from presynaptic to postsynaptic spike trains. In this study, we model the nonlinear dynamics of the threshold variation during synaptically driven broadband intracellular activity. First, membrane potentials of single CA1 pyramidal cells were recorded under physiologically plausible broadband stimulation conditions. Second, a method was developed to measure AP thresholds from the continuous recordings of membrane potentials. It involves measuring the turning points of APs by analyzing the third-order derivatives of the membrane potentials. Four stimulation paradigms with different temporal patterns were applied to validate this method by comparing the measured AP turning points and the actual AP thresholds estimated with varying stimulation intensities. Results show that the AP turning points provide consistent measurement of the AP thresholds, except for a constant offset. It indicates that 1) the variation of AP turning points represents the nonlinearities of threshold dynamics; and 2) an optimization of the constant offset is required to achieve accurate spike prediction. Third, a nonlinear dynamical third-order Volterra model was built to describe the relations between the threshold dynamics and the AP activities. Results show that the model can predict threshold accurately based on the preceding APs. Finally, the dynamic threshold model was integrated into a previously developed single neuron model and resulted in a 33% improvement in spike prediction. PMID:22156947

Subsystem design in aircraft power distribution systems using optimization

NASA Astrophysics Data System (ADS)

Chandrasekaran, Sriram

2000-10-01

The research reported in this dissertation focuses on the development of optimization tools for the design of subsystems in a modern aircraft power distribution system. The baseline power distribution system is built around a 270V DC bus. One of the distinguishing features of this power distribution system is the presence of regenerative power from the electrically driven flight control actuators and structurally integrated smart actuators back to the DC bus. The key electrical components of the power distribution system are bidirectional switching power converters, which convert, control and condition electrical power between the sources and the loads. The dissertation is divided into three parts. Part I deals with the formulation of an optimization problem for a sample system consisting of a regulated DC-DC buck converter preceded by an input filter. The individual subsystems are optimized first followed by the integrated optimization of the sample system. It is shown that the integrated optimization provides better results than that obtained by integrating the individually optimized systems. Part II presents a detailed study of piezoelectric actuators. This study includes modeling, optimization of the drive amplifier and the development of a current control law for piezoelectric actuators coupled to a simple mechanical structure. Linear and nonlinear methods to study subsystem interaction and stability are studied in Part III. A multivariable impedance ratio criterion applicable to three phase systems is proposed. Bifurcation methods are used to obtain global stability characteristics of interconnected systems. The application of a nonlinear design methodology, widely used in power systems, to incrementally improve the robustness of a system to Hopf bifurcation instability is discussed.

Influence of heat losses on nonlinear fingering dynamics of exothermic autocatalytic fronts

NASA Astrophysics Data System (ADS)

D'Hernoncourt, J.; De Wit, A.

2010-06-01

Across traveling exothermic autocatalytic fronts, a density jump can be observed due to changes in composition and temperature. These density changes are prone to induce buoyancy-driven convection around the front when the propagation takes place in absence of gel within the gravity field. Most recent experiments devoted to studying such reaction-diffusion-convection dynamics are performed in Hele-Shaw cells, two glass plates separated by a thin gap width and filled by the chemical solutions. We investigate here the influence of heat losses through the walls of such cells on the nonlinear fingering dynamics of exothermic autocatalytic fronts propagating in vertical Hele-Shaw cells. We show that these heat losses increase tip splittings and modify the properties of the flow field. A comparison of the differences between the dynamics in reactors with respectively insulating and conducting walls is performed as a function of the Lewis number Le, the Newton cooling coefficient α quantifying the amplitude of heat losses and the width of the system. We find that tip splitting is enhanced for intermediate values of α while coarsening towards one single finger dominates for insulated systems or large values of α leading to situations equivalent to isothermal ones.

Practical controller design for ultra-precision positioning of stages with a pneumatic artificial muscle actuator

NASA Astrophysics Data System (ADS)

Tang, T. F.; Chong, S. H.

