Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

NASA Astrophysics Data System (ADS)

Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

2015-12-01

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

Nonlinear channelizer.

PubMed

In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio

2012-12-01

The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.

Two-Photon Raman Gain in a Laser Driven Potassium Vapor

DTIC Science & Technology

1996-02-01

between light and matter becomes highly nonlinear and the light and matter strongly couple, the systems become much more difficult to understand both...theoretically and experimentally. One example of a strongly coupled, highly nonlinear system is the two-photon laser that is based on the two-photon

High-frequency vibration energy harvesting from impulsive excitation utilizing intentional dynamic instability caused by strong nonlinearity

NASA Astrophysics Data System (ADS)

Remick, Kevin; Dane Quinn, D.; Michael McFarland, D.; Bergman, Lawrence; Vakakis, Alexander

2016-05-01

The authors investigate a vibration-based energy harvesting system utilizing essential (nonlinearizable) nonlinearities and electromagnetic coupling elements. The system consists of a grounded, weakly damped linear oscillator (primary system) subjected to a single impulsive load. This primary system is coupled to a lightweight, damped oscillating attachment (denoted as nonlinear energy sink, NES) via a neodymium magnet and an inductance coil, and a piano wire, which generates an essential geometric cubic stiffness nonlinearity. Under impulsive input, the transient damped dynamics of this system exhibit transient resonance captures (TRCs) causing intentional large-amplitude and high-frequency instabilities in the response of the NES. These TRCs result in strong energy transfer from the directly excited primary system to the light-weight attachment. The energy is harvested by the electromagnetic elements in the coupling and, in the present case, dissipated in a resistive element in the electrical circuit. The primary goal of this work is to numerically, analytically, and experimentally demonstrate the efficacy of employing this type of intentional high-frequency dynamic instability to achieve enhanced vibration energy harvesting under impulsive excitation.

High-order rogue waves in vector nonlinear Schrödinger equations.

PubMed

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

2014-04-01

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

Digital nonlinearity compensation in high-capacity optical communication systems considering signal spectral broadening effect.

PubMed

Xu, Tianhua; Karanov, Boris; Shevchenko, Nikita A; Lavery, Domaniç; Liga, Gabriele; Killey, Robert I; Bayvel, Polina

2017-10-11

Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions.

Investigation of advanced pre- and post-equalization schemes in high-order CAP modulation based high-speed indoor VLC transmission system

NASA Astrophysics Data System (ADS)

Wang, Yiguang; Chi, Nan

2016-10-01

Light emitting diodes (LEDs) based visible light communication (VLC) has been considered as a promising technology for indoor high-speed wireless access, due to its unique advantages, such as low cost, license free and high security. To achieve high-speed VLC transmission, carrierless amplitude and phase (CAP) modulation has been utilized for its lower complexity and high spectral efficiency. Moreover, to compensate the linear and nonlinear distortions such as frequency attenuation, sampling time offset, LED nonlinearity etc., series of pre- and post-equalization schemes should be employed in high-speed VLC systems. In this paper, we make an investigation on several advanced pre- and postequalization schemes for high-order CAP modulation based VLC systems. We propose to use a weighted preequalization technique to compensate the LED frequency attenuation. In post-equalization, a hybrid post equalizer is proposed, which consists of a linear equalizer, a Volterra series based nonlinear equalizer, and a decision-directed least mean square (DD-LMS) equalizer. Modified cascaded multi-modulus algorithm (M-CMMA) is employed to update the weights of the linear and the nonlinear equalizer, while DD-LMS can further improve the performance after the preconvergence. Based on high-order CAP modulation and these equalization schemes, we have experimentally demonstrated a 1.35-Gb/s, a 4.5-Gb/s and a 8-Gb/s high-speed indoor VLC transmission systems. The results show the benefit and feasibility of the proposed equalization schemes for high-speed VLC systems.

Nonlinear dynamic analysis of rigid rotor supported by gas foil bearings: Effects of gas film and foil structure on subsynchronous vibrations

NASA Astrophysics Data System (ADS)

Guo, Zhiyang; Feng, Kai; Liu, Tianyu; Lyu, Peng; Zhang, Tao

2018-07-01

Highly nonlinear subsynchronous vibrations are the main causing factors of failure in gas foil bearing (GFB)-rotor systems. Thus, investigating the vibration generation mechanisms and the relationship between subsynchronous vibrations and GFBs is necessary to ensure the healthy operation of rotor systems. In this study, an integrated nonlinear dynamic model with the consideration of shaft motion, unsteady gas film, and deformations of foil structure is established to investigate the effect of gas film and foil structure on system subsynchronous response. One test rig of GFB-rotor system is developed for model comparison. High agreement is shown between the prediction and test data, especially in the frequency domain. The nonlinear dynamic response is analyzed using waterfall plots, operation deflection shapes, journal orbits, Poincaré maps, and fast Fourier transforms. The parameter studies reveal that subsynchronous vibrations are highly related to gas film and foil structure. Subsynchronous vibrations can be adjusted by parameters such as bump stiffness, nominal clearance, and static loads. Therefore, gas foil bearing parameters should be carefully adjusted by system manufacturers to achieve the best rotordynamic performance.

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

NASA Astrophysics Data System (ADS)

Yao, Jianyong

2018-06-01

Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

Small systems of Duffing oscillators and the Fermi-Pasta-Ulam-Tsingou system An examination of the possible reasons for the unusual stability of localized nonlinear excitations in these systems

NASA Astrophysics Data System (ADS)

Kashyap, Rahul; Westley, Alexandra; Sen, Surajit

The Duffing oscillator, a nonlinear oscillator with a potential energy with both quadratic and cubic terms, is known to show highly chaotic solutions in certain regions of its parameter space. Here, we examine the behaviors of small chains of harmonically and anharmonically coupled Duffing oscillators and show that these chains exhibit localized nonlinear excitations (LNEs) similar to the ones seen in the Fermi-Pasta-Ulam-Tsingou (FPUT) system. These LNEs demonstrate properties such as long-time energy localization, high periodicity, and slow energy leaking which rapidly accelerates upon frequency matching with the adjacent particles all of which have been observed in the FPUT system. Furthermore, by examining bifurcation diagrams, we will show that many qualitative properties of this system during the transition from weakly to strongly nonlinear behavior depend directly upon the frequencies associated with the individual Duffing oscillators.

Research on the Diesel Engine with Sliding Mode Variable Structure Theory

NASA Astrophysics Data System (ADS)

Ma, Zhexuan; Mao, Xiaobing; Cai, Le

2018-05-01

This study constructed the nonlinear mathematical model of the diesel engine high-pressure common rail (HPCR) system through two polynomial fitting which was treated as a kind of affine nonlinear system. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for affine nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrated that sliding-mode variable structure control algorithm shows favourable control performances which are overcoming the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.

Nonlinear control for a class of hydraulic servo system.

PubMed

Yu, Hong; Feng, Zheng-jin; Wang, Xu-yong

2004-11-01

The dynamics of hydraulic systems are highly nonlinear and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction, etc. Aside from the nonlinear nature of hydraulic dynamics, hydraulic servo systems also have large extent of model uncertainties. To address these challenging issues, a robust state-feedback controller is designed by employing backstepping design technique such that the system output tracks a given signal arbitrarily well, and all signals in the closed-loop system remain bounded. Moreover, a relevant disturbance attenuation inequality is satisfied by the closed-loop signals. Compared with previously proposed robust controllers, this paper's robust controller based on backstepping recursive design method is easier to design, and is more suitable for implementation.

Improvement of SPM nonlinear limit by chirped duobinary PolSK transmission

NASA Astrophysics Data System (ADS)

Yang, Lixiu; Fan, Jiayu; Wang, Lutang; Huang, Zhaoming

2005-02-01

In today's terrestrial long-haul optical fiber communication systems, high channel powers are required to obtain a large transmission distance with reasonable optical amplifier spacing. In such systems, however, the presence of nonlinear effects such as the self-phase modulation (SPM) and the fiber dispersion as well as their combined effects, called SPM-induced nonlinear limitation or SPM limit, will seriously degrade the system performances in respect of the effective transmission distance and ultimately become a limiting factor in high-speed, long-haul optical fiber transmission.In this paper, a new transmission format: chirped duobinary PolSK transmission, has been proposed to generate a pre-chirped duobianry signal with fixed polarity (either positive or negative), which is modulated by a PolSK modulator. This format is based on a transmitter setup consisting of a duobinary PolSK Modulation transmitter followed by an additional phase modulator. The chirped duobinary PolSK transmission reduces the signal degradation and spectral broadening in the nonlinear regime significantly. Thus it shifts this SPM nonlinear limit to enable more relaxed dispersion compensation at high optical power compared to the conventional duobinary schemes.The simulation results show chirped duobinary PolSK transmission enlarges the dispersion limited transmission distance, increases the dispersion tolerance and overcome the SPM nonlinear limit.

Nonlinear oscillation of a rigid body over high- Tc superconductors supported by electro-magnetic forces

NASA Astrophysics Data System (ADS)

Sugiura, T.; Ogawa, S.; Ura, H.

2005-10-01

Characteristics of high- Tc superconducting levitation systems are no contact support and stable levitation without control. They can be applied to supporting mechanisms in machines, such as linear-drives and magnetically levitated trains. But small damping due to noncontact support and nonlinearity in the magnetic force can easily cause complicated phenomena of nonlinear dynamics. This research deals with nonlinear oscillation of a rigid bar supported at its both ends by electro-magnetic forces between superconductors and permanent magnets as a simple modeling of the above application. Deriving the equation of motion, we discussed an effect of nonlinearity in the magnetic force on dynamics of the levitated body: occurrence of combination resonance in the asymmetrical system. Numerical analyses and experiments were also carried out, and their results confirmed the above theoretical prediction.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Attitude control/momentum management and payload pointing in advanced space vehicles

NASA Technical Reports Server (NTRS)

Parlos, Alexander G.; Jayasuriya, Suhada

1990-01-01

The design and evaluation of an attitude control/momentum management system for highly asymmetric spacecraft configurations are presented. The preliminary development and application of a nonlinear control system design methodology for tracking control of uncertain systems, such as spacecraft payload pointing systems are also presented. Control issues relevant to both linear and nonlinear rigid-body spacecraft dynamics are addressed, whereas any structural flexibilities are not taken into consideration. Results from the first task indicate that certain commonly used simplifications in the equations of motions result in unstable attitude control systems, when used for highly asymmetric spacecraft configurations. An approach is suggested circumventing this problem. Additionally, even though preliminary results from the second task are encouraging, the proposed nonlinear control system design method requires further investigation prior to its application and use as an effective payload pointing system design technique.

Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities

NASA Astrophysics Data System (ADS)

Triki, Houria; Biswas, Anjan; Milović, Daniela; Belić, Milivoj

2016-05-01

We consider a high-order nonlinear Schrödinger equation with competing cubic-quintic-septic nonlinearities, non-Kerr quintic nonlinearity, self-steepening, and self-frequency shift. The model describes the propagation of ultrashort (femtosecond) optical pulses in highly nonlinear optical fibers. A new ansatz is adopted to obtain nonlinear chirp associated with the propagating femtosecond soliton pulses. It is shown that the resultant elliptic equation of the problem is of high order, contains several new terms and is more general than the earlier reported results, thus providing a systematic way to find exact chirped soliton solutions of the septic model. Novel soliton solutions, including chirped bright, dark, kink and fractional-transform soliton solutions are obtained for special choices of parameters. Furthermore, we present the parameter domains in which these optical solitons exist. The nonlinear chirp associated with each of the solitonic solutions is also determined. It is shown that the chirping is proportional to the intensity of the wave and depends on higher-order nonlinearities. Of special interest is the soliton solution of the bright and dark type, determined for the general case when all coefficients in the equation have nonzero values. These results can be useful for possible chirped-soliton-based applications of highly nonlinear optical fiber systems.

Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems

NASA Astrophysics Data System (ADS)

Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei

2016-07-01

This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.

A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1998-01-01

This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.

Study of the use of a nonlinear, rate limited, filter on pilot control signals

NASA Technical Reports Server (NTRS)

Adams, J. J.

1977-01-01

The use of a filter on the pilot's control output could improve the performance of the pilot-aircraft system. What is needed is a filter with a sharp high frequency cut-off, no resonance peak, and a minimum of lag at low frequencies. The present investigation studies the usefulness of a nonlinear, rate limited, filter in performing the needed function. The nonlinear filter is compared with a linear, first order filter, and no filter. An analytical study using pilot models and a simulation study using experienced test pilots was performed. The results showed that the nonlinear filter does promote quick, steady maneuvering. It is shown that the nonlinear filter attenuates the high frequency remnant and adds less phase lag to the low frequency signal than does the linear filter. It is also shown that the rate limit in the nonlinear filter can be set to be too restrictive, causing an unstable pilot-aircraft system response.

A therapy inactivating the tumor angiogenic factors.

PubMed

Morales-Rodrigo, Cristian

2013-02-01

This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. The main feature of the model under consideration is a nonlinear flux production of tumor angiogenic factors at the boundary of the tumor. It is proved the global existence for the nonlinear system and the effect in the large time behavior of the system for high doses of the therapeutic agent.

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.

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.

Relationships between nonlinear normal modes and response to random inputs

NASA Astrophysics Data System (ADS)

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2017-02-01

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.

Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle.

PubMed

Serebryannikov, E E; Zheltikov, A M

2014-07-25

Ultrafast ionization dynamics within the field half cycle is shown to be the key physical factor that controls the properties of optical nonlinearity as a function of the carrier wavelength and intensity of a driving laser field. The Schrödinger-equation analysis of a generic hydrogen quantum system reveals universal tendencies in the wavelength dependence of optical nonlinearity, shedding light on unusual properties of optical nonlinearities in the midinfrared. For high-intensity low-frequency fields, free-state electrons are shown to dominate over bound electrons in the overall nonlinear response of a quantum system. In this regime, semiclassical models are shown to offer useful insights into the physics behind optical nonlinearity.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Voltage-Induced Nonlinear Conduction Properties of Epoxy Resin/Micron-Silver Particles Composites

NASA Astrophysics Data System (ADS)

Qu, Zhaoming; Lu, Pin; Yuan, Yang; Wang, Qingguo

2018-01-01

The nonlinear conduction properties of epoxy resin (ER)/micron-silver particles (MP) composites were investigated. Under sufficient high intensity applied constant voltage, the obvious nonlinear conduction properties of the samples with volume fraction 25% were found. With increments in the voltage, the conductive switching effect was observed. The nonlinear conduction mechanism of the ER/MP composites under high applied voltages could be attributed to the electrical current conducted via discrete paths of conductive particles induced by the electric field. The test results show that the ER/MP composites with nonlinear conduction properties are of great potential application in electromagnetic protection of electron devices and systems.

Distributed Adaptive Neural Network Output Tracking of Leader-Following High-Order Stochastic Nonlinear Multiagent Systems With Unknown Dead-Zone Input.

PubMed

Hua, Changchun; Zhang, Liuliu; Guan, Xinping

2017-01-01

This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

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

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

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.

Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.

PubMed

Li, Yafeng; Hua, Changchun; Wu, Shuangshuang; Guan, Xinping

2017-01-31

In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.

Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

NASA Technical Reports Server (NTRS)

Mukhopadhyay, A. K.

1975-01-01

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

Efficient techniques for forced response involving linear modal components interconnected by discrete nonlinear connection elements

NASA Astrophysics Data System (ADS)

Avitabile, Peter; O'Callahan, John

2009-01-01

Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources. Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration. Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as: equivalent reduced model technique (ERMT);modal modification response technique (MMRT); andcomponent element method (CEM); are presented in this paper and are compared to traditional methods.

LDV measurement of small nonlinearities in flat and curved membranes. A model for eardrum nonlinear acoustic behaviour

NASA Astrophysics Data System (ADS)

Kilian, Gladiné; Pieter, Muyshondt; Joris, Dirckx

2016-06-01

Laser Doppler Vibrometry is an intrinsic highly linear measurement technique which makes it a great tool to measure extremely small nonlinearities in the vibration response of a system. Although the measurement technique is highly linear, other components in the experimental setup may introduce nonlinearities. An important source of artificially introduced nonlinearities is the speaker, which generates the stimulus. In this work, two correction methods to remove the effects of stimulus nonlinearity are investigated. Both correction methods were found to give similar results but have different pros and cons. The aim of this work is to investigate the importance of the conical shape of the eardrum as a source of nonlinearity in hearing. We present measurements on flat and indented membranes. The data shows that the curved membrane exhibit slightly higher levels of nonlinearity compared to the flat membrane.

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

PubMed

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

2017-12-19

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

Analytical simulation of nonlinear response to seismic test excitations of HDR-VKL (Heissdampfreaktor-Versuchskreislauf) piping system

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

Srinivasan, M.G.; Kot, C.A.; Mojtahed, M.

The paper describes the analytical modeling, calculations, and results of the posttest nonlinear simulation of high-level seismic testing of the VKL piping system at the HDR Test Facility in Germany. One of the objectives of the tests was to evaluate analytical methods for calculating the nonlinear response of realistic piping systems subjected to high-level seismic excitation that would induce significant plastic deformation. Two out of the six different pipe-support configurations, (ranging from a stiff system with struts and snubbers to a very flexible system with practically no seismic supports), subjected to simulated earthquakes, were tested at very high levels. Themore » posttest nonlinear calculations cover the KWU configuration, a reasonably compliant system with only rigid struts. Responses for 800% safe-shutdown-earthquake loading were calculated using the NONPIPE code. The responses calculated with NONPIPE were found generally to have the same time trends as the measurements but contained under-, over-, and correct estimates of peak values, almost in equal proportions. The only exceptions were the peak strut forces, which were underestimated as a group. The scatter in the peak value estimate of displacements and strut forces was smaller than that for the strains. The possible reasons for the differences and the effort on further analysis are discussed.« less

An accurate nonlinear stochastic model for MEMS-based inertial sensor error with wavelet networks

NASA Astrophysics Data System (ADS)

El-Diasty, Mohammed; El-Rabbany, Ahmed; Pagiatakis, Spiros

2007-12-01

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been widely used in many applications for positioning and orientation purposes. Traditionally, random walk (RW), Gauss-Markov (GM), and autoregressive (AR) processes have been used to develop the stochastic model in classical Kalman filters. The main disadvantage of classical Kalman filter is the potentially unstable linearization of the nonlinear dynamic system. Consequently, a nonlinear stochastic model is not optimal in derivative-based filters due to the expected linearization error. With a derivativeless-based filter such as the unscented Kalman filter or the divided difference filter, the filtering process of a complicated highly nonlinear dynamic system is possible without linearization error. This paper develops a novel nonlinear stochastic model for inertial sensor error using a wavelet network (WN). A wavelet network is a highly nonlinear model, which has recently been introduced as a powerful tool for modelling and prediction. Static and kinematic data sets are collected using a MEMS-based IMU (DQI-100) to develop the stochastic model in the static mode and then implement it in the kinematic mode. The derivativeless-based filtering method using GM, AR, and the proposed WN-based processes are used to validate the new model. It is shown that the first-order WN-based nonlinear stochastic model gives superior positioning results to the first-order GM and AR models with an overall improvement of 30% when 30 and 60 seconds GPS outages are introduced.

Nonlinear analysis and performance evaluation of the Annular Suspension and Pointing System (ASPS)

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1978-01-01

The Annular Suspension and Pointing System (ASPS) can provide high accurate fine pointing for a variety of solar-, stellar-, and Earth-viewing scientific instruments during space shuttle orbital missions. In this report, a detailed nonlinear mathematical model is developed for the ASPS/Space Shuttle system. The equations are augmented with nonlinear models of components such as magnetic actuators and gimbal torquers. Control systems and payload attitude state estimators are designed in order to obtain satisfactory pointing performance, and statistical pointing performance is predicted in the presence of measurement noise and disturbances.

The Characteristics of Vibration Isolation System with Damping and Stiffness Geometrically Nonlinear

NASA Astrophysics Data System (ADS)

Lu, Ze-Qi; Chen, Li-Qun; Brennan, Michael J.; Li, Jue-Ming; Ding, Hu

2016-09-01

The paper concerns an investigation into the use of both stiffness and damping nonlinearity in the vibration isolator to improve its effectiveness. The nonlinear damping and nonlinear stiffness are both achieved by horizontal damping and stiffness as the way of the geometrical nonlinearity. The harmonic balance method is used to analyze the force transmissibility of such vibration isolation system. It is found that as the horizontal damping increasing, the height of the force transmissibility peak is decreased and the high-frequency force transmissibility is almost the same. The results are also validated by some numerical method. Then the RMS of transmissibility under Gaussian white noise is calculated numerically, the results demonstrate that the beneficial effects of the damping nonlinearity can be achieved under random excitation.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

Reinforcement-learning-based dual-control methodology for complex nonlinear discrete-time systems with application to spark engine EGR operation.

PubMed

Shih, Peter; Kaul, Brian C; Jagannathan, S; Drallmeier, James A

2008-08-01

A novel reinforcement-learning-based dual-control methodology adaptive neural network (NN) controller is developed to deliver a desired tracking performance for a class of complex feedback nonlinear discrete-time systems, which consists of a second-order nonlinear discrete-time system in nonstrict feedback form and an affine nonlinear discrete-time system, in the presence of bounded and unknown disturbances. For example, the exhaust gas recirculation (EGR) operation of a spark ignition (SI) engine is modeled by using such a complex nonlinear discrete-time system. A dual-controller approach is undertaken where primary adaptive critic NN controller is designed for the nonstrict feedback nonlinear discrete-time system whereas the secondary one for the affine nonlinear discrete-time system but the controllers together offer the desired performance. The primary adaptive critic NN controller includes an NN observer for estimating the states and output, an NN critic, and two action NNs for generating virtual control and actual control inputs for the nonstrict feedback nonlinear discrete-time system, whereas an additional critic NN and an action NN are included for the affine nonlinear discrete-time system by assuming the state availability. All NN weights adapt online towards minimization of a certain performance index, utilizing gradient-descent-based rule. Using Lyapunov theory, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight estimates, and observer estimates are shown. The adaptive critic NN controller performance is evaluated on an SI engine operating with high EGR levels where the controller objective is to reduce cyclic dispersion in heat release while minimizing fuel intake. Simulation and experimental results indicate that engine out emissions drop significantly at 20% EGR due to reduction in dispersion in heat release thus verifying the dual-control approach.

Adaptive output feedback control of uncertain nonlinear systems using single-hidden-layer neural networks.

PubMed

Hovakimyan, N; Nardi, F; Calise, A; Kim, Nakwan

2002-01-01

We consider adaptive output feedback control of uncertain nonlinear systems, in which both the dynamics and the dimension of the regulated system may be unknown. However, the relative degree of the regulated output is assumed to be known. Given a smooth reference trajectory, the problem is to design a controller that forces the system measurement to track it with bounded errors. The classical approach requires a state observer. Finding a good observer for an uncertain nonlinear system is not an obvious task. We argue that it is sufficient to build an observer for the output tracking error. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. The theoretical results are illustrated in the design of a controller for a fourth-order nonlinear system of relative degree two and a high-bandwidth attitude command system for a model R-50 helicopter.

Relationships between nonlinear normal modes and response to random inputs

DOE PAGES

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2016-07-25

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). Here, this work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing.more » Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.« less

Connective stability of nonlinear matrix systems

NASA Technical Reports Server (NTRS)

Siljak, D. D.

1974-01-01

Consideration of stability under structural perturbations of free dynamic systems described by the differential equation dx/dt = A(t,x)x, where the matrix A(t,x) has time-varying nonlinear elements. The concept of 'connective stability' is introduced to study the structural properties of competitive-cooperative nonlinear matrix systems. It is shown that stability reliability in such systems is high and that they remain stable despite time-varying (including 'on-off') interaction among individual agents present in the system. The results obtained can be used to study stability aspects of mathematical models arising in as diverse fields as economics, biology, arms races, and transistor circuits.

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.

The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Efficient computational nonlinear dynamic analysis using modal modification response technique

NASA Astrophysics Data System (ADS)

Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2012-08-01

Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

PubMed

Si, Wenjie; Dong, Xunde; Yang, Feifei

2018-03-01

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

A deep belief network with PLSR for nonlinear system modeling.

PubMed

Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

2018-08-01

Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

PubMed

Ecke, Robert E

2015-09-01

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

The Vestibular System Implements a Linear–Nonlinear Transformation In Order to Encode Self-Motion

PubMed Central

Massot, Corentin; Schneider, Adam D.; Chacron, Maurice J.; Cullen, Kathleen E.

2012-01-01

Although it is well established that the neural code representing the world changes at each stage of a sensory pathway, the transformations that mediate these changes are not well understood. Here we show that self-motion (i.e. vestibular) sensory information encoded by VIIIth nerve afferents is integrated nonlinearly by post-synaptic central vestibular neurons. This response nonlinearity was characterized by a strong (∼50%) attenuation in neuronal sensitivity to low frequency stimuli when presented concurrently with high frequency stimuli. Using computational methods, we further demonstrate that a static boosting nonlinearity in the input-output relationship of central vestibular neurons accounts for this unexpected result. Specifically, when low and high frequency stimuli are presented concurrently, this boosting nonlinearity causes an intensity-dependent bias in the output firing rate, thereby attenuating neuronal sensitivities. We suggest that nonlinear integration of afferent input extends the coding range of central vestibular neurons and enables them to better extract the high frequency features of self-motion when embedded with low frequency motion during natural movements. These findings challenge the traditional notion that the vestibular system uses a linear rate code to transmit information and have important consequences for understanding how the representation of sensory information changes across sensory pathways. PMID:22911113

Generalized nonlinear Schrödinger equation and ultraslow optical solitons in a cold four-state atomic system.

PubMed

Hang, Chao; Huang, Guoxiang; Deng, L

2006-03-01

We investigate the influence of high-order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a lifetime broadened four-state atomic system under a Raman excitation. Using a standard method of multiple-scales we derive a generalized nonlinear Schrödinger equation and show that for realistic physical parameters and at the pulse duration of 10(-6)s, the effects of third-order linear dispersion, nonlinear dispersion, and delay in nonlinear refractive index can be significant and may not be considered as perturbations. We provide exact soliton solutions for the generalized nonlinear Schrödinger equation and demonstrate that optical solitons obtained may still have ultraslow propagating velocity. Numerical simulations on the stability and interaction of these ultraslow optical solitons in the presence of linear and differential absorptions are also presented.

A new kind of nonlinear disturbance observer for nonlinear systems with applications to cruise control of air-breathing hypersonic vehicles

NASA Astrophysics Data System (ADS)

Yang, Zhiling; Meng, Bin; Sun, Hongfei

2017-09-01

The nonlinear disturbance observer (NDO) proposed by W. H. Chen et al. needs an assumption that the disturbance varies slowly relative to the observer dynamics (i.e. ?), so as to ensure the convergence of the disturbance observer. When ?, however, there is no guarantee of the convergence in theory. To solve the problem, this paper presents a new NDO, namely high-order nonlinear disturbance observer (HONDO), for a nonlinear system with an unknown fast time-varying disturbance (i.e. ?). The HONDO not only inherits all the advantages of the usual NDO, but also guarantees the convergence of the estimated error for a nonlinear system with a fast time-varying disturbance. Therefore, the HONDO proposed in this paper broadens the application scope of the conventional NDOs, thus is a supplement to the theory of NDO. The numerical simulation for the cruise control of an air-breathing hypersonic vehicle further verifies the effectiveness of the HONDO-based control.

Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

A nonlinear vibration isolator achieving high-static-low-dynamic stiffness and tunable anti-resonance frequency band

NASA Astrophysics Data System (ADS)

Sun, Xiuting; Jing, Xingjian

2016-12-01

This study investigates theoretically and experimentally a vibration isolator constructed by an n-layer Scissor-Like Structure (SLS), focusing on the analysis and design of nonlinear stiffness and damping characteristics for advantageous isolation performance in both orthogonal directions. With the mathematical modeling, the influence incurred by different structural parameters on system isolation performance is studied. It is shown that, (a) nonlinear high-static-low-dynamic stiffness and damping characteristics can be seen such that the system can achieve good isolation performance in both directions, (b) an anti-resonance frequency band exists due to the coupling effect between the linear and nonlinear stiffness in the two orthogonal directions within the structure, and (c) all these performances are designable with several structural parameters. The advantages of the proposed system are shown through comparisons with an existing quasi-zero-stiffness vibration isolator (QZS-VI) and a traditional mass-spring-damper vibration isolator (MSD-VI), and further validated by experimental results.

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

PubMed

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

On the Modeling of Shells in Multibody Dynamics

NASA Technical Reports Server (NTRS)

Bauchau, Olivier A.; Choi, Jou-Young; Bottasso, Carlo L.

2000-01-01

Energy preserving/decaying schemes are presented for the simulation of the nonlinear multibody systems involving shell components. The proposed schemes are designed to meet four specific requirements: unconditional nonlinear stability of the scheme, a rigorous treatment of both geometric and material nonlinearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. The kinematic nonlinearities associated with arbitrarily large displacements and rotations of shells are treated in a rigorous manner, and the material nonlinearities can be handled when the, constitutive laws stem from the existence of a strain energy density function. The efficiency and robustness of the proposed approach is illustrated with specific numerical examples that also demonstrate the need for integration schemes possessing high frequency numerical dissipation.

Energy transfer in mesoscopic vibrational systems enabled by eigenfrequency fluctuations

NASA Astrophysics Data System (ADS)

Atalaya, Juan

Energy transfer between low-frequency vibrational modes can be achieved by means of nonlinear coupling if their eigenfrequencies fulfill certain nonlinear resonance conditions. Because of the discreteness of the vibrational spectrum at low frequencies, such conditions may be difficult to satisfy for most low-frequency modes in typical mesoscopic vibrational systems. Fluctuations of the vibrational eigenfrequencies can also be relatively strong in such systems. We show that energy transfer between modes can occur in the absence of nonlinear resonance if frequency fluctuations are allowed. The case of three modes with cubic nonlinear coupling and no damping is particularly interesting. It is found that the system has a non-thermal equilibrium state which depends only on the initial conditions. The rate at which the system approaches to such state is determined by the parameters such as the noise strength and correlation time, the nonlinearity strength and the detuning from exact nonlinear resonance. We also discuss the case of many weakly coupled modes. Our results shed light on the problem of energy relaxation of low-frequency vibrational modes into the continuum of high-frequency vibrational modes. The results have been obtained with Mark Dykman. Alternative email: jatalaya2012@gmail.com.

Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber.

PubMed

Ta'eed, Vahid G; Fu, Libin; Pelusi, Mark; Rochette, Martin; Littler, Ian C; Moss, David J; Eggleton, Benjamin J

2006-10-30

We present the first demonstration of all optical wavelength conversion in chalcogenide glass fiber including system penalty measurements at 10 Gb/s. Our device is based on As2Se3 chalcogenide glass fiber which has the highest Kerr nonlinearity (n(2)) of any fiber to date for which either advanced all optical signal processing functions or system penalty measurements have been demonstrated. We achieve wavelength conversion via cross phase modulation over a 10 nm wavelength range near 1550 nm with 7 ps pulses at 2.1 W peak pump power in 1 meter of fiber, achieving only 1.4 dB excess system penalty. Analysis and comparison of the fundamental fiber parameters, including nonlinear coefficient, two-photon absorption coefficient and dispersion parameter with other nonlinear glasses shows that As(2)Se(3) based devices show considerable promise for radically integrated nonlinear signal processing devices.

Model Capabilities | Regional Energy Deployment System Model | Energy

Science.gov Websites

representation of those effects throughout the scenario. Because those effects are highly non-linear and other models, limited foresight, price penalties for rapid growth, and other non-linear effects

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

NASA Astrophysics Data System (ADS)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-04-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

Neural network L1 adaptive control of MIMO systems with nonlinear uncertainty.

PubMed

Zhen, Hong-tao; Qi, Xiao-hui; Li, Jie; Tian, Qing-min

2014-01-01

An indirect adaptive controller is developed for a class of multiple-input multiple-output (MIMO) nonlinear systems with unknown uncertainties. This control system is comprised of an L 1 adaptive controller and an auxiliary neural network (NN) compensation controller. The L 1 adaptive controller has guaranteed transient response in addition to stable tracking. In this architecture, a low-pass filter is adopted to guarantee fast adaptive rate without generating high-frequency oscillations in control signals. The auxiliary compensation controller is designed to approximate the unknown nonlinear functions by MIMO RBF neural networks to suppress the influence of uncertainties. NN weights are tuned on-line with no prior training and the project operator ensures the weights bounded. The global stability of the closed-system is derived based on the Lyapunov function. Numerical simulations of an MIMO system coupled with nonlinear uncertainties are used to illustrate the practical potential of our theoretical results.

Ultra-low-power hybrid light–matter solitons

PubMed Central

Walker, P. M.; Tinkler, L.; Skryabin, D. V.; Yulin, A.; Royall, B.; Farrer, I.; Ritchie, D. A.; Skolnick, M. S.; Krizhanovskii, D. N.

2015-01-01

New functionalities in nonlinear optics will require systems with giant optical nonlinearity as well as compatibility with photonic circuit fabrication techniques. Here we introduce a platform based on strong light–matter coupling between waveguide photons and quantum-well excitons. On a sub-millimetre length scale we generate picosecond bright temporal solitons at a pulse energy of only 0.5 pJ. From this we deduce a nonlinear refractive index three orders of magnitude larger than in any other ultrafast system. We study both temporal and spatio-temporal nonlinear effects and observe dark–bright spatio-temporal polariton solitons. Theoretical modelling of soliton formation in the strongly coupled system confirms the experimental observations. These results show the promise of our system as a high speed, low power, integrated platform for physics and devices based on strong interactions between photons. PMID:26400748

Ultra-low-power hybrid light-matter solitons.

PubMed

Walker, P M; Tinkler, L; Skryabin, D V; Yulin, A; Royall, B; Farrer, I; Ritchie, D A; Skolnick, M S; Krizhanovskii, D N

2015-09-24

New functionalities in nonlinear optics will require systems with giant optical nonlinearity as well as compatibility with photonic circuit fabrication techniques. Here we introduce a platform based on strong light-matter coupling between waveguide photons and quantum-well excitons. On a sub-millimetre length scale we generate picosecond bright temporal solitons at a pulse energy of only 0.5 pJ. From this we deduce a nonlinear refractive index three orders of magnitude larger than in any other ultrafast system. We study both temporal and spatio-temporal nonlinear effects and observe dark-bright spatio-temporal polariton solitons. Theoretical modelling of soliton formation in the strongly coupled system confirms the experimental observations. These results show the promise of our system as a high speed, low power, integrated platform for physics and devices based on strong interactions between photons.

Linearizing an intermodulation radar transmitter by filtering switched tones

NASA Astrophysics Data System (ADS)

Mazzaro, Gregory J.; Sherbondy, Andrew J.; Ranney, Kenneth I.; Sherbondy, Kelly D.; Martone, Anthony F.

2017-05-01

For nonlinear radar, the transmit power required to measure a detectable response from a target is relatively high, and generating that high power is achieved at the cost of linearity. This paper applies the distortion mitigation technique Linearization by Time-Multiplexed Spectrum (LITMUS) to intermodulation radar, a type of nonlinear radar which receives spectral content produced by the mixing of multiple frequencies at a nonlinear target. By implementing LITMUS, an experimental detection system for an intermodulation radar achieves a signal-to-noise ratio up to 20 dB for a total transmit power of approximately 80 mW and nonlinear targets placed at a standoff distance of 2 meters.

Nonlinear refraction and two-photon absorption in dense 2Bi{sub 2}O{sub 3}-B{sub 2}O{sub 3} glasses

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

Paramesh, Gadige; Varma, K. B. R.

2012-06-05

High density transparent glasses (7.86 g/cc) were fabricated in the 2Bi{sub 2}O{sub 3}-B{sub 2}O{sub 3} (BBO) system. Optical band gap of the obtained glasses was found to be 2.6eV. The refractive index measured for these glasses was 2.25{+-}0.05 at {lambda}=543 nm. Nonlinear refraction and absorption studies were carried out on the BBO glasses using z-scan technique at {lambda}=532 nm of 10 ns pulse width. The nonlinear refractive index obtained was n{sub 2}=12.1x10{sup -14} cm{sup 2}/W and nonlinear absorption coefficient was {beta}=15.2 cm/GW. The n{sub 2} and {beta} values of the BBO glasses were large compared to the other reported highmore » index bismuth based oxide glass systems in the literature. These were attributed to the high density, high linear refractive index, low band gap and two photon absorption associated with these glasses. The electronic origin of large nonlinearities was discussed based on bond-orbital theory.« less

Dynamic analysis of nonlinear rotor-housing systems

NASA Technical Reports Server (NTRS)

Noah, Sherif T.

1988-01-01

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

Nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating embedded in water

NASA Astrophysics Data System (ADS)

Jiménez, N.; Romero-García, V.; Picó, R.; Garcia-Raffi, L. M.; Staliunas, K.

2015-11-01

We report the nonlinear focusing of ultrasonic waves by an axisymmetric diffraction grating immersed in water. In the linear regime, the system presents high focal gain (32 dB), with a narrow beam-width and intense side lobes as it is common in focusing by Fresnel-like lenses. Activating the nonlinearity of the host medium by using high amplitude incident waves, the focusing properties of the lens dramatically change. Theoretical predictions show that the focal gain of the system extraordinary increases in the strongly nonlinear regime (Mach number of 6.1 × 10-4). Particularly, the harmonic generation is locally activated at the focal spot, and the second harmonic beam is characterized by strongly reduced side-lobes and an excellent beam profile as experiments show in agreement with theory. The results can motivate applications in medical therapy or second harmonic imaging.

Single axis control of ball position in magnetic levitation system using fuzzy logic control

NASA Astrophysics Data System (ADS)

Sahoo, Narayan; Tripathy, Ashis; Sharma, Priyaranjan

2018-03-01

This paper presents the design and real time implementation of Fuzzy logic control(FLC) for the control of the position of a ferromagnetic ball by manipulating the current flowing in an electromagnet that changes the magnetic field acting on the ball. This system is highly nonlinear and open loop unstable. Many un-measurable disturbances are also acting on the system, making the control of it highly complex but interesting for any researcher in control system domain. First the system is modelled using the fundamental laws, which gives a nonlinear equation. The nonlinear model is then linearized at an operating point. Fuzzy logic controller is designed after studying the system in closed loop under PID control action. The controller is then implemented in real time using Simulink real time environment. The controller is tuned manually to get a stable and robust performance. The set point tracking performance of FLC and PID controllers were compared and analyzed.

Vertically homogeneous stationary tornado-type vortex

NASA Astrophysics Data System (ADS)

Rutkevich, P. B.; Rutkevych, P. P.

2010-05-01

Tornado is regarded as one of the most dangerous atmosphere phenomena. The tornado phenomenon has been intensively studied so far, however, there is still no established and accepted theory of how tornadoes form, an uncertainty still exists concerning extreme winds and pressure drops in tornadoes. It is commonly accepted that it is possible to describe tornado from the set of nonlinear hydrodynamical equations, however, it is still unclear which non-linear processes are responsible for its formation. Nonlinear terms in the system are associated with either centrifugal force, or entropy transport, or transport of humidity. It appears that the amount and spatial distribution of precipitation with the convection are important indicators of the weather phenomena associated with a particular storm. The low-precipitation supercells that produce relatively little precipitation and yet show clear visual signs of rotation. Low-precipitation supercells occur most often near the surface dryline and, owing to the sparse precipitation and relatively dry environments with little cloudiness. Low-precipitation storms are frequently non-tornadic and many are non-severe despite exhibiting persistent rotation. On the other hand, the so-called high-precipitation storms are characterized by substantial precipitation within their mesocyclonic circulations. When high-precipitation storms have a recognizable hook radar echo, reflectivity in the hook is comparable to those in the precipitation core. High-precipitation supercells are probably the most common form of supercell and produce severe weather of all types including tornadoes. Therefore, in this work we consider a hydrodynamic system with only one nonlinear term associated with atmosphere humidity, which yields energy to the system. The tornado vortex is usually to a good approximation cylindrical so we use cylindrical geometry and homogeneity in vertical direction. In this case the problem reduces to a system of ordinary differential equations. Rotation in the vortex is associated with compressibility so we also take into account the compressibility of the gas. Under certain approximations the problem reduces to a single high-order nonlinear equation. Numerical solution of the obtained high-order equation describes all three velocity components and all thermodynamic parameters in the system. The system exhibits high rotation and strong vertical air flow in the middle part of the vortex.