2017-06-01

This paper presents a practical controller design method for ultra-precision positioning of pneumatic artificial muscle actuator stages. Pneumatic artificial muscle (PAM) actuators are safe to use and have numerous advantages which have brought these actuators to wide applications. However, PAM exhibits strong non-linear characteristics, and these limitations lead to low controllability and limit its application. In practice, the non-linear characteristics of PAM mechanism are difficult to be precisely modeled, and time consuming to model them accurately. The purpose of the present study is to clarify a practical controller design method that emphasizes a simple design procedure that does not acquire plants parameters modeling, and yet is able to demonstrate ultra-precision positioning performance for a PAM driven stage. The practical control approach adopts continuous motion nominal characteristic trajectory following (CM NCTF) control as the feedback controller. The constructed PAM driven stage is in low damping characteristic and causes severe residual vibration that deteriorates motion accuracy of the system. Therefore, the idea to increase the damping characteristic by having an acceleration feedback compensation to the plant has been proposed. The effectiveness of the proposed controller was verified experimentally and compared with a classical PI controller in point-to-point motion. The experiment results proved that the CM NCTF controller demonstrates better positioning performance in smaller motion error than the PI controller. Overall, the CM NCTF controller has successfully to reduce motion error to 3µm, which is 88.7% smaller than the PI controller.

Laser-driven planar Rayleigh-Taylor instability experiments

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

Glendinning, S.G.; Weber, S.V.; Bell, P.

1992-08-24

We have performed a series of experiments on the Nova Laser Facility to examine the hydrodynamic behavior of directly driven planar foils with initial perturbations of varying wavelength. The foils were accelerated with a single, frequency doubled, smoothed and temporally shaped laser beam at 0.8{times}10{sup 14} W/cm{sup 2}. The experiments are in good agreement with numerical simulations using the computer codes LASNEX and ORCHID which show growth rates reduced to about 70% of classical for this nonlinear regime.

Numerical investigation of bubble nonlinear dynamics characteristics

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

Shi, Jie, E-mail: shijie@hrbeu.edu.cn; Yang, Desen; Shi, Shengguo

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.

Independence screening for high dimensional nonlinear additive ODE models with applications to dynamic gene regulatory networks.

PubMed

Xue, Hongqi; Wu, Shuang; Wu, Yichao; Ramirez Idarraga, Juan C; Wu, Hulin

2018-05-02

Mechanism-driven low-dimensional ordinary differential equation (ODE) models are often used to model viral dynamics at cellular levels and epidemics of infectious diseases. However, low-dimensional mechanism-based ODE models are limited for modeling infectious diseases at molecular levels such as transcriptomic or proteomic levels, which is critical to understand pathogenesis of diseases. Although linear ODE models have been proposed for gene regulatory networks (GRNs), nonlinear regulations are common in GRNs. The reconstruction of large-scale nonlinear networks from time-course gene expression data remains an unresolved issue. Here, we use high-dimensional nonlinear additive ODEs to model GRNs and propose a 4-step procedure to efficiently perform variable selection for nonlinear ODEs. To tackle the challenge of high dimensionality, we couple the 2-stage smoothing-based estimation method for ODEs and a nonlinear independence screening method to perform variable selection for the nonlinear ODE models. We have shown that our method possesses the sure screening property and it can handle problems with non-polynomial dimensionality. Numerical performance of the proposed method is illustrated with simulated data and a real data example for identifying the dynamic GRN of Saccharomyces cerevisiae. Copyright © 2018 John Wiley & Sons, Ltd.

Nonlinear Dynamics of Multi-Component Bose-Einstein Condensates ---Anti-Gravity Transport and Vortex Chaos---

NASA Astrophysics Data System (ADS)

Nakamura, K.

Bose-Einstein condensate(BEC) provides a nice stage when the nonlinearSchrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the magnetic field leads to a striking anti-gravity transport of BEC. This phenomenon is a manifestation of macroscopic non-adiabatic tunneling in a system with two internal(electronic) degrees of freedom. The dynamics splits into a fast complex spatio-temporal oscillation of each condensate wavefunctions together with a slow levitation of the total center of mass. Secondly, we examine the three-component repulsive BEC in 2 dimensions in a harmonic trap in the absence of magnetic field, and construct a model of conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which represents three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance r_{ij} on short scale and logarithmic in r_{ij} on large scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore ``the chaos in the three-body problem" in the context of vortices with inertia.

Explosive electromagnetic radiation by the relaxation of a multimode magnon system.

PubMed

Vasyuchka, V I; Serga, A A; Sandweg, C W; Slobodianiuk, D V; Melkov, G A; Hillebrands, B

2013-11-01

Microwave emission from a parametrically pumped ferrimagnetic film of yttrium iron garnet was studied versus the magnon density evolution, which was detected by Brillouin light scattering spectroscopy. It has been found that the shutdown of external microwave pumping leads to an unexpected effect: The conventional monotonic decrease of the population of parametrically injected magnons is accompanied by an explosive behavior of electromagnetic radiation at the magnon frequency. The developed theory shows that this explosion is caused by a nonlinear energy transfer from parametrically driven short-wavelength dipolar-exchange magnons to a long-wavelength dipolar magnon mode effectively coupled to an electromagnetic wave.