Adaptive Control for Uncertain Nonlinear Multi-Input Multi-Output Systems

NASA Technical Reports Server (NTRS)

Cao, Chengyu (Inventor); Hovakimyan, Naira (Inventor); Xargay, Enric (Inventor)

2014-01-01

Systems and methods of adaptive control for uncertain nonlinear multi-input multi-output systems in the presence of significant unmatched uncertainty with assured performance are provided. The need for gain-scheduling is eliminated through the use of bandwidth-limited (low-pass) filtering in the control channel, which appropriately attenuates the high frequencies typically appearing in fast adaptation situations and preserves the robustness margins in the presence of fast adaptation.

A simple attitude control of quadrotor helicopter based on Ziegler-Nichols rules for tuning PD parameters.

PubMed

He, ZeFang; Zhao, Long

2014-01-01

An attitude control strategy based on Ziegler-Nichols rules for tuning PD (proportional-derivative) parameters of quadrotor helicopters is presented to solve the problem that quadrotor tends to be instable. This problem is caused by the narrow definition domain of attitude angles of quadrotor helicopters. The proposed controller is nonlinear and consists of a linear part and a nonlinear part. The linear part is a PD controller with PD parameters tuned by Ziegler-Nichols rules and acts on the quadrotor decoupled linear system after feedback linearization; the nonlinear part is a feedback linearization item which converts a nonlinear system into a linear system. It can be seen from the simulation results that the attitude controller proposed in this paper is highly robust, and its control effect is better than the other two nonlinear controllers. The nonlinear parts of the other two nonlinear controllers are the same as the attitude controller proposed in this paper. The linear part involves a PID (proportional-integral-derivative) controller with the PID controller parameters tuned by Ziegler-Nichols rules and a PD controller with the PD controller parameters tuned by GA (genetic algorithms). Moreover, this attitude controller is simple and easy to implement.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

NASA Astrophysics Data System (ADS)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

A high-accuracy algorithm for solving nonlinear PDEs with high-order spatial derivatives in 1 + 1 dimensions

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

Yao, Jian Hua; Gooding, R.J.

1994-06-01

We propose an algorithm to solve a system of partial differential equations of the type u[sub t](x,t) = F(x, t, u, u[sub x], u[sub xx], u[sub xxx], u[sub xxxx]) in 1 + 1 dimensions using the method of lines with piecewise ninth-order Hermite polynomials, where u and F and N-dimensional vectors. Nonlinear boundary conditions are easily incorporated with this method. We demonstrate the accuracy of this method through comparisons of numerically determine solutions to the analytical ones. Then, we apply this algorithm to a complicated physical system involving nonlinear and nonlocal strain forces coupled to a thermal field. 4 refs.,more » 5 figs., 1 tab.« less

Analysis of Nonlinear Dynamics by Square Matrix Method

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

Yu, Li Hua

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. Andmore » more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.« less

The coupled nonlinear dynamics of a lift system

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

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk

2014-12-10

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This papermore » presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.« less

RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios.

PubMed

Tang, Zhi-Ling; Li, Si-Min; Yu, Li-Juan

2016-06-09

Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system's starting oscillation is determined, and the simulation results of the system's response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured.

Roles of dispersal, stochasticity, and nonlinear dynamics in the spatial structuring of seasonal natural enemy-victim populations

Treesearch

Patrick C. Tobin; Ottar N. Bjornstad

2005-01-01

Natural enemy-victim systems may exhibit a range of dynamic space-time patterns. We used a theoretical framework to study spatiotemporal structuring in a transient natural enemy-victim system subject to differential rates of dispersal, stochastic forcing, and nonlinear dynamics. Highly mobile natural enemies that attacked less mobile victims were locally spatially...

Fibre-optic nonlinear optical microscopy and endoscopy.

PubMed

Fu, L; Gu, M

2007-06-01

Nonlinear optical microscopy has been an indispensable laboratory tool of high-resolution imaging in thick tissue and live animals. Rapid developments of fibre-optic components in terms of growing functionality and decreasing size provide enormous opportunities for innovations in nonlinear optical microscopy. Fibre-based nonlinear optical endoscopy is the sole instrumentation to permit the cellular imaging within hollow tissue tracts or solid organs that are inaccessible to a conventional optical microscope. This article reviews the current development of fibre-optic nonlinear optical microscopy and endoscopy, which includes crucial technologies for miniaturized nonlinear optical microscopy and their embodiments of endoscopic systems. A particular attention is given to several classes of photonic crystal fibres that have been applied to nonlinear optical microscopy due to their unique properties for ultrashort pulse delivery and signal collection. Furthermore, fibre-optic nonlinear optical imaging systems can be classified into portable microscopes suitable for imaging behaving animals, rigid endoscopes that allow for deep tissue imaging with minimally invasive manners, and flexible endoscopes enabling imaging of internal organs. Fibre-optic nonlinear optical endoscopy is coming of age and a paradigm shift leading to optical microscope tools for early cancer detection and minimally invasive surgery.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

NASA Astrophysics Data System (ADS)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

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.

Adaptive variable structure hierarchical fuzzy control for a class of high-order nonlinear dynamic systems.

PubMed

Mansouri, Mohammad; Teshnehlab, Mohammad; Aliyari Shoorehdeli, Mahdi

2015-05-01

In this paper, a novel adaptive hierarchical fuzzy control system based on the variable structure control is developed for a class of SISO canonical nonlinear systems in the presence of bounded disturbances. It is assumed that nonlinear functions of the systems be completely unknown. Switching surfaces are incorporated into the hierarchical fuzzy control scheme to ensure the system stability. A fuzzy soft switching system decides the operation area of the hierarchical fuzzy control and variable structure control systems. All the nonlinearly appeared parameters of conclusion parts of fuzzy blocks located in different layers of the hierarchical fuzzy control system are adjusted through adaptation laws deduced from the defined Lyapunov function. The proposed hierarchical fuzzy control system reduces the number of rules and consequently the number of tunable parameters with respect to the ordinary fuzzy control system. Global boundedness of the overall adaptive system and the desired precision are achieved using the proposed adaptive control system. In this study, an adaptive hierarchical fuzzy system is used for two objectives; it can be as a function approximator or a control system based on an intelligent-classic approach. Three theorems are proven to investigate the stability of the nonlinear dynamic systems. The important point about the proposed theorems is that they can be applied not only to hierarchical fuzzy controllers with different structures of hierarchical fuzzy controller, but also to ordinary fuzzy controllers. Therefore, the proposed algorithm is more general. To show the effectiveness of the proposed method four systems (two mechanical, one mathematical and one chaotic) are considered in simulations. Simulation results demonstrate the validity, efficiency and feasibility of the proposed approach to control of nonlinear dynamic systems. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Data-driven methods towards learning the highly nonlinear inverse kinematics of tendon-driven surgical manipulators.

PubMed

Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang

2017-09-01

Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.

Structure Detection of Nonlinear Aeroelastic Systems with Application to Aeroelastic Flight Test Data. Part 2

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Brenner, martin J.

2006-01-01

This viewgraph presentation reviews the 1. Motivation for the study 2. Nonlinear Model Form 3. Structure Detection 4. Least Absolute Shrinkage and Selection Operator (LASSO) 5. Objectives 6. Results 7. Assess LASSO as a Structure Detection Tool: Simulated Nonlinear Models 8. Applicability to Complex Systems: F/A-18 Active Aeroelastic Wing Flight Test Data. The authors conclude that 1. this is a novel approach for detecting the structure of highly over-parameterised nonlinear models in situations where other methods may be inadequate 2. that it is a practical significance in the analysis of aircraft dynamics during envelope expansion and could lead to more efficient control strategies and 3. this could allow greater insight into the functionality of various systems dynamics, by providing a quantitative model which is easily interpretable

Global output feedback control for a class of high-order feedforward nonlinear systems with input delay.

PubMed

Zha, Wenting; Zhai, Junyong; Fei, Shumin

2013-07-01

This paper investigates the problem of output feedback stabilization for a class of high-order feedforward nonlinear systems with time-varying input delay. First, a scaling gain is introduced into the system under a set of coordinate transformations. Then, the authors construct an observer and controller to make the nominal system globally asymptotically stable. Based on homogeneous domination approach and Lyapunov-Krasovskii functional, it is shown that the closed-loop system can be rendered globally asymptotically stable by the scaling gain. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Linear and nonlinear dynamics of isospectral granular chains

NASA Astrophysics Data System (ADS)

Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

2017-04-01

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

NASA Astrophysics Data System (ADS)

Khatri, Devvrath

A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications. The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a finite element model (FEM) using the commercially available software Abaqus, which takes into account many of these characteristic features. The finite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specific application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation in the applications of HNSWs as information carriers.

Blended particle filters for large-dimensional chaotic dynamical systems

PubMed Central

Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

2014-01-01

A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

Koopman operator theory: Past, present, and future

NASA Astrophysics Data System (ADS)

Brunton, Steven; Kaiser, Eurika; Kutz, Nathan

2017-11-01

Koopman operator theory has emerged as a dominant method to represent nonlinear dynamics in terms of an infinite-dimensional linear operator. The Koopman operator acts on the space of all possible measurement functions of the system state, advancing these measurements with the flow of the dynamics. A linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. Dynamic mode decomposition has become the leading data-driven method to approximate the Koopman operator, although there are still open questions and challenges around how to obtain accurate approximations for strongly nonlinear systems. This talk will provide an introductory overview of modern Koopman operator theory, reviewing the basics and describing recent theoretical and algorithmic developments. Particular emphasis will be placed on the use of data-driven Koopman theory to characterize and control high-dimensional fluid dynamic systems. This talk will also address key advances in the rapidly growing fields of machine learning and data science that are likely to drive future developments.

Six-component semi-discrete integrable nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2018-01-01

We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.

Intelligent Tracking Control for a Class of Uncertain High-Order Nonlinear Systems.

PubMed

Zhao, Xudong; Shi, Peng; Zheng, Xiaolong; Zhang, Jianhua

2016-09-01

This brief is concerned with the problem of intelligent tracking control for a class of high-order nonlinear systems with completely unknown nonlinearities. An intelligent adaptive control algorithm is presented by combining the adaptive backstepping technique with the neural networks' approximation ability. It is shown that the practical output tracking performance of the system is achieved using the proposed state-feedback controller under two mild assumptions. In particular, by introducing a parameter in the derivations, the tracking error between the time-varying target signal and the output can be reduced via tuning the controller design parameters. Moreover, in order to solve the problem of overparameterization, which is a common issue in adaptive control design, a controller with one adaptive law is also designed. Finally, simulation results are given to show the effectiveness of the theoretical approaches and the potential of the proposed new design techniques.

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.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

PubMed

Ren, Pengyu; Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons

PubMed Central

Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system. PMID:29304173

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.

Investigation of a mathematical model of the system of electro-optical sensors for monitoring nonlinear surfaces

NASA Astrophysics Data System (ADS)

Petrochenko, Andrew V.; Konyakhin, Igor A.

2015-06-01

Actually during construction of the high building actively are used objects of various nonlinear surface, for example, sinuous (parabolic or hyperbolic) roofs of the sport complexes that require automatic deformation control [1,2,3,4]. This type of deformation has character of deflection that is impossible to monitor objectively with just one optoelectronic sensor (which is fixed on this surface). In this article is described structure of remote optoelectronic sensor, which is part of the optoelectronic monitoring system of nonlinear surface, and mathematical transformation of exterior orientation sensor elements in the coordinates of control points.

Application of dynamical systems theory to nonlinear aircraft dynamics

NASA Technical Reports Server (NTRS)

Culick, Fred E. C.; Jahnke, Craig C.

1988-01-01

Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.

Nonlinearity analysis of measurement model for vision-based optical navigation system

NASA Astrophysics Data System (ADS)

Li, Jianguo; Cui, Hutao; Tian, Yang

2015-02-01

In the autonomous optical navigation system based on line-of-sight vector observation, nonlinearity of measurement model is highly correlated with the navigation performance. By quantitatively calculating the degree of nonlinearity of the focal plane model and the unit vector model, this paper focuses on determining which optical measurement model performs better. Firstly, measurement equations and measurement noise statistics of these two line-of-sight measurement models are established based on perspective projection co-linearity equation. Then the nonlinear effects of measurement model on the filter performance are analyzed within the framework of the Extended Kalman filter, also the degrees of nonlinearity of two measurement models are compared using the curvature measure theory from differential geometry. Finally, a simulation of star-tracker-based attitude determination is presented to confirm the superiority of the unit vector measurement model. Simulation results show that the magnitude of curvature nonlinearity measurement is consistent with the filter performance, and the unit vector measurement model yields higher estimation precision and faster convergence properties.

Fault Detection for Nonlinear Process With Deterministic Disturbances: A Just-In-Time Learning Based Data Driven Method.

PubMed

Yin, Shen; Gao, Huijun; Qiu, Jianbin; Kaynak, Okyay

2017-11-01

Data-driven fault detection plays an important role in industrial systems due to its applicability in case of unknown physical models. In fault detection, disturbances must be taken into account as an inherent characteristic of processes. Nevertheless, fault detection for nonlinear processes with deterministic disturbances still receive little attention, especially in data-driven field. To solve this problem, a just-in-time learning-based data-driven (JITL-DD) fault detection method for nonlinear processes with deterministic disturbances is proposed in this paper. JITL-DD employs JITL scheme for process description with local model structures to cope with processes dynamics and nonlinearity. The proposed method provides a data-driven fault detection solution for nonlinear processes with deterministic disturbances, and owns inherent online adaptation and high accuracy of fault detection. Two nonlinear systems, i.e., a numerical example and a sewage treatment process benchmark, are employed to show the effectiveness of the proposed method.

Plasmon resonance enhancement of nonlinear properties of amino acids

NASA Astrophysics Data System (ADS)

de Araujo, Renato E.; Rativa, Diego; Gomes, Anderson S. L.

2007-02-01

Here we analyze the influence of 9 nm (mean diameter) silver particles on the nonlinear properties of intrinsic cell molecules. A novel high sensitivity thermal managed eclipse Z-scan technique with a femtosecond laser system was used to analyze the nonlinear susceptibility of water solution of fluorescent and non-fluorescent amino acids (Tryptophan, Tyrosine, Phenylalanine, Proline and Histidine) with different concentration of silver nanoparticles. The generalized Maxwell Garnett model is used to explain the behavior of the measured nonlinear refractive index with the change of the nanoparticles concentration in the sample.

Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Internal resonance of an elastic body levitated above high-Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Kokuzawa, T.; Toshihiko, S.; Yoshizawa, M.

2010-06-01

In high-Tc superconducting magnetic levitation systems, levitated bodies can keep stable levitation with no contact and no control and thus their damping is very small. Thanks to these features, their applications to various apparatus are expected. However, on account of their small damping, the nonlinearity of electromagnetic levitation force can give notable effects upon motion of the levitated bodies. Therefore this nonlinearity must be taken into account to accurately analyze the dynamical behavior of the levitated bodies. Structures of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Therefore, we need to deal with the model as an elastic body. As mentioned above, nonlinear characteristics easily appear in this elastic vibration on account of the small damping. Especially when the ratio of the natural frequencies of the eigenmodes is integer, internal resonance can occur. This nonlinear resonance is derived from nonlinear interactions among the eigenmodes of the elastic levitated body. This kind of internal resonance of an elastic body appearing in high-Tc superconducting levitation systems has not been studied so far. This research especially deals with internal resonance of a beam supported at both its ends by electromagnetic forces acting on permanent magnets. The governing equation with the nonlinear boundary conditions for the dynamics of a levitated beam has been derived. Numerical results show internal resonance of the 1st mode and the 3rd mode. Experimental results are qualitatively in good agreement with numerical ones.

Design of Life Extending Controls Using Nonlinear Parameter Optimization

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Holmes, Michael S.; Ray, Asok

1998-01-01

This report presents the conceptual development of a life extending control system where the objective is to achieve high performance and structural durability of the plant. A life extending controller is designed for a reusable rocket engine via damage mitigation in both the fuel and oxidizer turbines while achieving high performance for transient responses of the combustion chamber pressure and the O2/H2 mixture ratio. This design approach makes use of a combination of linear and nonlinear controller synthesis techniques and also allows adaptation of the life extending controller module to augment a conventional performance controller of a rocket engine. The nonlinear aspect of the design is achieved using nonlinear parameter optimization of a prescribed control structure.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

PubMed

Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F

2016-10-21

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

NASA Astrophysics Data System (ADS)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-10-01

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Vibrational energy harvesting by exploring structural benefits and nonlinear characteristics

NASA Astrophysics Data System (ADS)

Wei, Chongfeng; Jing, Xingjian

2017-07-01

Traditional energy harvesters are often of low efficiency due to very limited energy harvesting bandwidth, which should also be enough close to the ambient excitation frequency. To overcome this difficulty, some attempts can be seen in the literature typically with the purposes of either increasing the energy harvesting bandwidth with a harvester array, or enhancing the energy harvesting bandwidth and peak with nonlinear coupling effect etc. This paper presents an alternative way which can achieve tuneable resonant frequency (from high frequency to ultralow frequency) and improved energy harvesting bandwidth and peak simultaneously by employing special structural benefits and advantageous displacement-dependent nonlinear damping property. The proposed energy harvesting system employs a lever systems combined with an X-shape supporting structure and demonstrates very adjustable stiffness and unique nonlinear damping characteristics which are very beneficial for energy harvesting. It is shown that the energy harvesting performance of the proposed system is directly determined by several easy-to-tune structural parameters and also by the relative displacement in a special nonlinear manner, which provides a great flexibility and/or a unique tool for tuning and improving energy harvesting efficiency via matching excitation frequencies and covering a broader frequency band. This study potentially provides a new insight into the design of energy harvesting systems by employing structural benefits and geometrical nonlinearities.

A Simple Attitude Control of Quadrotor Helicopter Based on Ziegler-Nichols Rules for Tuning PD Parameters

PubMed Central

He, ZeFang

2014-01-01

An attitude control strategy based on Ziegler-Nichols rules for tuning PD (proportional-derivative) parameters of quadrotor helicopters is presented to solve the problem that quadrotor tends to be instable. This problem is caused by the narrow definition domain of attitude angles of quadrotor helicopters. The proposed controller is nonlinear and consists of a linear part and a nonlinear part. The linear part is a PD controller with PD parameters tuned by Ziegler-Nichols rules and acts on the quadrotor decoupled linear system after feedback linearization; the nonlinear part is a feedback linearization item which converts a nonlinear system into a linear system. It can be seen from the simulation results that the attitude controller proposed in this paper is highly robust, and its control effect is better than the other two nonlinear controllers. The nonlinear parts of the other two nonlinear controllers are the same as the attitude controller proposed in this paper. The linear part involves a PID (proportional-integral-derivative) controller with the PID controller parameters tuned by Ziegler-Nichols rules and a PD controller with the PD controller parameters tuned by GA (genetic algorithms). Moreover, this attitude controller is simple and easy to implement. PMID:25614879

Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Tikan, Alexey; Billet, Cyril; El, Gennady; Tovbis, Alexander; Bertola, Marco; Sylvestre, Thibaut; Gustave, Francois; Randoux, Stephane; Genty, Goëry; Suret, Pierre; Dudley, John M.

2017-07-01

We report experimental confirmation of the universal emergence of the Peregrine soliton predicted to occur during pulse propagation in the semiclassical limit of the focusing nonlinear Schrödinger equation. Using an optical fiber based system, measurements of temporal focusing of high power pulses reveal both intensity and phase signatures of the Peregrine soliton during the initial nonlinear evolution stage. Experimental and numerical results are in very good agreement, and show that the universal mechanism that yields the Peregrine soliton structure is highly robust and can be observed over a broad range of parameters.