Invited review article: high-speed flexure-guided nanopositioning: mechanical design and control issues.

PubMed

Yong, Y K; Moheimani, S O R; Kenton, B J; Leang, K K

2012-12-01

Recent interest in high-speed scanning probe microscopy for high-throughput applications including video-rate atomic force microscopy and probe-based nanofabrication has sparked attention on the development of high-bandwidth flexure-guided nanopositioning systems (nanopositioners). Such nanopositioners are designed to move samples with sub-nanometer resolution with positioning bandwidth in the kilohertz range. State-of-the-art designs incorporate uniquely designed flexure mechanisms driven by compact and stiff piezoelectric actuators. This paper surveys key advances in mechanical design and control of dynamic effects and nonlinearities, in the context of high-speed nanopositioning. Future challenges and research topics are also discussed.

Recent advances on glass-forming systems driven far from equilibrium. Special issue marking the completion of the Research Unit FOR 1394 `Nonlinear response to probe vitrification'

NASA Astrophysics Data System (ADS)

Fuchs, Matthias

2017-08-01

The nature of the glass transition is one of the frontier questions in Statistical Physics and Materials Science. Highly cooperative structural processes develop in glass-forming melts exhibiting relaxational dynamics which is spread out over many decades in time. While considerable progress has been made in recent decades towards understanding dynamical slowing-down in quiescent systems, the interplay of glassy dynamics with external fields reveals a wealth of novel phenomena yet to be explored. This special issue focuses on recent results obtained by the Research Unit FOR 1394 `Nonlinear response to probe vitrification' which was funded by the German Science Foundation (DFG). In the projects of the research unit, strong external fields were used in order to gain insights into the complex structural and transport phenomena at the glass transition under far-from-equilibrium conditions. This aimed inter alia to test theories of the glass transition developed for quiescent systems by pushing them beyond their original regime. Combining experimental, simulational, and theoretical efforts, the eight projects within the FOR 1394 measured and determined aspects of the nonlinear response of supercooled metallic, polymeric, and silica melts, of colloidal dispersions, and of ionic liquids. Applied fields included electric and mechanic fields, and forced active probing (`micro-rheology'), where a single probe is forced through the glass-forming host. Nonlinear stress-strain and force-velocity relations as well as nonlinear dielectric susceptibilities and conductivities were observed. While the physical manipulation of melts and glasses is interesting in its own right, especially technologically, the investigations performed by the FOR 1394 suggest to use the response to strong homogeneous and inhomogeneous fields as technique to explore on the microscopic level the cooperative mechanisms in dense melts of strongly interacting constituents. Questions considered concern the (de-)coupling of different dynamical degrees of freedom in an external field, and the ensuing state diagrams. What forces are required to detach a localized probe particle from its initial environment in a supercooled liquid, in a glassy or granular system? Do metallic and colloidal glasses yield homogeneously or by strain localization under differently applied stresses? Which mechanisms determine field-dependent susceptibilities in dielectric and ionically conducting glass formers?

A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference

PubMed Central

Zenil, Hector; Kiani, Narsis A.; Ball, Gordon; Gomez-Cabrero, David

2016-01-01

Systems in nature capable of collective behaviour are nonlinear, operating across several scales. Yet our ability to account for their collective dynamics differs in physics, chemistry and biology. Here, we briefly review the similarities and differences between mathematical modelling of adaptive living systems versus physico-chemical systems. We find that physics-based chemistry modelling and computational neuroscience have a shared interest in developing techniques for model reductions aiming at the identification of a reduced subsystem or slow manifold, capturing the effective dynamics. By contrast, as relations and kinetics between biological molecules are less characterized, current quantitative analysis under the umbrella of bioinformatics focuses on signal extraction, correlation, regression and machine-learning analysis. We argue that model reduction analysis and the ensuing identification of manifolds bridges physics and biology. Furthermore, modelling living systems presents deep challenges as how to reconcile rich molecular data with inherent modelling uncertainties (formalism, variables selection and model parameters). We anticipate a new generative data-driven modelling paradigm constrained by identified governing principles extracted from low-dimensional manifold analysis. The rise of a new generation of models will ultimately connect biology to quantitative mechanistic descriptions, thereby setting the stage for investigating the character of the model language and principles driving living systems. This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’. PMID:27698038