A computationally efficient scheme for the non-linear diffusion equation

NASA Astrophysics Data System (ADS)

Termonia, P.; Van de Vyver, H.

2009-04-01

This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank-Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.

A simple new filter for nonlinear high-dimensional data assimilation

NASA Astrophysics Data System (ADS)

Tödter, Julian; Kirchgessner, Paul; Ahrens, Bodo

2015-04-01

The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational data assimilation schemes and are applied in a wide range of operational and research activities. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the analysis mean and covariance are biased, and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) only relies on Bayes' theorem, which guarantees an exact asymptotic behavior, but because of the so-called curse of dimensionality it is exposed to weight collapse. This work shows how to obtain a new analysis ensemble whose mean and covariance exactly match the Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The forecast step remains as in the ETKF. The proposed algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF). The properties and performance of the proposed algorithm are investigated via a set of Lorenz experiments. They indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. Furthermore, localization enhances the potential applicability of this PF-inspired scheme in larger-dimensional systems. Finally, the novel algorithm is coupled to a large-scale ocean general circulation model. The NETF is stable, behaves reasonably and shows a good performance with a realistic ensemble size. The results confirm that, in principle, it can be applied successfully and as simple as the ETKF in high-dimensional problems without further modifications of the algorithm, even though it is only based on the particle weights. This proves that the suggested method constitutes a useful filter for nonlinear, high-dimensional data assimilation, and is able to overcome the curse of dimensionality even in deterministic systems.

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

A semi-active H∞ control strategy with application to the vibration suppression of nonlinear high-rise building under earthquake excitations.

PubMed

Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong

2016-01-01

Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibration. In this strategy, a modified Kalman-Bucy observer which is suitable for the proposed semi-active strategy is developed to obtain the state vector from the measured semi-active control force and acceleration feedback, taking into account of the effects of nonlinearity, disturbance and uncertainty of controlled system parameters by the observed nonlinear accelerations. Then, the proposed semi-active H∞ control strategy is applied to the ASCE 20-story benchmark building when subjected to earthquake excitation and compared with the other control approaches by some control criteria. It is indicated that the proposed semi-active H∞ control strategy provides much better control performances by comparison with the semi-active MPC and Clipped-LQG control approaches, and can reduce nonlinear seismic response and minimize the damage in the buildings. Besides, it enhances the reliability of the control performance when compared with the active control strategy. Thus, the proposed semi-active H∞ control strategy is suitable for suppressing the nonlinear vibration of high-rise buildings.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

NASA Technical Reports Server (NTRS)

McKinley, David P.

2006-01-01

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

Finite time control for MIMO nonlinear system based on higher-order sliding mode.

PubMed

Liu, Xiangjie; Han, Yaozhen

2014-11-01

Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Feedback linearization for control of air breathing engines

NASA Technical Reports Server (NTRS)

Phillips, Stephen; Mattern, Duane

1991-01-01

The method of feedback linearization for control of the nonlinear nozzle and compressor components of an air breathing engine is presented. This method overcomes the need for a large number of scheduling variables and operating points to accurately model highly nonlinear plants. Feedback linearization also results in linear closed loop system performance simplifying subsequent control design. Feedback linearization is used for the nonlinear partial engine model and performance is verified through simulation.

1/f Noise Inside a Faraday Cage

NASA Astrophysics Data System (ADS)

Handel, Peter H.; George, Thomas F.

2009-04-01

We show that quantum 1/f noise does not have a lower frequency limit given by the lowest free electromagnetic field mode in a Faraday cage, even in an ideal cage. Indeed, quantum 1/f noise comes from the infrared-divergent coupling of the field with the charges, in their joint nonlinear system, where the charges cause the field that reacts back on the charges, and so on. This low-frequency limitation is thus not applicable for the nonlinear system of matter and field in interaction. Indeed, this nonlinear system is governed by Newton's laws, Maxwell's equations, in general also by the diffusion equations for particles and heat, or reaction kinetics given by quantum matrix elements. Nevertheless, all the other quantities can be eliminated in principle, resulting in highly nonlinear integro-differential equations for the electromagnetic field only, which no longer yield a fundamental frequency. Alternatively, we may describe this through the presence of an infinite system of subharmonics. We show how this was proven early in the classical and quantum domains, adding new insight.

Nonlinear system controller design based on domain of attaction: An application to CELSS analysis and control

NASA Technical Reports Server (NTRS)

Babcock, P. S., IV

1986-01-01

Nonlinear system controller design based on the domain of attraction is presented. This is particularly suited to investigating Closed Ecological Life Support Systems (CELSS) models. In particular, the dynamic consequences of changes in the waste storage capacity and system mass, and how information is used for control in CELSS models are examined. The models' high dimensionality and nonlinear state equations make them difficult to analyze by any other technique. The domain of attraction is the region in initial conditions that tend toward an attractor and it is delineated by randomly selecting initial conditions from the region of state space being investigated. Error analysis is done by repeating the domain simulations with independent samples. A refinement of this region is the domain of performance which is the region of initial conditions meeting a performance criteria. In nonlinear systems, local stability does not insure stability over a larger region. The domain of attraction marks out this stability region; hence, it can be considered a measure of a nonlinear system's ability to recovery from state perturbations. Considering random perturbations, the minimum radius of the domain is a measure of the magnitude of perturbations for which recovery is guaranteed. Design of both linear and nonlinear controllers are shown. Three CELSS models, with 9 to 30 state variable, are presented. Measures of the domain of attraction are used to show the global behavior of these models under a variety of design and controller scenarios.

An Analytical Dynamics Approach to the Control of Mechanical Systems

NASA Astrophysics Data System (ADS)

Mylapilli, Harshavardhan

A new and novel approach to the control of nonlinear mechanical systems is presented in this study. The approach is inspired by recent results in analytical dynamics that deal with the theory of constrained motion. The control requirements on the dynamical system are viewed from an analytical dynamics perspective and the theory of constrained motion is used to recast these control requirements as constraints on the dynamical system. Explicit closed form expressions for the generalized nonlinear control forces are obtained by using the fundamental equation of mechanics. The control so obtained is optimal at each instant of time and causes the constraints to be exactly satisfied. No linearizations and/or approximations of the nonlinear dynamical system are made, and no a priori structure is imposed on the nature of nonlinear controller. Three examples dealing with highly nonlinear complex dynamical systems that are chosen from diverse areas of discrete and continuum mechanics are presented to demonstrate the control approach. The first example deals with the energy control of underactuated inhomogeneous nonlinear lattices (or chains), the second example deals with the synchronization of the motion of multiple coupled slave gyros with that of a master gyro, and the final example deals with the control of incompressible hyperelastic rubber-like thin cantilever beams. Numerical simulations accompanying these examples show the ease, simplicity and the efficacy with which the control methodology can be applied and the accuracy with which the desired control objectives can be met.

Analytical filtration model for nonlinear viscoplastic oil in the theory of oil production stimulation and heating of oil reservoir in a dual-well system

NASA Astrophysics Data System (ADS)

Ivanovich Astafev, Vladimir; Igorevich Gubanov, Sergey; Alexandrovna Olkhovskaya, Valeria; Mikhailovna Sylantyeva, Anastasia; Mikhailovich Zinovyev, Alexey

2018-02-01

Production of high-viscosity oil and design of field development systems for such oil is one of the most promising directions in the development of world oil industry. The ability of high-viscosity oil to show in filtration process properties typical for non-Newtonian systems is proven by experimental studies. Nonlinear relationship between the pressure gradient and the rate of oil flow is due to interaction of high-molecular substances, in particular, asphaltenes and tars that form a plastic structure in it. The authors of this article have used the analytical model of stationary influx of nonlinear viscoplastic oil to the well bottom in order to provide rationale for the intensifying impact on a reservoir. They also have analyzed the method of periodic heating of productive reservoir by means of dual-wells. The high-temperature source is placed at the bottom of the vertical well, very close to the reservoir; at the same time the side well, located outside the zone of expected rock damage, is used for production. Suggested method of systemic treatment of reservoirs with dual wells can be useful for small fields of high-viscosity oil. The effect is based on the opportunity to control the structural and mechanical properties of high-viscosity oil and to increase depletion of reserves.

PI and repetitive control for single phase inverter based on virtual rotating coordinate system

NASA Astrophysics Data System (ADS)

Li, Mengqi; Tong, Yibin; Jiang, Jiuchun; Liang, Jiangang

2018-03-01

Microgrid technology developed rapidly and nonlinear loads were connected increasingly. A new control strategy was proposed for single phase inverter when connected nonlinear loads under island condition. PI and repetitive compound controller was realized under synchronous rotating coordinate system and acquired high quality sinusoidal voltage output without voltage spike when loads step changed. Validity and correctness were verified by simulation using MATLAB/Simulink.

Effects of unbalance location on dynamic characteristics of high-speed gasoline engine turbocharger with floating ring bearings

NASA Astrophysics Data System (ADS)

Wang, Longkai; Bin, Guangfu; Li, Xuejun; Liu, Dingqu

2016-03-01

For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings(FRBs), the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.

Applications of high average power nonlinear optics

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

Velsko, S.P.; Krupke, W.F.

1996-02-05

Nonlinear optical frequency convertors (harmonic generators and optical parametric oscillators are reviewed with an emphasis on high average power performance and limitations. NLO materials issues and NLO device designs are discussed in reference to several emerging scientific, military and industrial commercial applications requiring {approx} 100 watt average power level in the visible and infrared spectral regions. Research efforts required to enable practical {approx} 100 watt class NLO based laser systems are identified.

Continuous uniformly finite time exact disturbance observer based control for fixed-time stabilization of nonlinear systems with mismatched disturbances

PubMed Central

Liu, Chongxin; Liu, Hang

2017-01-01

This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme. PMID:28406966

Intelligent robust control for uncertain nonlinear time-varying systems and its application to robotic systems.

PubMed

Chang, Yeong-Chan

2005-12-01

This paper addresses the problem of designing adaptive fuzzy-based (or neural network-based) robust controls for a large class of uncertain nonlinear time-varying systems. This class of systems can be perturbed by plant uncertainties, unmodeled perturbations, and external disturbances. Nonlinear H(infinity) control technique incorporated with adaptive control technique and VSC technique is employed to construct the intelligent robust stabilization controller such that an H(infinity) control is achieved. The problem of the robust tracking control design for uncertain robotic systems is employed to demonstrate the effectiveness of the developed robust stabilization control scheme. Therefore, an intelligent robust tracking controller for uncertain robotic systems in the presence of high-degree uncertainties can easily be implemented. Its solution requires only to solve a linear algebraic matrix inequality and a satisfactorily transient and asymptotical tracking performance is guaranteed. A simulation example is made to confirm the performance of the developed control algorithms.

Sliding Mode Thermal Control System for Space Station Furnace Facility

NASA Technical Reports Server (NTRS)

Jackson Mark E.; Shtessel, Yuri B.

1998-01-01

The decoupled control of the nonlinear, multiinput-multioutput, and highly coupled space station furnace facility (SSFF) thermal control system is addressed. Sliding mode control theory, a subset of variable-structure control theory, is employed to increase the performance, robustness, and reliability of the SSFF's currently designed control system. This paper presents the nonlinear thermal control system description and develops the sliding mode controllers that cause the interconnected subsystems to operate in their local sliding modes, resulting in control system invariance to plant uncertainties and external and interaction disturbances. The desired decoupled flow-rate tracking is achieved by optimization of the local linear sliding mode equations. The controllers are implemented digitally and extensive simulation results are presented to show the flow-rate tracking robustness and invariance to plant uncertainties, nonlinearities, external disturbances, and variations of the system pressure supplied to the controlled subsystems.

Bayesian dynamical systems modelling in the social sciences.

PubMed

Ranganathan, Shyam; Spaiser, Viktoria; Mann, Richard P; Sumpter, David J T

2014-01-01

Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.

Development and validation of a general purpose linearization program for rigid aircraft models

NASA Technical Reports Server (NTRS)

Duke, E. L.; Antoniewicz, R. F.

1985-01-01

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.

Nonlinear stability and control study of highly maneuverable high performance aircraft

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1993-01-01

This project is intended to research and develop new nonlinear methodologies for the control and stability analysis of high-performance, high angle-of-attack aircraft such as HARV (F18). Past research (reported in our Phase 1, 2, and 3 progress reports) is summarized and more details of final Phase 3 research is provided. While research emphasis is on nonlinear control, other tasks such as associated model development, system identification, stability analysis, and simulation are performed in some detail as well. An overview of various models that were investigated for different purposes such as an approximate model reference for control adaptation, as well as another model for accurate rigid-body longitudinal motion is provided. Only a very cursory analysis was made relative to type 8 (flexible body dynamics). Standard nonlinear longitudinal airframe dynamics (type 7) with the available modified F18 stability derivatives, thrust vectoring, actuator dynamics, and control constraints are utilized for simulated flight evaluation of derived controller performance in all cases studied.

A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics.

PubMed

Zeng, Cheng; Liang, Shan; Xiang, Shuwen

2017-05-01

Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

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

Tracing the transition of a macro electron shuttle into nonlinear response

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

Kim, Chulki; Prada, Marta; Qin, Hua

We present a study on a macroscopic electron shuttle in the transition from linear to nonlinear response. The shuttle consists of a classical mechanical pendulum situated between two capacitor plates. The metallic pendulum enables mechanical transfer of electrons between the plates, hence allowing to directly trace electron shuttling in the time domain. By applying a high voltage to the plates, we drive the system into a controlled nonlinear response, where we observe period doubling.

Neural network based adaptive control for nonlinear dynamic regimes

NASA Astrophysics Data System (ADS)

Shin, Yoonghyun

Adaptive control designs using neural networks (NNs) based on dynamic inversion are investigated for aerospace vehicles which are operated at highly nonlinear dynamic regimes. NNs play a key role as the principal element of adaptation to approximately cancel the effect of inversion error, which subsequently improves robustness to parametric uncertainty and unmodeled dynamics in nonlinear regimes. An adaptive control scheme previously named 'composite model reference adaptive control' is further developed so that it can be applied to multi-input multi-output output feedback dynamic inversion. It can have adaptive elements in both the dynamic compensator (linear controller) part and/or in the conventional adaptive controller part, also utilizing state estimation information for NN adaptation. This methodology has more flexibility and thus hopefully greater potential than conventional adaptive designs for adaptive flight control in highly nonlinear flight regimes. The stability of the control system is proved through Lyapunov theorems, and validated with simulations. The control designs in this thesis also include the use of 'pseudo-control hedging' techniques which are introduced to prevent the NNs from attempting to adapt to various actuation nonlinearities such as actuator position and rate saturations. Control allocation is introduced for the case of redundant control effectors including thrust vectoring nozzles. A thorough comparison study of conventional and NN-based adaptive designs for a system under a limit cycle, wing-rock, is included in this research, and the NN-based adaptive control designs demonstrate their performances for two highly maneuverable aerial vehicles, NASA F-15 ACTIVE and FQM-117B unmanned aerial vehicle (UAV), operated under various nonlinearities and uncertainties.

An equivalent unbalance identification method for the balancing of nonlinear squeeze-film damped rotordynamic systems

NASA Astrophysics Data System (ADS)

Torres Cedillo, Sergio G.; Bonello, Philip

2016-01-01

The high pressure (HP) rotor in an aero-engine assembly cannot be accessed under operational conditions because of the restricted space for instrumentation and high temperatures. This motivates the development of a non-invasive inverse problem approach for unbalance identification and balancing, requiring prior knowledge of the structure. Most such methods in the literature necessitate linear bearing models, making them unsuitable for aero-engine applications which use nonlinear squeeze-film damper (SFD) bearings. A previously proposed inverse method for nonlinear rotating systems was highly limited in its application (e.g. assumed circular centered SFD orbits). The methodology proposed in this paper overcomes such limitations. It uses the Receptance Harmonic Balance Method (RHBM) to generate the backward operator using measurements of the vibration at the engine casing, provided there is at least one linear connection between rotor and casing, apart from the nonlinear connections. A least-squares solution yields the equivalent unbalance distribution in prescribed planes of the rotor, which is consequently used to balance it. The method is validated on distinct rotordynamic systems using simulated casing vibration readings. The method is shown to provide effective balancing under hitherto unconsidered practical conditions. The repeatability of the method, as well as its robustness to noise, model uncertainty and balancing errors, are satisfactorily demonstrated and the limitations of the process discussed.

Parametric Analytical Studies for the Nonlinear Dynamic Response of the Tile/Pad Space Shuttle Thermal Protection System

NASA Technical Reports Server (NTRS)

Edighoffer, H.

1981-01-01

The studies examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. Studies are performed using the computer code DYNOTA which takes into account the highly nonlinear stiffening hysteresis and viscous behavior of the pad joining the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude.

Data based identification and prediction of nonlinear and complex dynamical systems

NASA Astrophysics Data System (ADS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods outlined in this Review are principled on various concepts in complexity science and engineering such as phase transitions, bifurcations, stabilities, and robustness. The methodologies have the potential to significantly improve our ability to understand a variety of complex dynamical systems ranging from gene regulatory systems to social networks toward the ultimate goal of controlling such systems.

Performance improvement of 64-QAM coherent optical communication system by optimizing symbol decision boundary based on support vector machine

NASA Astrophysics Data System (ADS)

Chen, Wei; Zhang, Junfeng; Gao, Mingyi; Shen, Gangxiang

2018-03-01

High-order modulation signals are suited for high-capacity communication systems because of their high spectral efficiency, but they are more vulnerable to various impairments. For the signals that experience degradation, when symbol points overlap on the constellation diagram, the original linear decision boundary cannot be used to distinguish the classification of symbol. Therefore, it is advantageous to create an optimum symbol decision boundary for the degraded signals. In this work, we experimentally demonstrated the 64-quadrature-amplitude modulation (64-QAM) coherent optical communication system using support-vector machine (SVM) decision boundary algorithm to create the optimum symbol decision boundary for improving the system performance. We investigated the influence of various impairments on the 64-QAM coherent optical communication systems, such as the impairments caused by modulator nonlinearity, phase skew between in-phase (I) arm and quadrature-phase (Q) arm of the modulator, fiber Kerr nonlinearity and amplified spontaneous emission (ASE) noise. We measured the bit-error-ratio (BER) performance of 75-Gb/s 64-QAM signals in the back-to-back and 50-km transmission. By using SVM to optimize symbol decision boundary, the impairments caused by I/Q phase skew of the modulator, fiber Kerr nonlinearity and ASE noise are greatly mitigated.

Enhancing Security of Double Random Phase Encoding Based on Random S-Box

NASA Astrophysics Data System (ADS)

Girija, R.; Singh, Hukum

2018-06-01

In this paper, we propose a novel asymmetric cryptosystem for double random phase encoding (DRPE) using random S-Box. While utilising S-Box separately is not reliable and DRPE does not support non-linearity, so, our system unites the effectiveness of S-Box with an asymmetric system of DRPE (through Fourier transform). The uniqueness of proposed cryptosystem lies on employing high sensitivity dynamic S-Box for our DRPE system. The randomness and scalability achieved due to applied technique is an additional feature of the proposed solution. The firmness of random S-Box is investigated in terms of performance parameters such as non-linearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. S-Boxes convey nonlinearity to cryptosystems which is a significant parameter and very essential for DRPE. The strength of proposed cryptosystem has been analysed using various parameters such as MSE, PSNR, correlation coefficient analysis, noise analysis, SVD analysis, etc. Experimental results are conferred in detail to exhibit proposed cryptosystem is highly secure.

Nonlinear degradation of a visible-light communication link: A Volterra-series approach

NASA Astrophysics Data System (ADS)

Kamalakis, Thomas; Dede, Georgia

2018-06-01

Visible light communications can be used to provide illumination and data communication at the same time. In this paper, a reverse-engineering approach is presented for assessing the impact of nonlinear signal distortion in visible light communication links. The approach is based on the Volterra series expansion and has the advantage of accurately accounting for memory effects in contrast to the static nonlinear models that are popular in the literature. Volterra kernels describe the end-to-end system response and can be inferred from measurements. Consequently, this approach does not rely on any particular physical models and assumptions regarding the individual link components. We provide the necessary framework for estimating the nonlinear distortion on the symbol estimates of a discrete multitone modulated link. Various design aspects such as waveform clipping and predistortion are also incorporated in the analysis. Using this framework, the nonlinear signal-to-interference is calculated for the system at hand. It is shown that at high signal amplitudes, the nonlinear signal-to-interference can be less than 25 dB.

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

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

Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio

2004-03-01

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [F. Dell'Anno, S. De Siena, and F. Illuminati, Phys. Rev. A 69, 033812 (2004)], we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of Hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing nondegenerate and degenerate multiphoton processes. We determine the coherent states associated with the canonical transformations, which generalize the nondegenerate two-photon squeezed states. Such heterodyne multiphoton squeezed states are defined asmore » the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non-Gaussian, highly nonclassical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two-mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.« less

Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

NASA Astrophysics Data System (ADS)

dell'Anno, Fabio; de Siena, Silvio; Illuminati, Fabrizio

2004-03-01

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [

Engineering non-linear resonator mode interactions in circuit QED by continuous driving: Manipulation of a photonic quantum memory

NASA Astrophysics Data System (ADS)

Reagor, Matthew; Pfaff, Wolfgang; Heeres, Reinier; Ofek, Nissim; Chou, Kevin; Blumoff, Jacob; Leghtas, Zaki; Touzard, Steven; Sliwa, Katrina; Holland, Eric; Albert, Victor V.; Frunzio, Luigi; Devoret, Michel H.; Jiang, Liang; Schoelkopf, Robert J.

2015-03-01

Recent advances in circuit QED have shown great potential for using microwave resonators as quantum memories. In particular, it is possible to encode the state of a quantum bit in non-classical photonic states inside a high-Q linear resonator. An outstanding challenge is to perform controlled operations on such a photonic state. We demonstrate experimentally how a continuous drive on a transmon qubit coupled to a high-Q storage resonator can be used to induce non-linear dynamics of the resonator. Tailoring the drive properties allows us to cancel or enhance non-linearities in the system such that we can manipulate the state stored in the cavity. This approach can be used to either counteract undesirable evolution due to the bare Hamiltonian of the system or, ultimately, to perform logical operations on the state encoded in the cavity field. Our method provides a promising pathway towards performing universal control for quantum states stored in high-coherence resonators in the circuit QED platform.

GA-optimized feedforward-PID tracking control for a rugged electrohydraulic system design.

PubMed

Sarkar, B K; Mandal, P; Saha, R; Mookherjee, S; Sanyal, D

2013-11-01

Rugged electrohydraulic systems are preferred for remote and harsh applications. Despite the low bandwidth, large deadband and flow nonlinearities in proportional valves valve and highly nonlinear friction in industry-grade cylinders that comprise rugged systems, their maintenance are much easier than very sophisticated and delicate servocontrol and servocylinder systems. With the target of making the easily maintainable system to perform comparably to a servosystem, a feedforward control has been designed here for compensating the nonlinearities. A PID feedback of the piston displacement has been employed in tandem for absorbing the unmodeled effects. All the controller parameters have been optimized by a real-coded genetic algorithm. The agreement between the achieved real-time responses for step and sinusoidal demands with those achieved by modern servosystems clearly establishes the acceptability of the controller design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

High-resolution broadband terahertz spectroscopy via electronic heterodyne detection of photonically generated terahertz frequency comb.

PubMed

Pavelyev, D G; Skryl, A S; Bakunov, M I

2014-10-01

We report an alternative approach to the terahertz frequency-comb spectroscopy (TFCS) based on nonlinear mixing of a photonically generated terahertz pulse train with a continuous wave signal from an electronic synthesizer. A superlattice is used as a nonlinear mixer. Unlike the standard TFCS technique, this approach does not require a complex double-laser system but retains the advantages of TFCS-high spectral resolution and wide bandwidth.

Vibrational resonance in an inhomogeneous medium with periodic dissipation

NASA Astrophysics Data System (ADS)

Roy-Layinde, T. O.; Laoye, J. A.; Popoola, O. O.; Vincent, U. E.; McClintock, P. V. E.

2017-09-01

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

The effect of low velocity impact in the strength characteristics of composite materials laminates

NASA Technical Reports Server (NTRS)

Liebowitz, H.

1983-01-01

The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system.

Sensor fault detection and isolation system for a condensation process.

PubMed

Castro, M A López; Escobar, R F; Torres, L; Aguilar, J F Gómez; Hernández, J A; Olivares-Peregrino, V H

2016-11-01

This article presents the design of a sensor Fault Detection and Isolation (FDI) system for a condensation process based on a nonlinear model. The condenser is modeled by dynamic and thermodynamic equations. For this work, the dynamic equations are described by three pairs of differential equations which represent the energy balance between the fluids. The thermodynamic equations consist in algebraic heat transfer equations and empirical equations, that allow for the estimation of heat transfer coefficients. The FDI system consists of a bank of two nonlinear high-gain observers, in order to detect, estimate and to isolate the fault in any of both outlet temperature sensors. The main contributions of this work were the experimental validation of the condenser nonlinear model and the FDI system. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems

NASA Astrophysics Data System (ADS)

Williams, Rube B.

2004-02-01

Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.

Investigation of non-uniform airflow signal oscillation during high frequency chest compression

PubMed Central

Sohn, Kiwon; Warwick, Warren J; Lee, Yong W; Lee, Jongwon; Holte, James E

2005-01-01

Background High frequency chest compression (HFCC) is a useful and popular therapy for clearing bronchial airways of excessive or thicker mucus. Our observation of respiratory airflow of a subject during use of HFCC showed the airflow oscillation by HFCC was strongly influenced by the nonlinearity of the respiratory system. We used a computational model-based approach to analyse the respiratory airflow during use of HFCC. Methods The computational model, which is based on previous physiological studies and represented by an electrical circuit analogue, was used for simulation of in vivo protocol that shows the nonlinearity of the respiratory system. Besides, airflow was measured during use of HFCC. We compared the simulation results to either the measured data or the previous research, to understand and explain the observations. Results and discussion We could observe two important phenomena during respiration pertaining to the airflow signal oscillation generated by HFCC. The amplitudes of HFCC airflow signals varied depending on spontaneous airflow signals. We used the simulation results to investigate how the nonlinearity of airway resistance, lung capacitance, and inertance of air characterized the respiratory airflow. The simulation results indicated that lung capacitance or the inertance of air is also not a factor in the non-uniformity of HFCC airflow signals. Although not perfect, our circuit analogue model allows us to effectively simulate the nonlinear characteristics of the respiratory system. Conclusion We found that the amplitudes of HFCC airflow signals behave as a function of spontaneous airflow signals. This is due to the nonlinearity of the respiratory system, particularly variations in airway resistance. PMID:15904523

Hysteresis in the trade cycle

NASA Astrophysics Data System (ADS)

Mc Namara, Hugh A.; Pokrovskii, Alexei V.

2006-02-01

The Kaldor model-one of the first nonlinear models of macroeconomics-is modified to incorporate a Preisach nonlinearity. The new dynamical system thus created shows highly complicated behaviour. This paper presents a rigorous (computer aided) proof of chaos in this new model, and of the existence of unstable periodic orbits of all minimal periods p>57.

Analysis of stochastic model for non-linear volcanic dynamics

NASA Astrophysics Data System (ADS)

Alexandrov, D.; Bashkirtseva, I.; Ryashko, L.

2014-12-01

Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed with increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related with the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

Nonlinear Wave Chaos and the Random Coupling Model

NASA Astrophysics Data System (ADS)

Zhou, Min; Ott, Edward; Antonsen, Thomas M.; Anlage, Steven

The Random Coupling Model (RCM) has been shown to successfully predict the statistical properties of linear wave chaotic cavities in the highly over-moded regime. It is of interest to extend the RCM to strongly nonlinear systems. To introduce nonlinearity, an active nonlinear circuit is connected to two ports of the wave chaotic 1/4-bowtie cavity. The active nonlinear circuit consists of a frequency multiplier, an amplifier and several passive filters. It acts to double the input frequency in the range from 3.5 GHz to 5 GHz, and operates for microwaves going in only one direction. Measurements are taken between two additional ports of the cavity and we measure the statistics of the second harmonic voltage over an ensemble of realizations of the scattering system. We developed an RCM-based model of this system as two chaotic cavities coupled by means of a nonlinear transfer function. The harmonics received at the output are predicted to be the product of three statistical quantities that describe the three elements correspondingly. Statistical results from simulation, RCM-based modeling, and direct experimental measurements will be compared. ONR under Grant No. N000141512134, AFOSR under COE Grant FA9550-15-1-0171,0 and the Maryland Center for Nanophysics and Advanced Materials.

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.

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.

1996-01-01

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA-High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high order characteristics of the system. In this paper, only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles at attack : 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.

1999-01-01

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high-order characteristics of the system. In this paper only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles of attack: 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of the identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the estimated closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks.

PubMed

Yan, Zheng; Wang, Jun

2014-03-01

This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.

Efficient Lookup Table-Based Adaptive Baseband Predistortion Architecture for Memoryless Nonlinearity

NASA Astrophysics Data System (ADS)

Ba, Seydou N.; Waheed, Khurram; Zhou, G. Tong

2010-12-01

Digital predistortion is an effective means to compensate for the nonlinear effects of a memoryless system. In case of a cellular transmitter, a digital baseband predistorter can mitigate the undesirable nonlinear effects along the signal chain, particularly the nonlinear impairments in the radiofrequency (RF) amplifiers. To be practically feasible, the implementation complexity of the predistorter must be minimized so that it becomes a cost-effective solution for the resource-limited wireless handset. This paper proposes optimizations that facilitate the design of a low-cost high-performance adaptive digital baseband predistorter for memoryless systems. A comparative performance analysis of the amplitude and power lookup table (LUT) indexing schemes is presented. An optimized low-complexity amplitude approximation and its hardware synthesis results are also studied. An efficient LUT predistorter training algorithm that combines the fast convergence speed of the normalized least mean squares (NLMSs) with a small hardware footprint is proposed. Results of fixed-point simulations based on the measured nonlinear characteristics of an RF amplifier are presented.

Waveguide structures in anisotropic nonlinear crystals

NASA Astrophysics Data System (ADS)

Li, Da; Hong, Pengda; Meissner, Helmuth E.

2017-02-01

We report on the design and manufacturing parameters of waveguiding structures of anisotropic nonlinear crystals that are employed for harmonic conversions, using Adhesive-Free Bonding (AFB®). This technology enables a full range of predetermined refractive index differences that are essential for the design of single mode or low-mode propagation with high efficiency in anisotropic nonlinear crystals which in turn results in compact frequency conversion systems. Examples of nonlinear optical waveguides include periodically bonded walk-off corrected nonlinear optical waveguides and periodically poled waveguide components, such as lithium triborate (LBO), beta barium borate (β-BBO), lithium niobate (LN), potassium titanyl phosphate (KTP), zinc germanium phosphide (ZGP) and silver selenogallate (AGSE). Simulation of planar LN waveguide shows that when the electric field vector E lies in the k-c plane, the power flow is directed precisely along the propagation direction, demonstrating waveguiding effect in the planar waveguide. Employment of anisotropic nonlinear optical waveguides, for example in combination with AFB® crystalline fiber waveguides (CFW), provides access to the design of a number of novel high power and high efficiency light sources spanning the range of wavelengths from deep ultraviolet (as short as 200 nm) to mid-infrared (as long as about 18 μm). To our knowledge, the technique is the only generally applicable one because most often there are no compatible cladding crystals available to nonlinear optical cores, especially not with an engineer-able refractive index difference and large mode area.

Adaptive Neural Tracking Control for Switched High-Order Stochastic Nonlinear Systems.

PubMed

Zhao, Xudong; Wang, Xinyong; Zong, Guangdeng; Zheng, Xiaolong

2017-10-01

This paper deals with adaptive neural tracking control design for a class of switched high-order stochastic nonlinear systems with unknown uncertainties and arbitrary deterministic switching. The considered issues are: 1) completely unknown uncertainties; 2) stochastic disturbances; and 3) high-order nonstrict-feedback system structure. The considered mathematical models can represent many practical systems in the actual engineering. By adopting the approximation ability of neural networks, common stochastic Lyapunov function method together with adding an improved power integrator technique, an adaptive state feedback controller with multiple adaptive laws is systematically designed for the systems. Subsequently, a controller with only two adaptive laws is proposed to solve the problem of over parameterization. Under the designed controllers, all the signals in the closed-loop system are bounded-input bounded-output stable in probability, and the system output can almost surely track the target trajectory within a specified bounded error. Finally, simulation results are presented to show the effectiveness of the proposed approaches.

Nonlinear frequency response based adaptive vibration controller design for a class of nonlinear systems

NASA Astrophysics Data System (ADS)

Thenozhi, Suresh; Tang, Yu

2018-01-01

Frequency response functions (FRF) are often used in the vibration controller design problems of mechanical systems. Unlike linear systems, the FRF derivation for nonlinear systems is not trivial due to their complex behaviors. To address this issue, the convergence property of nonlinear systems can be studied using convergence analysis. For a class of time-invariant nonlinear systems termed as convergent systems, the nonlinear FRF can be obtained. The present paper proposes a nonlinear FRF based adaptive vibration controller design for a mechanical system with cubic damping nonlinearity and a satellite system. Here the controller gains are tuned such that a desired closed-loop frequency response for a band of harmonic excitations is achieved. Unlike the system with cubic damping, the satellite system is not convergent, therefore an additional controller is utilized to achieve the convergence property. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller.

Parametrically excited motion of a levitated rigid bar over high- Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Shimizu, T.; Sugiura, T.; Ogawa, S.

2006-10-01

High-Tc superconducting levitation systems achieve, under no contact support, stable levitation without control. This feature can be applied to flywheels, magnetically levitated trains, and so on. But no contact support has small damping. So these mechanisms can show complicated phenomena of dynamics due to nonlinearity in their magnetic force. For application to large-scale machines, we need to analyze dynamics of a large levitated body supported at multiple points. This research deals with nonlinearly coupled oscillation of a homogeneous and symmetric rigid bar supported at its both ends by equal electromagnetic forces between superconductors and permanent magnets. In our past study, using a rigid bar, we found combination resonance. Combination resonance happens owing to the asymmetry of the system. But, even if support forces are symmetric, parametric resonance can happen. With a simple symmetric model, this research focuses on especially the parametric resonance, and evaluates nonlinear effect of the symmetric support forces by experiment and numerical analysis. Obtained results show that two modes, caused by coupling of horizontal translation and roll motion, can be excited nonlinearly when the superconductor is excited vertically in the neighborhood of twice the natural frequencies of those modes. We confirmed these resonances have nonlinear characteristics of soft-spring, hysteresis and so on.

Imitative modeling automatic system Control of steam pressure in the main steam collector with the influence on the main Servomotor steam turbine

NASA Astrophysics Data System (ADS)

Andriushin, A. V.; Zverkov, V. P.; Kuzishchin, V. F.; Ryzhkov, O. S.; Sabanin, V. R.

2017-11-01

The research and setting results of steam pressure in the main steam collector “Do itself” automatic control system (ACS) with high-speed feedback on steam pressure in the turbine regulating stage are presented. The ACS setup is performed on the simulation model of the controlled object developed for this purpose with load-dependent static and dynamic characteristics and a non-linear control algorithm with pulse control of the turbine main servomotor. A method for tuning nonlinear ACS with a numerical algorithm for multiparametric optimization and a procedure for separate dynamic adjustment of control devices in a two-loop ACS are proposed and implemented. It is shown that the nonlinear ACS adjusted with the proposed method with the regulators constant parameters ensures reliable and high-quality operation without the occurrence of oscillations in the transient processes the operating range of the turbine loads.

Implementation of Nonlinear Control Laws for an Optical Delay Line

NASA Technical Reports Server (NTRS)

Hench, John J.; Lurie, Boris; Grogan, Robert; Johnson, Richard

2000-01-01

This paper discusses the implementation of a globally stable nonlinear controller algorithm for the Real-Time Interferometer Control System Testbed (RICST) brassboard optical delay line (ODL) developed for the Interferometry Technology Program at the Jet Propulsion Laboratory. The control methodology essentially employs loop shaping to implement linear control laws. while utilizing nonlinear elements as means of ameliorating the effects of actuator saturation in its coarse, main, and vernier stages. The linear controllers were implemented as high-order digital filters and were designed using Bode integral techniques to determine the loop shape. The nonlinear techniques encompass the areas of exact linearization, anti-windup control, nonlinear rate limiting and modal control. Details of the design procedure are given as well as data from the actual mechanism.

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

PubMed

Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

A practical application of the geometrical theory on fibered manifolds to an autonomous bicycle motion in mechanical system with nonholonomic constraints

NASA Astrophysics Data System (ADS)

Haddout, Soufiane

2018-01-01

The equations of motion of a bicycle are highly nonlinear and rolling of wheels without slipping can only be expressed by nonholonomic constraint equations. A geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by O. Krupková (Rossi) in 1990's. Her approach is suitable for study of all kinds of mechanical systems-without restricting to Lagrangian, time-independent, or regular ones, and is applicable to arbitrary constraints (holonomic, semiholonomic, linear, nonlinear or general nonholonomic). The goal of this paper is to apply Krupková's geometric theory of nonholonomic mechanical systems to study a concrete problem in nonlinear nonholonomic dynamics, i.e., autonomous bicycle. The dynamical model is preserved in simulations in its original nonlinear form without any simplifying. The results of numerical solutions of constrained equations of motion, derived within the theory, are in good agreement with measurements and thus they open the possibility of direct application of the theory to practical situations.

Singularity perturbed zero dynamics of nonlinear systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.

1992-01-01

Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.

A design methodology for nonlinear systems containing parameter uncertainty: Application to nonlinear controller design

NASA Technical Reports Server (NTRS)

Young, G.

1982-01-01

A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.

Non-linear dynamic compensation system

NASA Technical Reports Server (NTRS)

Lin, Yu-Hwan (Inventor); Lurie, Boris J. (Inventor)

1992-01-01

A non-linear dynamic compensation subsystem is added in the feedback loop of a high precision optical mirror positioning control system to smoothly alter the control system response bandwidth from a relatively wide response bandwidth optimized for speed of control system response to a bandwidth sufficiently narrow to reduce position errors resulting from the quantization noise inherent in the inductosyn used to measure mirror position. The non-linear dynamic compensation system includes a limiter for limiting the error signal within preselected limits, a compensator for modifying the limiter output to achieve the reduced bandwidth response, and an adder for combining the modified error signal with the difference between the limited and unlimited error signals. The adder output is applied to control system motor so that the system response is optimized for accuracy when the error signal is within the preselected limits, optimized for speed of response when the error signal is substantially beyond the preselected limits and smoothly varied therebetween as the error signal approaches the preselected limits.

Nonlinear damping for vibration isolation of microsystems using shear thickening fluid

NASA Astrophysics Data System (ADS)

Iyer, S. S.; Vedad-Ghavami, R.; Lee, H.; Liger, M.; Kavehpour, H. P.; Candler, R. N.

2013-06-01

This work reports the measurement and analysis of nonlinear damping of micro-scale actuators immersed in shear thickening fluids (STFs). A power-law damping term is added to the linear second-order model to account for the shear-dependent viscosity of the fluid. This nonlinear model is substantiated by measurements of oscillatory motion of a torsional microactuator. At high actuation forces, the vibration velocity amplitude saturates. The model accurately predicts the nonlinear damping characteristics of the STF using a power-law index extracted from independent rheology experiments. This result reveals the potential to use STFs as adaptive, passive dampers for vibration isolation of microelectromechanical systems.