Direct adaptive fuzzy control of a translating piezoelectric flexible manipulator driven by a pneumatic rodless cylinder

NASA Astrophysics Data System (ADS)

Qiu, Zhi-cheng; Wang, Bin; Zhang, Xian-min; Han, Jian-da

2013-04-01

This study presents a novel translating piezoelectric flexible manipulator driven by a rodless cylinder. Simultaneous positioning control and vibration suppression of the flexible manipulator is accomplished by using a hybrid driving scheme composed of the pneumatic cylinder and a piezoelectric actuator. Pulse code modulation (PCM) method is utilized for the cylinder. First, the system dynamics model is derived, and its standard multiple input multiple output (MIMO) state-space representation is provided. Second, a composite proportional derivative (PD) control algorithms and a direct adaptive fuzzy control method are designed for the MIMO system. Also, a time delay compensation algorithm, bandstop and low-pass filters are utilized, under consideration of the control hysteresis and the caused high-frequency modal vibration due to the long stroke of the cylinder, gas compression and nonlinear factors of the pneumatic system. The convergence of the closed loop system is analyzed. Finally, experimental apparatus is constructed and experiments are conducted. The effectiveness of the designed controllers and the hybrid driving scheme is verified through simulation and experimental comparison studies. The numerical simulation and experimental results demonstrate that the proposed system scheme of employing the pneumatic drive and piezoelectric actuator can suppress the vibration and achieve the desired positioning location simultaneously. Furthermore, the adopted adaptive fuzzy control algorithms can significantly enhance the control performance.

Cascading events in linked ecological and socioeconomic systems

USGS Publications Warehouse

Peters, Debra P.C.; Sala, O.E.; Allen, Craig D.; Covich, A.; Brunson, M.

2007-01-01

Cascading events that start at small spatial scales and propagate non-linearly through time to influence larger areas often have major impacts on ecosystem goods and services. Events such as wildfires and hurricanes are increasing in frequency and magnitude as systems become more connected through globalization processes. We need to improve our understanding of these events in order to predict their occurrence, minimize potential impacts, and allow for strategic recovery. Here, we synthesize information about cascading events in systems located throughout the Americas. We discuss a variety of examples of cascading events that share a common feature: they are often driven by linked ecological and human processes across scales. In this era of globalization, we recommend studies that explicitly examine connections across scales and examine the role of connectivity among non-contiguous as well as contiguous areas.

Cooperating reduction machines

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

Kluge, W.E.

1983-11-01

This paper presents a concept and a system architecture for the concurrent execution of program expressions of a concrete reduction language based on lamda-expressions. If formulated appropriately, these expressions are well-suited for concurrent execution, following a demand-driven model of computation. In particular, recursive program expressions with nonlinear expansion may, at run time, recursively be partitioned into a hierarchy of independent subexpressions which can be reduced by a corresponding hierarchy of virtual reduction machines. This hierarchy unfolds and collapses dynamically, with virtual machines recursively assuming the role of masters that create and eventually terminate, or synchronize with, slaves. The paper alsomore » proposes a nonhierarchically organized system of reduction machines, each featuring a stack architecture, that effectively supports the allocation of virtual machines to the real machines of the system in compliance with their hierarchical order of creation and termination. 25 references.« less

A novel determination of calcite dissolution kinetics in seawater

NASA Astrophysics Data System (ADS)

Subhas, Adam V.; Rollins, Nick E.; Berelson, William M.; Dong, Sijia; Erez, Jonathan; Adkins, Jess F.

2015-12-01

We present a novel determination of the dissolution kinetics of inorganic calcite in seawater. We dissolved 13 C -labeled calcite in unlabeled seawater, and traced the evolving δ13 C composition of the fluid over time to establish dissolution rates. This method provides sensitive determinations of dissolution rate, which we couple with tight constraints on both seawater saturation state and surface area of the dissolving minerals. We have determined dissolution rates for two different abiotic calcite materials and three different grain sizes. Near-equilibrium dissolution rates are highly nonlinear, and are well normalized by geometric surface area, giving an empirical dissolution rate dependence on saturation state (Ω) of: This result substantiates the non-linear response of calcite dissolution to undersaturation. The bulk dissolution rate constant calculated here is in excellent agreement with those determined in far from equilibrium and dilute solution experiments. Plots of dissolution versus undersaturation indicates the presence of at least two dissolution mechanisms, implying a criticality in the calcite-seawater system. Finally, our new rate determination has implications for modeling of pelagic and seafloor dissolution. Nonlinear dissolution kinetics in a simple 1-D lysocline model indicate a possible transition from kinetic to diffusive control with increasing water depth, and also confirm the importance of respiration-driven dissolution in setting the shape of the calcite lysocline.