An introduction to chaos theory in CFD

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

1990-01-01

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

A Static and Dynamic Investigation of Quantum Nonlinear Transport in Highly Dense and Mobile 2D Electron Systems

NASA Astrophysics Data System (ADS)

Dietrich, Scott

Heterostructures made of semiconductor materials may be one of most versatile environments for the study of the physics of electron transport in two dimensions. These systems are highly customizable and demonstrate a wide range of interesting physical phenomena. In response to both microwave radiation and DC excitations, strongly nonlinear transport that gives rise to non-equilibrium electron states has been reported and investigated. We have studied GaAs quantum wells with a high density of high mobility two-dimensional electrons placed in a quantizing magnetic field. This study presents the observation of several nonlinear transport mechanisms produced by the quantum nature of these materials. The quantum scattering rate, 1tau/q, is an important parameter in these systems, defining the width of the quantized energy levels. Traditional methods of extracting 1tau/q involve studying the amplitude of Shubnikov-de Haas oscillations. We analyze the quantum positive magnetoresistance due to the cyclotron motion of electrons in a magnetic field. This method gives 1tau/q and has the additional benefit of providing access to the strength of electron-electron interactions, which is not possible by conventional techniques. The temperature dependence of the quantum scattering rate is found to be proportional to the square of the temperature and is in very good agreement with theory that considers electron-electron interactions in 2D systems. In quantum wells with a small scattering rate - which corresponds to well-defined Landau levels - quantum oscillations of nonlinear resistance that are independent of magnetic field strength have been observed. These oscillations are periodic in applied bias current and are connected to quantum oscillations of resistance at zero bias: either Shubnikov-de Haas oscillations for single subband systems or magnetointersubband oscillations for two subband systems. The bias-induced oscillations can be explained by a spatial variation of electron density across the sample. The theoretical model predicts the period of these oscillations to depend on the total electron density, which has been confirmed by controlling the density through a voltage top-gate on the sample. The peculiar nonlinear mechanism of quantal heating has garned much attention recently. This bulk phenomenon is a quantum manifestation of Joule heating where an applied bias current causes selective flattening in the electron distribution function but conserves overall broadening. This produces a highly non-equilibrium distribution of electrons that drastically effects the transport properties of the system. Recent studies have proposed contributions from edge states and/or skipping orbitals. We have shown that these contributions are minimal by studying the transition to the zero differential conductance state and comparing results between Hall and Corbino geometries. This demonstrated quantal heating as the dominant nonlinear mechanism in these systems. To study the dynamics of quantal heating, we applied microwave radiation simultaneously from two sources at frequencies ƒ1 and ƒ2 and measured the response of the system at the difference frequency, ƒ=|ƒ 1-ƒ2|. This provides direct access to the rate of inelastic scattering processes, 1tau/in, that tend to bring the electron distribution back to thermal equilibrium. While conventional measurements of the temperature dependence indicate that 1tau/in is proportional to temperature, recent DC investigations and our new dynamic measurements show either T2 or T3 dependence in different magnetic fields. Our microwave experiment is the first direct access to the inelastic relaxation rate and confirms the non-linear temperature dependence.

Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters

NASA Astrophysics Data System (ADS)

Sun, Tao; Xin, Ming

2017-05-01

Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.

Non-linear optical techniques and optical properties of condensed molecular systems

NASA Astrophysics Data System (ADS)

Citroni, Margherita

2013-06-01

Structure, dynamics, and optical properties of molecular systems can be largely modified by the applied pressure, with remarkable consequences on their chemical stability. Several examples of selective reactions yielding technologically attractive products can be cited, which are particularly efficient when photochemical effects are exploited in conjunction with the structural conditions attained at high density. Non-linear optical techniques are a basic tool to unveil key aspects of the chemical reactivity and dynamic properties of molecules. Their application to high-pressure samples is experimentally challenging, mainly because of the small sample dimensions and of the non-linear effects generated in the anvil materials. In this talk I will present results on the electronic spectra of several aromatic crystals obtained through two-photon induced fluorescence and two-photon excitation profiles measured as a function of pressure (typically up to about 25 GPa), and discuss the relationship between the pressure-induced modifications of the electronic structure and the chemical reactivity at high pressure. I will also present the first successful pump-probe infrared measurement performed as a function of pressure on a condensed molecular system. The system under examination is liquid water, in a sapphire anvil cell, up to 1 GPa along isotherms at 298 and 363 K. These measurements give a new enlightening insight into the dynamical properties of low- and high-density water allowing a definition of the two structures.

Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations

NASA Technical Reports Server (NTRS)

Padovan, J.; Lackney, J.

1986-01-01

The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

Coherent nonlinear optical imaging: beyond fluorescence microscopy.

PubMed

Min, Wei; Freudiger, Christian W; Lu, Sijia; Xie, X Sunney

2011-01-01

The quest for ultrahigh detection sensitivity with spectroscopic contrasts other than fluorescence has led to various novel approaches to optical microscopy of biological systems. Coherent nonlinear optical imaging, especially the recently developed nonlinear dissipation microscopy (including stimulated Raman scattering and two-photon absorption) and pump-probe microscopy (including excited-state absorption, stimulated emission, and ground-state depletion), provides new image contrasts for nonfluorescent species. Thanks to the high-frequency modulation transfer scheme, these imaging techniques exhibit superb detection sensitivity. By directly interrogating vibrational and/or electronic energy levels of molecules, they offer high molecular specificity. Here we review the underlying principles and excitation and detection schemes, as well as exemplary biomedical applications of this emerging class of molecular imaging techniques.

Multimodal fiber source for nonlinear microscopy based on a dissipative soliton laser

PubMed Central

Lamb, Erin S.; Wise, Frank W.

2015-01-01

Recent developments in high energy femtosecond fiber lasers have enabled robust and lower-cost sources for multiphoton-fluorescence and harmonic-generation imaging. However, picosecond pulses are better suited for Raman scattering microscopy, so the ideal multimodal source for nonlinear microcopy needs to provide both durations. Here we present spectral compression of a high-power femtosecond fiber laser as a route to producing transform-limited picosecond pulses. These pulses pump a fiber optical parametric oscillator to yield a robust fiber source capable of providing the synchronized picosecond pulse trains needed for Raman scattering microscopy. Thus, this system can be used as a multimodal platform for nonlinear microscopy techniques. PMID:26417497

Robust optimization for nonlinear time-delay dynamical system of dha regulon with cost sensitivity constraint in batch culture

NASA Astrophysics Data System (ADS)

Yuan, Jinlong; Zhang, Xu; Liu, Chongyang; Chang, Liang; Xie, Jun; Feng, Enmin; Yin, Hongchao; Xiu, Zhilong

2016-09-01

Time-delay dynamical systems, which depend on both the current state of the system and the state at delayed times, have been an active area of research in many real-world applications. In this paper, we consider a nonlinear time-delay dynamical system of dha-regulonwith unknown time-delays in batch culture of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumonia. Some important properties and strong positive invariance are discussed. Because of the difficulty in accurately measuring the concentrations of intracellular substances and the absence of equilibrium points for the time-delay system, a quantitative biological robustness for the concentrations of intracellular substances is defined by penalizing a weighted sum of the expectation and variance of the relative deviation between system outputs before and after the time-delays are perturbed. Our goal is to determine optimal values of the time-delays. To this end, we formulate an optimization problem in which the time delays are decision variables and the cost function is to minimize the biological robustness. This optimization problem is subject to the time-delay system, parameter constraints, continuous state inequality constraints for ensuring that the concentrations of extracellular and intracellular substances lie within specified limits, a quality constraint to reflect operational requirements and a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved. It is approximated as a sequence of nonlinear programming sub-problems through the application of constraint transcription and local smoothing approximation techniques. Due to the highly complex nature of this optimization problem, the computational cost is high. Thus, a parallel algorithm is proposed to solve these nonlinear programming sub-problems based on the filled function method. Finally, it is observed that the obtained optimal estimates for the time-delays are highly satisfactory via numerical simulations.

RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios

PubMed Central

Tang, Zhi-Ling; Li, Si-Min; Yu, Li-Juan

2016-01-01

Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC) to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system’s starting oscillation is determined, and the simulation results of the system’s response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured. PMID:27294928

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

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.

Probing Atomic Dynamics and Structures Using Optical Patterns

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie L.; Gauthier, Daniel J.

2015-05-01

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

Sensitivity analysis and nonlinearity assessment of steam cracking furnace process

NASA Astrophysics Data System (ADS)

Rosli, M. N.; Sudibyo, Aziz, N.

2017-11-01

In this paper, sensitivity analysis and nonlinearity assessment of cracking furnace process are presented. For the sensitivity analysis, the fractional factorial design method is employed as a method to analyze the effect of input parameters, which consist of four manipulated variables and two disturbance variables, to the output variables and to identify the interaction between each parameter. The result of the factorial design method is used as a screening method to reduce the number of parameters, and subsequently, reducing the complexity of the model. It shows that out of six input parameters, four parameters are significant. After the screening is completed, step test is performed on the significant input parameters to assess the degree of nonlinearity of the system. The result shows that the system is highly nonlinear with respect to changes in an air-to-fuel ratio (AFR) and feed composition.

Nonlinear dynamics of the human lumbar intervertebral disc.

PubMed

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J

2015-02-05

Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. Copyright © 2014 Elsevier Ltd. All rights reserved.

High power laser perforating tools and systems

DOEpatents

Zediker, Mark S; Rinzler, Charles C; Faircloth, Brian O; Koblick, Yeshaya; Moxley, Joel F

2014-04-22

ystems devices and methods for the transmission of 1 kW or more of laser energy deep into the earth and for the suppression of associated nonlinear phenomena. Systems, devices and methods for the laser perforation of a borehole in the earth. These systems can deliver high power laser energy down a deep borehole, while maintaining the high power to perforate such boreholes.

Nonlinear Whirl Response of a High-Speed Seal Test Rotor With Marginal and Extended Squeeze-Film Dampers

NASA Technical Reports Server (NTRS)

Proctor, Margaret P.; Gunter, Edgar J.

2005-01-01

Synchronous and nonsynchronous whirl response analysis of a double overhung, high-speed seal test rotor with ball bearings supported in 5.84- and 12.7-mm-long, un-centered squeeze-film oil dampers is presented. Test performance with the original damper of length 5.84 mm was marginal, with nonsynchronous whirling at the overhung seal test disk and high amplitude synchronous response above 32,000 rpm near the drive spline section occurring. A system critical speed analysis of the drive system and the high-speed seal test rotor indicated that the first two critical speeds are associated with the seal test rotor. Nonlinear synchronous unbalance and time transient whirl studies were conducted on the seal test rotor with the original and extended damper lengths. With the original damper design, the nonlinear synchronous response showed that unbalance could cause damper lockup at 33,000 rpm. Alford cross-coupling forces were also included at the overhung seal test disk for the whirl analysis. Sub-synchronous whirling at the seal test disk was observed in the nonlinear time transient analysis. With the extended damper length of 12.7 mm, the sub-synchronous motion was eliminated and the rotor unbalance response was acceptable to 45,000 rpm with moderate rotor unbalance. However, with high rotor unbalance, damper lockup could still occur at 33,000 rpm, even with the extended squeeze-film dampers. Therefore, the test rotor must be reasonably balanced in order for the un-centered dampers to be effective.

Large-area and highly crystalline MoSe2 for optical modulator

NASA Astrophysics Data System (ADS)

Yin, Jinde; Chen, Hao; Lu, Wei; Liu, Mengli; Li, Irene Ling; Zhang, Min; Zhang, Wenfei; Wang, Jinzhang; Xu, Zihan; Yan, Peiguang; Liu, Wenjun; Ruan, Shuangchen

2017-12-01

Transition metal dichalcogenides (TMDs) have been successfully used as broadband optical modulator materials for pulsed fiber laser systems. However, the nonlinear optical absorptions of exfoliated TMDs are strongly limited by their nanoflakes morphology with uncontrollable lateral size and thickness. In this work, we provide an effective method to fully explore the nonlinear optical properties of MoSe2. Large-area and high quality lattice MoSe2 grown by chemical vapor deposition method was adopted as an optical modulator for the first time. The large-area MoSe2 shows excellent nonlinear optical absorption with a large modulation depth of 21.7% and small saturable intensity of 9.4 MW cm-2. After incorporating the MoSe2 optical modulator into fiber laser cavity as a saturable absorber, a highly stable Q-switching operation with single pulse energy of 224 nJ is achieved. The large-area MoSe2 possessing superior nonlinear optical properties compared to exfoliated nanoflakes affords possibility for the larger-area two-dimensional materials family as high performance optical devices.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.

Asymmetric nonlinear system is not sufficient for a nonreciprocal wave diode

NASA Astrophysics Data System (ADS)

Wu, Gaomin; Long, Yang; Ren, Jie

2018-05-01

We demonstrate symmetric wave propagations in asymmetric nonlinear systems. By solving the nonlinear Schördinger equation, we first analytically prove the existence of symmetric transmission in asymmetric systems with a single nonlinear delta-function interface. We then point out that a finite width of the nonlinear interface region is necessary to produce nonreciprocity in asymmetric systems. However, a geometrical resonant condition for breaking nonreciprocal propagation is then identified theoretically and verified numerically. With such a resonant condition, the nonlinear interface region of finite width behaves like a single nonlinear delta-barrier so that wave propagations in the forward and backward directions are identical under arbitrary incident wave intensity. As such, reciprocity reemerges periodically in the asymmetric nonlinear system when changing the width of interface region. Finally, similar resonant conditions of discrete nonlinear Schördinger equation are discussed. Therefore, we have identified instances of reciprocity that breaking spatial symmetry in nonlinear interface systems is not sufficient to produce nonreciprocal wave propagation.

Nonlinear and non-Hermitian optical systems applied to the development of filters and optical sensors

NASA Astrophysics Data System (ADS)

Amaro de Faria Júnior, A. C.

2015-09-01

In this work we present a method of investigation of nonlinear optical beams generated from non-Hermitian optical systems1 . This method can be applied in the development of optical filters and optical sensors to process, analyze and choose the passband of the propagation modes of an optical pulse from an non-Hermitian optical system. Non-Hermitian optical systems can be used to develop optical fiber sensors that suppress certain propagation modes of optical pulses that eventually behave as quantum noise. Such systems are described by the Nonlinear Schrödinger-like Equation with Parity-Time (PT) Symmetric Optical Potentials. There are optical fiber sensors that due to high laser intensity and frequency can produce quantum noise, such as Raman and Brillouin scattering. However, the optical fiber, for example, can be designed so that its geometry suppress certain propagation modes of the beam. We apply some results of non- Hermitian optical systems with PT symmetry to simulate optical lattice by a appropriate potential function, which among other applications, can naturally suppress certain propagation modes of an optical beam propagating through a waveguide. In other words, the optical system is modeled by a potential function in the Nonlinear Schrödinger-like Equation that one relates with the geometric aspects of the wave guides and with the optical beam interacting with the waveguide material. The paper is organized as follows: sections 1 and 2 present a brief description about nonlinear optical systems and non-Hermitian optical systems with PT symmetry. Section 3 presents a description of the dynamics of nonlinear optical pulses propagating through optical networks described by a optical potential non-Hermitian. Sections 4 and 5 present a general description of this non-Hermitian optical systems and how to get them from a more general model. Section 6 presents some conclusions and comment and the final section presents the references. Begin the abstract two lines below author names and addresses.

Human middle-ear nonlinearity measurements using laser Doppler vibrometry

NASA Astrophysics Data System (ADS)

Gladiné, Kilian; Muyshondt, Pieter G. G.; Dirckx, Joris J. J.

2017-12-01

It has long been supposed that the middle-ear has near to perfect linear characteristics, and several attempts have been made to investigate this hypothesis. In conclusion, the middle-ear was regarded as a linear system at least up till sound pressure levels of 120 dB. Because of the linear relationship between Doppler shift of light and the vibration velocity of the object on which the light is reflected, laser Doppler vibrometry (LDV) is an intrinsically highly linear measurement technique. Therefore it allows straightforward detection of very small nonlinearities in a vibration response. In this paper, laser Doppler vibrometry and multisine stimulation are used to detect nonlinear distortions in the vibration response at the umbo of the tympanic membrane of seven human cadaver temporal bones. Nonlinear distortions were detected starting from sound pressure levels of 99 dB and measurements were performed up to 120 dB. These distortions can be subdivided into even degree (e.g. quadratic distortion tones) and odd degree nonlinear distortions (e.g. cubic distortion tones). We illustrate that with odd multisine stimulation the level of even and odd degree nonlinear distortions can be investigated separately. In conclusion, laser Doppler vibrometry is an adequate tool to detect nonlinear distortions in the middle-ear system and to quantify the level of such distortions even at 57 dB below the vibration response. The possibility to analyze even degree and odd degree nonlinear distortion levels separately can help in future work to pinpoint the source of the nonlinearity.

Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru

2017-11-01

This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2  +  1)D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2  +  1)D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.

Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

NASA Astrophysics Data System (ADS)

Rozdeba, Paul J.

The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts

PubMed Central

Sugihara, George; Casdagli, Martin; Habjan, Edward; Hess, Dale; Dixon, Paul; Holland, Greg

1999-01-01

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meridional variation of midlatitude storm track frequency. We extract the specific functional form of this nonlinearity, a V shape in the lagged residuals that appears to be a basic feature of midlatitude synoptic weather systems associated with frontal passages. We present evidence that this form arises from the relative time scales of high-pressure versus low-pressure events. Finally, we show that this nonlinear feature is weaker in a well regarded numerical forecast model (European Centre for Medium-Range Forecasts) because small-scale temporal and spatial variation is smoothed out in the grided inputs. This is significant, in that it allows us to demonstrate how application of statistical corrections based on the residual-delay map may provide marked increases in local forecast accuracy, especially for severe weather systems. PMID:10588685

High-resolution mapping of bifurcations in nonlinear biochemical circuits

NASA Astrophysics Data System (ADS)

Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.

2016-08-01

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

Nonlinear SVM-DTC for induction motor drive using input-output feedback linearization and high order sliding mode control.

PubMed

Ammar, Abdelkarim; Bourek, Amor; Benakcha, Abdelhamid

2017-03-01

This paper presents a nonlinear Direct Torque Control (DTC) strategy with Space Vector Modulation (SVM) for an induction motor. A nonlinear input-output feedback linearization (IOFL) is implemented to achieve a decoupled torque and flux control and the SVM is employed to reduce high torque and flux ripples. Furthermore, the control scheme performance is improved by inserting a super twisting speed controller in the outer loop and a load torque observer to enhance the speed regulation. The combining of dual nonlinear strategies ensures a good dynamic and robustness against parameters variation and disturbance. The system stability has been analyzed using Lyapunov stability theory. The effectiveness of the control algorithm is investigated by simulation and experimental validation using Matlab/Simulink software with real-time interface based on dSpace 1104. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

PubMed

Zhou, Shengxi; Yan, Bo; Inman, Daniel J

2018-05-09

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Nonlinear Flying Qualities Criteria for Large-Amplitude Maneuvers

DTIC Science & Technology

1984-12-01

theory which are pertinent to the formation of a nonlinear flying qualities methodology. This report surveys nonlinear system theory and describes...the development of an applied flying qualities methodology based on a canonical system theory and using research in relative controllability...The Nonlinear Flying Qualities (NFQ) for Large-Amplitude Maneuvers Program examined promising techniques from nonlinear analysis and nonlinear system

A comprehensive inversion approach for feedforward compensation of piezoactuator system at high frequency

NASA Astrophysics Data System (ADS)

Tian, Lizhi; Xiong, Zhenhua; Wu, Jianhua; Ding, Han

2016-09-01

Motion control of the piezoactuator system over broadband frequencies is limited due to its inherent hysteresis and system dynamics. One of the suggested ways is to use feedforward controller to linearize the input-output relationship of the piezoactuator system. Although there have been many feedforward approaches, it is still a challenge to develop feedforward controller for the piezoactuator system at high frequency. Hence, this paper presents a comprehensive inversion approach in consideration of the coupling of hysteresis and dynamics. In this work, the influence of dynamics compensation on the input-output relationship of the piezoactuator system is investigated first. With system dynamics compensation, the input-output relationship of the piezoactuator system will be further represented as rate-dependent nonlinearity due to the inevitable dynamics compensation error, especially at high frequency. Base on this result, the feedforward controller composed by a cascade of linear dynamics inversion and rate-dependent nonlinearity inversion is developed. Then, the system identification of the comprehensive inversion approach is proposed. Finally, experimental results show that the proposed approach can improve the performance on tracking of both periodic and non-periodic trajectories at medium and high frequency compared with the conventional feedforward approaches.

Nonlinear Structured Illumination Using a Fluorescent Protein Activating at the Readout Wavelength

PubMed Central

Hou, Wenya; Kielhorn, Martin; Arai, Yoshiyuki; Nagai, Takeharu; Kessels, Michael M.; Qualmann, Britta; Heintzmann, Rainer

2016-01-01

Structured illumination microscopy (SIM) is a wide-field technique in fluorescence microscopy that provides fast data acquisition and two-fold resolution improvement beyond the Abbe limit. We observed a further resolution improvement using the nonlinear emission response of a fluorescent protein. We demonstrated a two-beam nonlinear structured illumination microscope by introducing only a minor change into the system used for linear SIM (LSIM). To achieve the required nonlinear dependence in nonlinear SIM (NL-SIM) we exploited the photoswitching of the recently introduced fluorophore Kohinoor. It is particularly suitable due to its positive contrast photoswitching characteristics. Contrary to other reversibly photoswitchable fluorescent proteins which only have high photostability in living cells, Kohinoor additionally showed little degradation in fixed cells over many switching cycles. PMID:27783656

FRF decoupling of nonlinear systems

NASA Astrophysics Data System (ADS)

Kalaycıoğlu, Taner; Özgüven, H. Nevzat

2018-03-01

Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

Multi-linear model set design based on the nonlinearity measure and H-gap metric.

PubMed

Shaghaghi, Davood; Fatehi, Alireza; Khaki-Sedigh, Ali

2017-05-01

This paper proposes a model bank selection method for a large class of nonlinear systems with wide operating ranges. In particular, nonlinearity measure and H-gap metric are used to provide an effective algorithm to design a model bank for the system. Then, the proposed model bank is accompanied with model predictive controllers to design a high performance advanced process controller. The advantage of this method is the reduction of excessive switch between models and also decrement of the computational complexity in the controller bank that can lead to performance improvement of the control system. The effectiveness of the method is verified by simulations as well as experimental studies on a pH neutralization laboratory apparatus which confirms the efficiency of the proposed algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Direct modeling parameter signature analysis and failure mode prediction of physical systems using hybrid computer optimization

NASA Technical Reports Server (NTRS)

Drake, R. L.; Duvoisin, P. F.; Asthana, A.; Mather, T. W.

1971-01-01

High speed automated identification and design of dynamic systems, both linear and nonlinear, are discussed. Special emphasis is placed on developing hardware and techniques which are applicable to practical problems. The basic modeling experiment and new results are described. Using the improvements developed successful identification of several systems, including a physical example as well as simulated systems, was obtained. The advantages of parameter signature analysis over signal signature analysis in go-no go testing of operational systems were demonstrated. The feasibility of using these ideas in failure mode prediction in operating systems was also investigated. An improved digital controlled nonlinear function generator was developed, de-bugged, and completely documented.

Autoresonant control of nonlinear mode in ultrasonic transducer for machining applications.

PubMed

Babitsky, V I; Astashev, V K; Kalashnikov, A N

2004-04-01

Experiments conducted in several countries have shown that the improvement of machining quality can be promoted through conversion of the cutting process into one involving controllable high-frequency vibration at the cutting zone. This is achieved through the generation and maintenance of ultrasonic vibration of the cutting tool to alter the fracture process of work-piece material cutting to one in which loading of the materials at the tool tip is incremental, repetitive and controlled. It was shown that excitation of the high-frequency vibro-impact mode of the tool-workpiece interaction is the most effective way of ultrasonic influence on the dynamic characteristics of machining. The exploitation of this nonlinear mode needs a new method of adaptive control for excitation and stabilisation of ultrasonic vibration known as autoresonance. An approach has been developed to design an autoresonant ultrasonic cutting unit as an oscillating system with an intelligent electronic feedback controlling self-excitation in the entire mechatronic system. The feedback produces the exciting force by means of transformation and amplification of the motion signal. This allows realisation for robust control of fine resonant tuning to bring the nonlinear high Q-factor systems into technological application. The autoresonant control provides the possibility of self-tuning and self-adaptation mechanisms for the system to keep the nonlinear resonant mode of oscillation under unpredictable variation of load, structure and parameters. This allows simple regulation of intensity of the process whilst keeping maximum efficiency at all times. An autoresonant system with supervisory computer control was developed, tested and used for the control of the piezoelectric transducer during ultrasonically assisted cutting. The system has been developed as combined analog-digital, where analog devices process the control signal, and parameters of the devices are controlled digitally by computer. The system was applied for advanced machining of aviation materials.

High power laser downhole cutting tools and systems

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

Zediker, Mark S; Rinzler, Charles C; Faircloth, Brian O

Downhole cutting systems, devices and methods for utilizing 10 kW or more laser energy transmitted deep into the earth with the suppression of associated nonlinear phenomena. Systems and devices for the laser cutting operations within a borehole in the earth. These systems and devices can deliver high power laser energy down a deep borehole, while maintaining the high power to perform cutting operations in such boreholes deep within the earth.

Nonlinear Aerodynamic Modeling From Flight Data Using Advanced Piloted Maneuvers and Fuzzy Logic

NASA Technical Reports Server (NTRS)

Brandon, Jay M.; Morelli, Eugene A.

2012-01-01

Results of the Aeronautics Research Mission Directorate Seedling Project Phase I research project entitled "Nonlinear Aerodynamics Modeling using Fuzzy Logic" are presented. Efficient and rapid flight test capabilities were developed for estimating highly nonlinear models of airplane aerodynamics over a large flight envelope. Results showed that the flight maneuvers developed, used in conjunction with the fuzzy-logic system identification algorithms, produced very good model fits of the data, with no model structure inputs required, for flight conditions ranging from cruise to departure and spin conditions.

Remote optoelectronic sensors for monitoring of nonlinear surfaces

NASA Astrophysics Data System (ADS)

Petrochenko, Andrew V.; Konyakhin, Igor A.

2015-05-01

Actually during construction of the high building actively are used objects of various nonlinear surface, for example, sinuous (parabolic or hyperbolic) roofs of the sport complexes that require automatic deformation control [1]. This type of deformation has character of deflection that is impossible to monitor objectively with just one optoelectronic sensor (which is fixed on this surface). In this article is described structure of remote optoelectronic sensor, which is part of the optoelectronic monitoring system of nonlinear surface, and mathematical transformation of exterior orientation sensor elements in the coordinates of control points.

Photonic nonlinearities via quantum Zeno blockade.

PubMed

Sun, Yu-Zhu; Huang, Yu-Ping; Kumar, Prem

2013-05-31

Realizing optical-nonlinear effects at a single-photon level is a highly desirable but also extremely challenging task, because of both fundamental and practical difficulties. We present an avenue to surmounting these difficulties by exploiting quantum Zeno blockade in nonlinear optical systems. Considering specifically a lithium-niobate microresonator, we find that a deterministic phase gate can be realized between single photons with near-unity fidelity. Supported by established techniques for fabricating and operating such devices, our approach can provide an enabling tool for all-optical applications in both classical and quantum domains.

Fuzzy model-based servo and model following control for nonlinear systems.

PubMed

Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O

2009-12-01

This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.

Advanced laser architectures for high power eyesafe illuminators

NASA Astrophysics Data System (ADS)

Baranova, N.; Pati, B.; Stebbins, K.; Bystryak, I.; Rayno, M.; Ezzo, K.; DePriest, C.

2018-02-01

Q-Peak has demonstrated a novel pulsed eyesafe laser architecture operating with >50 mJ pulse energies at Pulse Repetition Frequencies (PRFs) as high as 320 Hz. The design leverages an Optical Parametric Oscillator (OPO) and Optical Parametric Amplifier (OPA) geometry, which provides the unique capability for high power in a comparatively compact package, while also offering the potential for additional eyesafe power scaling. The laser consists of a Commercial Off-the-Shelf (COTS) Q-switched front-end seed laser to produce pulse-widths around 10 ns at 1.06-μm, which is then followed by a pair of Multi-Pass Amplifier (MPA) architectures (comprised of side-pumped, multi-pass Nd:YAG slabs with a compact diode-pump-array imaging system), and finally involving two sequential nonlinear optical conversion architectures for transfer into the eyesafe regime. The initial seed beam is first amplified through the MPA, and then split into parallel optical paths. An OPO provides effective nonlinear conversion on one optical path, while a second MPA further amplifies the 1.06-μm beam for use in pumping an OPA on the second optical path. These paths are then recombined prior to seeding the OPA. Each nonlinear conversion subsystem utilizes Potassium Titanyl Arsenate (KTA) for effective nonlinear conversion with lower risk to optical damage. This laser architecture efficiently produces pulse energies of >50 mJ in the eyesafe band at PRFs as high as 320 Hz, and has been designed to fit within a volume of 4,500 in3 (0.074 m3 ). We will discuss theoretical and experimental details of the nonlinear optical system for achieving higher eyesafe powers.

Method and apparatus for delivering high power laser energy over long distances

DOEpatents

Zediker, Mark S; Rinzler, Charles C; Faircloth, Brian O; Koblick, Yeshaya; Moxley, Joel F

2015-04-07

Systems, devices and methods for the transmission and delivery of high power laser energy deep into the earth and for the suppression of associated nonlinear phenomena. Systems, devices and methods for the laser drilling of a borehole in the earth. These systems can deliver high power laser energy down a deep borehole, while maintaining the high power to advance such boreholes deep into the earth and at highly efficient advancement rates.

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

NASA Technical Reports Server (NTRS)

Chin, T. M.; Turmon, M. J.; Jewell, J. B.; Ghil, M.

2006-01-01

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

An extended algebraic reconstruction technique (E-ART) for dual spectral CT.

PubMed

Zhao, Yunsong; Zhao, Xing; Zhang, Peng

2015-03-01

Compared with standard computed tomography (CT), dual spectral CT (DSCT) has many advantages for object separation, contrast enhancement, artifact reduction, and material composition assessment. But it is generally difficult to reconstruct images from polychromatic projections acquired by DSCT, because of the nonlinear relation between the polychromatic projections and the images to be reconstructed. This paper first models the DSCT reconstruction problem as a nonlinear system problem; and then extend the classic ART method to solve the nonlinear system. One feature of the proposed method is its flexibility. It fits for any scanning configurations commonly used and does not require consistent rays for different X-ray spectra. Another feature of the proposed method is its high degree of parallelism, which means that the method is suitable for acceleration on GPUs (graphic processing units) or other parallel systems. The method is validated with numerical experiments from simulated noise free and noisy data. High quality images are reconstructed with the proposed method from the polychromatic projections of DSCT. The reconstructed images are still satisfactory even if there are certain errors in the estimated X-ray spectra.

Nonlinear hybrid modal synthesis based on branch modes for dynamic analysis of assembled structure

NASA Astrophysics Data System (ADS)

Huang, Xing-Rong; Jézéquel, Louis; Besset, Sébastien; Li, Lin; Sauvage, Olivier

2018-01-01

This paper describes a simple and fast numerical procedure to study the steady state responses of assembled structures with nonlinearities along continuous interfaces. The proposed strategy is based on a generalized nonlinear modal superposition approach supplemented by a double modal synthesis strategy. The reduced nonlinear modes are derived by combining a single nonlinear mode method with reduction techniques relying on branch modes. The modal parameters containing essential nonlinear information are determined and then employed to calculate the stationary responses of the nonlinear system subjected to various types of excitation. The advantages of the proposed nonlinear modal synthesis are mainly derived in three ways: (1) computational costs are considerably reduced, when analyzing large assembled systems with weak nonlinearities, through the use of reduced nonlinear modes; (2) based on the interpolation models of nonlinear modal parameters, the nonlinear modes introduced during the first step can be employed to analyze the same system under various external loads without having to reanalyze the entire system; and (3) the nonlinear effects can be investigated from a modal point of view by analyzing these nonlinear modal parameters. The proposed strategy is applied to an assembled system composed of plates and nonlinear rubber interfaces. Simulation results have proven the efficiency of this hybrid nonlinear modal synthesis, and the computation time has also been significantly reduced.

Distributed robust adaptive control of high order nonlinear multi agent systems.

PubMed

Hashemi, Mahnaz; Shahgholian, Ghazanfar

2018-03-01

In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

DOE PAGES

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

2015-03-11

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

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

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

NASA Astrophysics Data System (ADS)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

Wind energy system time-domain (WEST) analyzers

NASA Technical Reports Server (NTRS)

Dreier, M. E.; Hoffman, J. A.

1981-01-01

A portable analyzer which simulates in real time the complex nonlinear dynamics of horizontal axis wind energy systems was constructed. Math models for an aeroelastic rotor featuring nonlinear aerodynamic and inertial terms were implemented with high speed digital controllers and analog calculation. This model was combined with other math models of elastic supports, control systems, a power train and gimballed rotor kinematics. A stroboscopic display system graphically depicting distributed blade loads, motion, and other aerodynamic functions on a cathode ray tube is included. Limited correlation efforts showed good comparison between the results of this analyzer and other sophisticated digital simulations. The digital simulation results were successfully correlated with test data.

A Merged IQC/SOS Theory for Analysis and Synthesis of Nonlinear Control Systems

DTIC Science & Technology

2015-06-23

constraints. As mentioned previously, this enables new applications of IQCs to analyze the robustness of time-varying and nonlinear systems . This...enables new applications of IQCs to analyze the robustness of time-varying and nonlinear systems . This section considers the analysis of nonlinear systems ...AFRL-AFOSR-VA-TR-2016-0008 A Merged IQC/SOS Theory for Analysis and Synthesis of Nonlinear Control Systems Gary Balas REGENTS OF THE UNIVERSITY OF

Non-linear HRV indices under autonomic nervous system blockade.

PubMed

Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel

2014-01-01

Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.

Three-dimensional vortex-induced vibrations of supported pipes conveying fluid based on wake oscillator models

NASA Astrophysics Data System (ADS)

Wang, L.; Jiang, T. L.; Dai, H. L.; Ni, Q.

2018-05-01

The present study develops a new three-dimensional nonlinear model for investigating vortex-induced vibrations (VIV) of flexible pipes conveying internal fluid flow. The unsteady hydrodynamic forces associated with the wake dynamics are modeled by two distributed van der Pol wake oscillators. In particular, the nonlinear partial differential equations of motion of the pipe and the wake are derived, taking into account the coupling between the structure and the fluid. The nonlinear equations of motion for the coupled system are then discretized by means of the Galerkin technique, resulting in a high-dimensional reduced-order model of the system. It is shown that the natural frequencies for in-plane and out-of-plane motions of the pipe may be different at high internal flow velocities beyond the threshold of buckling instability. The orientation angle of the postbuckling configuration is time-varying due to the disturbance of hydrodynamic forces, thus yielding sometimes unexpected results. For a buckled pipe with relatively low cross-flow velocity, interestingly, examining the nonlinear dynamics of the pipe indicates that the combined effects of the cross-flow-induced resonance of the in-plane first mode and the internal-flow-induced buckling on the IL and CF oscillation amplitudes may be significant. For higher cross-flow velocities, however, the effect of internal fluid flow on the nonlinear VIV responses of the pipe is not pronounced.

A Large-Particle Monte Carlo Code for Simulating Non-Linear High-Energy Processes Near Compact Objects

NASA Technical Reports Server (NTRS)

Stern, Boris E.; Svensson, Roland; Begelman, Mitchell C.; Sikora, Marek

1995-01-01

High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.

Multiple model self-tuning control for a class of nonlinear systems

NASA Astrophysics Data System (ADS)

Huang, Miao; Wang, Xin; Wang, Zhenlei

2015-10-01

This study develops a novel nonlinear multiple model self-tuning control method for a class of nonlinear discrete-time systems. An increment system model and a modified robust adaptive law are proposed to expand the application range, thus eliminating the assumption that either the nonlinear term of the nonlinear system or its differential term is global-bounded. The nonlinear self-tuning control method can address the situation wherein the nonlinear system is not subject to a globally uniformly asymptotically stable zero dynamics by incorporating the pole-placement scheme. A novel, nonlinear control structure based on this scheme is presented to improve control precision. Stability and convergence can be confirmed when the proposed multiple model self-tuning control method is applied. Furthermore, simulation results demonstrate the effectiveness of the proposed method.

Improving dynamic performances of PWM-driven servo-pneumatic systems via a novel pneumatic circuit.

PubMed

Taghizadeh, Mostafa; Ghaffari, Ali; Najafi, Farid

2009-10-01

In this paper, the effect of pneumatic circuit design on the input-output behavior of PWM-driven servo-pneumatic systems is investigated and their control performances are improved using linear controllers instead of complex and costly nonlinear ones. Generally, servo-pneumatic systems are well known for their nonlinear behavior. However, PWM-driven servo-pneumatic systems have the advantage of flexibility in the design of pneumatic circuits which affects the input-output linearity of the whole system. A simple pneumatic circuit with only one fast switching valve is designed which leads to a quasi-linear input-output relation. The quasi-linear behavior of the proposed circuit is verified both experimentally and by simulations. Closed loop position control experiments are then carried out using linear P- and PD-controllers. Since the output position is noisy and cannot be directly differentiated, a Kalman filter is designed to estimate the velocity of the cylinder. Highly improved tracking performances are obtained using these linear controllers, compared to previous works with nonlinear controllers.

Distributed ESO based cooperative tracking control for high-order nonlinear multiagent systems with lumped disturbance and application in multi flight simulators systems.

PubMed

Cong, Zhang

2018-03-01

Based on extended state observer, a novel and practical design method is developed to solve the distributed cooperative tracking problem of higher-order nonlinear multiagent systems with lumped disturbance in a fixed communication topology directed graph. The proposed method is designed to guarantee all the follower nodes ultimately and uniformly converge to the leader node with bounded residual errors. The leader node, modeled as a higher-order non-autonomous nonlinear system, acts as a command generator giving commands only to a small portion of the networked follower nodes. Extended state observer is used to estimate the local states and lumped disturbance of each follower node. Moreover, each distributed controller can work independently only requiring the relative states and/or the estimated relative states information between itself and its neighbors. Finally an engineering application of multi flight simulators systems is demonstrated to test and verify the effectiveness of the proposed algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Self-consistent projection operator theory in nonlinear quantum optical systems: A case study on degenerate optical parametric oscillators

NASA Astrophysics Data System (ADS)

Degenfeld-Schonburg, Peter; Navarrete-Benlloch, Carlos; Hartmann, Michael J.

2015-05-01

Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. We apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with a high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1997-01-01

In this paper, we study the Local Discontinuous Galerkin methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L(sup 2)-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

From non-linear magnetoacoustics and spin reorientation transition to magnetoelectric micro/nano-systems

NASA Astrophysics Data System (ADS)

Tiercelin, Nicolas; Preobrazhensky, Vladimir; BouMatar, Olivier; Talbi, Abdelkrim; Giordano, Stefano; Dusch, Yannick; Klimov, Alexey; Mathurin, Théo.; Elmazria, Omar; Hehn, Michel; Pernod, Philippe

2017-09-01

The interaction of a strongly nonlinear spin system with a crystalline lattice through magnetoelastic coupling results in significant modifications of the acoustic properties of magnetic materials, especially in the vicinity of magnetic instabilities associated with the spin-reorientation transition (SRT). The magnetoelastic coupling transfers the critical properties of the magnetic subsystem to the elastic one, which leads to a strong decrease of the sound velocity in the vicinity of the SRT, and allows a large control over acoustic nonlinearities. The general principles of the non-linear magneto-acoustics (NMA) will be introduced and illustrated in `bulk' applications such as acoustic wave phase conjugation, multi-phonon coupling, explosive instability of magneto-elastic vibrations, etc. The concept of the SRT coupled to magnetoelastic interaction has been transferred into nanostructured magnetoelastic multilayers with uni-axial anisotropy. The high sensitivity and the non-linear properties have been demonstrated in cantilever type actuators, and phenomena such as magneto-mechanical RF demodulation have been observed. The combination of the magnetic layers with piezoelectric materials also led to stress-mediated magnetoelectric (ME) composites with high ME coefficients, thanks to the SRT. The magnetoacoustic effects of the SRT have also been studied for surface acoustic waves propagating in the magnetoelastic layers and found to be promising for highly sensitive magnetic field sensors working at room temperature. On the other hand, mechanical stress is a very efficient way to control the magnetic subsystem. The principle of a very energy efficient stress-mediated magnetoelectric writing and reading in a magnetic memory is described.