Transition Manifolds of Complex Metastable Systems: Theory and Data-Driven Computation of Effective Dynamics.

PubMed

Bittracher, Andreas; Koltai, Péter; Klus, Stefan; Banisch, Ralf; Dellnitz, Michael; Schütte, Christof

2018-01-01

We consider complex dynamical systems showing metastable behavior, but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics.

Direct observation of the two-plasmon-decay common plasma wave using ultraviolet Thomson scattering.

PubMed

Follett, R K; Edgell, D H; Henchen, R J; Hu, S X; Katz, J; Michel, D T; Myatt, J F; Shaw, J; Froula, D H

2015-03-01

A 263-nm Thomson-scattering beam was used to directly probe two-plasmon-decay (TPD) excited electron plasma waves (EPWs) driven by between two and five 351-nm beams on the OMEGA Laser System. The amplitude of these waves was nearly independent of the number of drive beams at constant overlapped intensity, showing that the observed EPWs are common to the multiple beams. In an experimental configuration where the Thomson-scattering diagnostic was not wave matched to the common TPD EPWs, a broad spectrum of TPD-driven EPWs was observed, indicative of nonlinear effects associated with TPD saturation. Electron plasma waves corresponding to Langmuir decay of TPD EPWs were observed in both Thomson-scattering spectra, suggesting the Langmuir decay instability as a TPD saturation mechanism. Simulated Thomson-scattering spectra from three-dimensional numerical solutions of the extended Zakharov equations of TPD are in excellent agreement with the experimental spectra and verify the presence of the Langmuir decay instability.

Direct observation of the two-plasmon-decay common plasma wave using ultraviolet Thomson scattering

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

Follett, R. K.; Edgell, D. H.; Henchen, R. J.

2015-03-26

A 263-nm Thomson-scattering beam was used to directly probe two-plasmon-decay (TPD) excited electron plasma waves (EPWs) driven by between two and five 351-nm beams on the OMEGA Laser System. The amplitude of these waves was nearly independent of the number of drive beams at constant overlapped intensity, showing that the observed EPWs are common to the multiple beams. In an experimental configuration where the Thomson-scattering diagnostic was not wave matched to the common TPD EPWs, a broad spectrum of TPD-driven EPWs was observed, indicative of nonlinear effects associated with TPD saturation. Electron plasma waves corresponding to Langmuir decay of TPDmore » EPWs were observed in both Thomson-scattering spectra, suggesting the Langmuir decay instability as a TPD saturation mechanism. Simulated Thomson-scattering spectra from three-dimensional numerical solutions of the extended Zakharov equations of TPD are in excellent agreement with the experimental spectra and verify the presence of the Langmuir decay instability.« less

Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions.

PubMed

Sawlekar, Rucha; Montefusco, Francesco; Kulkarni, Vishwesh V; Bates, Declan G

2016-07-01

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.

Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving

NASA Astrophysics Data System (ADS)

Puri, Shruti; Boutin, Samuel; Blais, Alexandre

2017-04-01

Photonic cat states stored in high-Q resonators show great promise for hardware efficient universal quantum computing. We propose an approach to efficiently prepare such cat states in a Kerr-nonlinear resonator by the use of a two-photon drive. Significantly, we show that this preparation is robust against single-photon loss. An outcome of this observation is that a two-photon drive can eliminate undesirable phase evolution induced by a Kerr nonlinearity. By exploiting the concept of transitionless quantum driving, we moreover demonstrate how non-adiabatic initialization of cat states is possible. Finally, we present a universal set of quantum logical gates that can be performed on the engineered eigenspace of such a two-photon driven resonator and discuss a possible realization using superconducting circuits. The robustness of the engineered subspace to higher-order circuit nonlinearities makes this implementation favorable for scalable quantum computation.

Laser Imaging of Airborne Acoustic Emission by Nonlinear Defects

NASA Astrophysics Data System (ADS)

Solodov, Igor; Döring, Daniel; Busse, Gerd

2008-06-01

Strongly nonlinear vibrations of near-surface fractured defects driven by an elastic wave radiate acoustic energy into adjacent air in a wide frequency range. The variations of pressure in the emitted airborne waves change the refractive index of air thus providing an acoustooptic interaction with a collimated laser beam. Such an air-coupled vibrometry (ACV) is proposed for detecting and imaging of acoustic radiation of nonlinear spectral components by cracked defects. The photoelastic relation in air is used to derive induced phase modulation of laser light in the heterodyne interferometer setup. The sensitivity of the scanning ACV to different spatial components of the acoustic radiation is analyzed. The animated airborne emission patterns are visualized for the higher harmonic and frequency mixing fields radiated by planar defects. The results confirm a high localization of the nonlinear acoustic emission around the defects and complicated directivity patterns appreciably different from those observed for fundamental frequencies.

Nonlinear evolution of energetic-particles-driven waves in collisionless plasmas

NASA Astrophysics Data System (ADS)

Li, Shuhan; Liu, Jinyuan; Wang, Feng; Shen, Wei; Li, Dong

2018-06-01

A one-dimensional electrostatic collisionless particle-in-cell code has been developed to study the nonlinear interaction between electrostatic waves and energetic particles (EPs). For a single wave, the results are clear and agree well with the existing theories. For coexisting two waves, although the mode nonlinear coupling between two wave fields is ignored, the second-order phase space islands can still exist between first-order islands generated by the two waves. However, the second-order phase islands are not formed by the superposed wave fields and the perturbed motions of EPs induced by the combined effect of two main resonances make these structures in phase space. Owing to these second-order islands, energy can be transferred between waves, even if the overlap of two main resonances never occurs. Depending on the distance between the main resonance islands in velocity space, the second-order island can affect the nonlinear dynamics and saturations of waves.

Nonlinear Characterization of Half and Full Wavelength Power Ultrasonic Devices

NASA Astrophysics Data System (ADS)

Mathieson, Andrew; Cerisola, Niccolò; Cardoni, Andrea

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

A nonlinear dynamics for the scalar field in Randers spacetime

NASA Astrophysics Data System (ADS)

Silva, J. E. G.; Maluf, R. V.; Almeida, C. A. S.

2017-03-01

We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.

Long-lived fluctuations driven by shear flows

NASA Astrophysics Data System (ADS)

Kim, J.-H.; Horton, W.; Morrison, P.; Chagelishvili, G. D.; Gogoberidze, G.; Dahlburg, R.

2004-11-01

In flows that are stable in accordance to the Rayleigh criterion there are long lived transient fluctuations that can lead to the onset of turbulence. We show examples of transitions to turbulence due to the positive nonlinear feedback from the transients. Simulations show that the intensity of the nonlinear decay processes depends on the angle between wave vectors of the interacting spatial Fourier harmonics. Positive nonlinear feedback occurs when vorticities of the perturbation are the same direction. Above some amplitude the cyclonic perturbation is self-sustained due to the feedback loop. Generalization and applications of the simulations for atmospheric and plasma flows are discussed. This work was supported in part by the Department of Energy Grant No. DE-FG03-96ER-54346 and ISTC Grant G-5333.

Instabilities and transport in Hall plasmas with ExB drift

NASA Astrophysics Data System (ADS)

Smolyakov, Andrei

2016-10-01

Low temperature plasma with moderate magnetic field, where the ions are not or just weakly magnetized, i.e. the ion Larmor radius being larger or comparable to the characteristic length scale of interest (e.g. the size ofthe system), have distinctly different properties from strongly magnetized plasmas such as that for fusion applications. Such parameters regimes are generally defined here as Hall plasmas. The natural scale separation between the ion and electron Larmor radii in Hall plasma, further exploited by the application of the external electric field, offers unique applications in various plasma devices for material processing and electric propulsion. Plasmas in such devices are in strongly non-equilibrium state making it prone to a number of instabilities. This talk presents physics description of the dominant unstable modes in ExB Hall plasmas resulting in highly turbulent state with nonlinear coherent structures and anomalous electron current. Since ions are un-magnetized, fundamental instabilities operating in low temperature Hall plasmas are very different from much studied gradients (density, temperature and magnetic field) driven drift-wave turbulence in strongly magnetized plasmas for fusion applications. As a result the nonlinear saturation mechanisms, role of the ExB shear flows are also markedly different in such plasmas. We review the basic instabilities in these plasmas which are related to the ion-sound, low-hybrid and anti-drift modes, discuss nonlinear saturation and anomalous transport mechanisms. The advanced nonlinear fluid model for such plasmas and results of nonlinear simulations of turbulence and anomalous transport performed within a modified BOUT++ framework will be presented. Research supported by NSERC Canada and US AFOSR FA9550-15-1-0226.