Enriched Imperialist Competitive Algorithm for system identification of magneto-rheological dampers

NASA Astrophysics Data System (ADS)

Talatahari, Siamak; Rahbari, Nima Mohajer

2015-10-01

In the current research, the imperialist competitive algorithm is dramatically enhanced and a new optimization method dubbed as Enriched Imperialist Competitive Algorithm (EICA) is effectively introduced to deal with high non-linear optimization problems. To conduct a close examination of its functionality and efficacy, the proposed metaheuristic optimization approach is actively employed to sort out the parameter identification of two different types of hysteretic Bouc-Wen models which are simulating the non-linear behavior of MR dampers. Two types of experimental data are used for the optimization problems to minutely examine the robustness of the proposed EICA. The obtained results self-evidently demonstrate the high adaptability of EICA to suitably get to the bottom of such non-linear and hysteretic problems.

Nonlinear Acoustic and Ultrasonic NDT of Aeronautical Components

NASA Astrophysics Data System (ADS)

Van Den Abeele, Koen; Katkowski, Tomasz; Mattei, Christophe

2006-05-01

In response to the demand for innovative microdamage inspection systems, with high sensitivity and undoubted accuracy, we are currently investigating the use and robustness of several acoustic and ultrasonic NDT techniques based on Nonlinear Elastic Wave Spectroscopy (NEWS) for the characterization of microdamage in aeronautical components. In this report, we illustrate the results of an amplitude dependent analysis of the resonance behaviour, both in time (signal reverberation) and in frequency (sweep) domain. The technique is applied to intact and damaged samples of Carbon Fiber Reinforced Plastics (CFRP) composites after thermal loading or mechanical fatigue. The method shows a considerable gain in sensitivity and an incontestable interpretation of the results for nonlinear signatures in comparison with the linear characteristics. For highly fatigued samples, slow dynamical effects are observed.

FINDS: A fault inferring nonlinear detection system programmers manual, version 3.0

NASA Technical Reports Server (NTRS)

Lancraft, R. E.

1985-01-01

Detailed software documentation of the digital computer program FINDS (Fault Inferring Nonlinear Detection System) Version 3.0 is provided. FINDS is a highly modular and extensible computer program designed to monitor and detect sensor failures, while at the same time providing reliable state estimates. In this version of the program the FINDS methodology is used to detect, isolate, and compensate for failures in simulated avionics sensors used by the Advanced Transport Operating Systems (ATOPS) Transport System Research Vehicle (TSRV) in a Microwave Landing System (MLS) environment. It is intended that this report serve as a programmers guide to aid in the maintenance, modification, and revision of the FINDS software.

Dispersion compensation of fiber optic communication system with direct detection using artificial neural networks (ANNs)

NASA Astrophysics Data System (ADS)

Maghrabi, Mahmoud M. T.; Kumar, Shiva; Bakr, Mohamed H.

2018-02-01

This work introduces a powerful digital nonlinear feed-forward equalizer (NFFE), exploiting multilayer artificial neural network (ANN). It mitigates impairments of optical communication systems arising due to the nonlinearity introduced by direct photo-detection. In a direct detection system, the detection process is nonlinear due to the fact that the photo-current is proportional to the absolute square of the electric field intensity. The proposed equalizer provides the most efficient computational cost with high equalization performance. Its performance is comparable to the benchmark compensation performance achieved by maximum-likelihood sequence estimator. The equalizer trains an ANN to act as a nonlinear filter whose impulse response removes the intersymbol interference (ISI) distortions of the optical channel. Owing to the proposed extensive training of the equalizer, it achieves the ultimate performance limit of any feed-forward equalizer (FFE). The performance and efficiency of the equalizer is investigated by applying it to various practical short-reach fiber optic communication system scenarios. These scenarios are extracted from practical metro/media access networks and data center applications. The obtained results show that the ANN-NFFE compensates for the received BER degradation and significantly increases the tolerance to the chromatic dispersion distortion.

Nonlinear bleaching, absorption, and scattering of 532-nm-irradiated plasmonic nanoparticles

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

Liberman, V.; Sworin, M.; Kingsborough, R. P.

2013-02-07

Single-pulse irradiation of Au and Ag suspensions of nanospheres and nanodisks with 532-nm 4-ns pulses has identified complex optical nonlinearities while minimizing material damage. For all materials tested, we observe competition between saturable absorption (SA) and reverse SA (RSA), with RSA behavior dominating for intensities above {approx}50 MW/cm{sup 2}. Due to reduced laser damage in single-pulse experiments, the observed intrinsic nonlinear absorption coefficients are the highest reported to date for Au nanoparticles. We find size dependence to the nonlinear absorption enhancement for Au nanoparticles, peaking in magnitude for 80-nm nanospheres and falling off at larger sizes. The nonlinear absorption coefficientsmore » for Au and Ag spheres are comparable in magnitude. On the other hand, the nonlinear absorption for Ag disks, when corrected for volume fraction, is several times higher. These trends in nonlinear absorption are correlated to local electric field enhancement through quasi-static mean-field theory. Through variable size aperture measurements, we also separate nonlinear scattering from nonlinear absorption. For all materials tested, we find that nonlinear scattering is highly directional and that its magnitude is comparable to that of nonlinear absorption. These results indicate methods to improve the efficacy of plasmonic nanoparticles as optical limiters in pulsed laser systems.« less

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.

Polyspectral signal analysis techniques for condition based maintenance of helicopter drive-train system

NASA Astrophysics Data System (ADS)

Hassan Mohammed, Mohammed Ahmed

For an efficient maintenance of a diverse fleet of air- and rotorcraft, effective condition based maintenance (CBM) must be established based on rotating components monitored vibration signals. In this dissertation, we present theory and applications of polyspectral signal processing techniques for condition monitoring of critical components in the AH-64D helicopter tail rotor drive train system. Currently available vibration-monitoring tools are mostly built around auto- and cross-power spectral analysis which have limited performance in detecting frequency correlations higher than second order. Studying higher order correlations and their Fourier transforms, higher order spectra, provides more information about the vibration signals which helps in building more accurate diagnostic models of the mechanical system. Based on higher order spectral analysis, different signal processing techniques are developed to assess health conditions of different critical rotating-components in the AH-64D helicopter drive-train. Based on cross-bispectrum, quadratic nonlinear transfer function is presented to model second order nonlinearity in a drive-shaft running between the two hanger bearings. Then, quadratic-nonlinearity coupling coefficient between frequency harmonics of the rotating shaft is used as condition metric to study different seeded shaft faults compared to baseline case, namely: shaft misalignment, shaft imbalance, and combination of shaft misalignment and imbalance. The proposed quadratic-nonlinearity metric shows better capabilities in distinguishing the four studied shaft settings than the conventional linear coupling based on cross-power spectrum. We also develop a new concept of Quadratic-Nonlinearity Power-Index spectrum, QNLPI(f), that can be used in signal detection and classification, based on bicoherence spectrum. The proposed QNLPI(f) is derived as a projection of the three-dimensional bicoherence spectrum into two-dimensional spectrum that quantitatively describes how much of the mean square power at certain frequency f is generated due to nonlinear quadratic interaction between different frequency components. The proposed index, QNLPI(f), can be used to simplify the study of bispectrum and bicoherence signal spectra. It also inherits useful characteristics from the bicoherence such as high immunity to additive Gaussian noise, high capability of nonlinear-systems identifications, and amplification invariance. The quadratic-nonlinear power spectral density PQNL(f) and percentage of quadratic nonlinear power PQNLP are also introduced based on the QNLPI(f). Concept of the proposed indices and their computational considerations are discussed first using computer generated data, and then applied to real-world vibration data to assess health conditions of different rotating components in the drive train including drive-shaft, gearbox, and hanger bearing faults. The QNLPI(f) spectrum enables us to gain more details about nonlinear harmonic generation patterns that can be used to distinguish between different cases of mechanical faults, which in turn helps to gaining more diagnostic/prognostic capabilities.

Developing a local least-squares support vector machines-based neuro-fuzzy model for nonlinear and chaotic time series prediction.

PubMed

Miranian, A; Abdollahzade, M

2013-02-01

Local modeling approaches, owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models, seem appealing for modeling, identification, and prediction applications. In this paper, we propose a local neuro-fuzzy (LNF) approach based on the least-squares support vector machines (LSSVMs). The proposed LNF approach employs LSSVMs, which are powerful in modeling and predicting time series, as local models and uses hierarchical binary tree (HBT) learning algorithm for fast and efficient estimation of its parameters. The HBT algorithm heuristically partitions the input space into smaller subdomains by axis-orthogonal splits. In each partitioning, the validity functions automatically form a unity partition and therefore normalization side effects, e.g., reactivation, are prevented. Integration of LSSVMs into the LNF network as local models, along with the HBT learning algorithm, yield a high-performance approach for modeling and prediction of complex nonlinear time series. The proposed approach is applied to modeling and predictions of different nonlinear and chaotic real-world and hand-designed systems and time series. Analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed LNF approach with the HBT learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series.

Wideband electromagnetic energy harvesting from ambient vibrations

NASA Astrophysics Data System (ADS)

Mallick, Dhiman; Podder, Pranay; Roy, Saibal

2015-06-01

Different bandwidth widening schemes of electromagnetic energy harvesters have been reported in this work. The devices are fabricated on FR4 substrate using laser micromachining techniques. The linear device operate in a narrow band around the resonance; in order to tune resonant frequency of the device electrically, two different types of complex load topologies are adopted. Using capacitive load, the resonant frequency is tuned in the low frequency direction whereas using inductive load, the resonant frequency is tuned in the high frequency direction. An overall tuning range of ˜2.4 Hz is obtained at 0.3g though the output power dropped significantly over the tuning range. In order to improve the off-resonance performance, nonlinear oscillation based systems are adopted. A specially designed spring arm with fixed-guided configuration produced single well nonlinear monostable configuration. With increasing input acceleration, wider bandwidth is obtained with such a system as large displacement, stretching nonlinearity comes into play and 9.55 Hz bandwidth is obtained at 0.5g. The repulsive force between one static and one vibrating oppositely polarized magnets are used to generate bistable nonlinear potential system. The distance between the mentioned magnets is varied between 4 to 10 mm to produce tunable nonlinearity with a maximum half power bandwidth over 3 Hz at 0.5g.

Fast novel nonlinear optical NLC system with local response

NASA Astrophysics Data System (ADS)

Iljin, Andrey; Residori, Stefania; Bortolozzo, Umberto

2017-06-01

Nonlinear optical performance of a novel liquid crystalline (LC) cell has been studied in two-wave mixing experiments revealing high diffraction efficiency within extremely wide intensity range, fast recording times and spatial resolution. Photo-induced modulation of the LC order parameter resulting from trans-cis isomerisation of dye molecules causes consequent changes of refractive indices of the medium (Light-Induced Order Modification, LIOM-mechanism) and is proved to be the main mechanism of optical nonlinearity. The proposed arrangement of the electric-field-stabilised homeotropic alignment hinders the LC director reorientation, prevents appearance of surface effects and ensures the optical cell quality. The LIOM-type nonlinearity, characterised with the substantially local nonlinear optical response, could also be extended for the recording of arbitrary phase profiles as requested in several applications for light-beam manipulation, recording of dynamic volume holograms and photonic lattices.

Nonlinear adhesion dynamics of confined lipid membranes

NASA Astrophysics Data System (ADS)

To, Tung; Le Goff, Thomas; Pierre-Louis, Olivier

Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems. Supported by the grand ANR Biolub.

Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability

PubMed Central

Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.

2016-01-01

Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose–Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics. PMID:27991513

Nonlinear Prediction Model for Hydrologic Time Series Based on Wavelet Decomposition

NASA Astrophysics Data System (ADS)

Kwon, H.; Khalil, A.; Brown, C.; Lall, U.; Ahn, H.; Moon, Y.

2005-12-01

Traditionally forecasting and characterizations of hydrologic systems is performed utilizing many techniques. Stochastic linear methods such as AR and ARIMA and nonlinear ones such as statistical learning theory based tools have been extensively used. The common difficulty to all methods is the determination of sufficient and necessary information and predictors for a successful prediction. Relationships between hydrologic variables are often highly nonlinear and interrelated across the temporal scale. A new hybrid approach is proposed for the simulation of hydrologic time series combining both the wavelet transform and the nonlinear model. The present model employs some merits of wavelet transform and nonlinear time series model. The Wavelet Transform is adopted to decompose a hydrologic nonlinear process into a set of mono-component signals, which are simulated by nonlinear model. The hybrid methodology is formulated in a manner to improve the accuracy of a long term forecasting. The proposed hybrid model yields much better results in terms of capturing and reproducing the time-frequency properties of the system at hand. Prediction results are promising when compared to traditional univariate time series models. An application of the plausibility of the proposed methodology is provided and the results conclude that wavelet based time series model can be utilized for simulating and forecasting of hydrologic variable reasonably well. This will ultimately serve the purpose of integrated water resources planning and management.

Linear and nonlinear subspace analysis of hand movements during grasping.

PubMed

Cui, Phil Hengjun; Visell, Yon

2014-01-01

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

Experimental Control of Thermocapillary Convection in a Liquid Bridge

NASA Technical Reports Server (NTRS)

Petrov, Valery; Schatz, Michael F.; Muehlner, Kurt A.; VanHook, Stephen J.; McCormick, W. D.; Swift, Jack B.; Swinney, Harry L.

1996-01-01

We demonstrate the stabilization of an isolated unstable periodic orbit in a liquid bridge convection experiment. A model independent, nonlinear control algorithm uses temperature measurements near the liquid interface to compute control perturbations which are applied by a thermoelectric element. The algorithm employs a time series reconstruction of a nonlinear control surface in a high dimensional phase space to alter the system dynamics.

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

NASA Astrophysics Data System (ADS)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique

NASA Astrophysics Data System (ADS)

Zhang, X.; Huang, X. L.; Lu, H. Q.

2017-02-01

In this study, a quasi-finite-time control method for designing stabilising control laws is developed for high-order strict-feedback nonlinear systems with mismatched disturbances. By using mapping filtered forwarding technique, a virtual control is designed to force the off-the-manifold coordinate to converge to zero in quasi-finite time at each step of the design; at the same time, the manifold is rendered insensitive to time-varying, bounded and unknown disturbances. In terms of standard forwarding methodology, the algorithm proposed here not only does not require the Lyapunov function for controller design, but also avoids to calculate the derivative of sign function. As far as the dynamic performance of closed-loop systems is concerned, we essentially obtain the finite-time performances, which is typically reflected in the following aspects: fast and accurate responses, high tracking precision, and robust disturbance rejection. Spring, mass, and damper system and flexible joints robot are tested to demonstrate the proposed controller performance.

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

On the benefit of DMT modulation in nonlinear VLC systems.

PubMed

Qian, Hua; Cai, Sunzeng; Yao, Saijie; Zhou, Ting; Yang, Yang; Wang, Xudong

2015-02-09

In a visible light communication (VLC) system, the nonlinear characteristic of the light emitting diode (LED) in transmitter is a limiting factor of system performance. Modern modulation signals with large peak-to-power-ratio (PAPR) suffers uneven distortion. The nonlinear response directly impacts the intensity modulation and direct detection VLC system with pulse-amplitude modulation (PAM). The amplitude of the PAM signal is distorted unevenly and large signal is vulnerable to noise. Orthogonal linear transformations, such as discrete multi-tone (DMT) modulation, can spread the nonlinear effects evenly to each data symbol, thus perform better than PAM signals. In this paper, we provide theoretical analysis on the benefit of DMT modulation in nonlinear VLC system. We show that the DMT modulation is a better choice than the PAM modulation for the VLC system as the DMT modulation is more robust against nonlinearity. We also show that the post-distortion nonlinear elimination method, which is applied at the receiver, can be a reliable solution to the nonlinear VLC system. Simulation results show that the post-distortion greatly improves the system performance for the DMT modulation.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

PubMed

Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

2014-11-21

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

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.

Design of a nonlinear torsional vibration absorber

NASA Astrophysics Data System (ADS)

Tahir, Ammaar Bin

Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.

Global Regularity for the Fractional Euler Alignment System

NASA Astrophysics Data System (ADS)

Do, Tam; Kiselev, Alexander; Ryzhik, Lenya; Tan, Changhui

2018-04-01

We study a pressureless Euler system with a non-linear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density dependence is natural: the alignment rate increases in the areas of high density due to species discomfort. The diffusive term has the order of a fractional Laplacian {(-partial _{xx})^{α/2}, α \\in (0, 1)}. The corresponding Burgers equation with a linear dissipation of this type develops shocks in a finite time. We show that the alignment nonlinearity enhances the dissipation, and the solutions are globally regular for all {α \\in (0, 1)}. To the best of our knowledge, this is the first example of such regularization due to the non-local nonlinear modulation of dissipation.

Models for short-wave instability in inviscid shear flows

NASA Astrophysics Data System (ADS)

Grimshaw, Roger

1999-11-01

The generation of instability in an invsicid fluid occurs by a resonance between two wave modes, where here the resonance occurs by a coincidence of phase speeds for a finite, non-zero wavenumber. We show that in the weakly nonlinear limit, the appropriate model consists of two coupled equations for the envelopes of the wave modes, in which the nonlinear terms are balanced with low-order cross-coupling linear dispersive terms rather than the more familiar high-order terms which arise in the nonlinear Schrodinger equation, for instance. We will show that this system may either contain gap solitons as solutions in the linearly stable case, or wave breakdown in the linearly unstable case. In this latter circumstance, the system either exhibits wave collapse in finite time, or disintegration into fine-scale structures.

Swarming behaviors in multi-agent systems with nonlinear dynamics

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

Yu, Wenwu, E-mail: wenwuyu@gmail.com; School of Electrical and Computer Engineering, RMIT University, Melbourne VIC 3001; Chen, Guanrong

2013-12-15

The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agentmore » is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.« less

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

PubMed Central

Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

2014-01-01

The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

Multi-application controls: Robust nonlinear multivariable aerospace controls applications

NASA Technical Reports Server (NTRS)

Enns, Dale F.; Bugajski, Daniel J.; Carter, John; Antoniewicz, Bob

1994-01-01

This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented as a method for analyzing robust performance and the mu-synthesis method will be presented as a method for synthesizing a robust control system. The paper concludes with the author's expectations regarding future applications of robust nonlinear multivariable controls.

Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

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

Dorofeenko, V. G.; Krasovitskiy, V. B.; Turikov, V. A.

2012-06-15

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of 'slow' equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period,more » is used to describe steady-state nonlinear oscillations in plasma.« less

Nonlinear dynamics and cavity cooling of levitated nanoparticles

NASA Astrophysics Data System (ADS)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-09-01

We investigate a dynamic nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. An optical cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, whilst simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. Through the rich sideband structure displayed by the cavity output we can observe cooling of the linear and non-linear particle's motion. Here we present an experimental setup which allows full control over the cavity resonant frequencies, and shows cooling of the particle's motion as a function of the detuning. This work paves the way to strong-coupled quantum dynamics between a cavity and a mesoscopic object largely decoupled from its environment.

Nonlinear dielectric effects in liquids: a guided tour

NASA Astrophysics Data System (ADS)

Richert, Ranko

2017-09-01

Dielectric relaxation measurements probe how the polarization of a material responds to the application of an external electric field, providing information on structure and dynamics of the sample. In the limit of small fields and thus linear response, such experiments reveal the properties of the material in the same thermodynamic state it would have in the absence of the external field. At sufficiently high fields, reversible changes in enthalpy and entropy of the system occur even at constant temperature, and these will in turn alter the polarization responses. The resulting nonlinear dielectric effects feature field induced suppressions (saturation) and enhancements (chemical effect) of the amplitudes, as well as time constant shifts towards faster (energy absorption) and slower (entropy reduction) dynamics. This review focuses on the effects of high electric fields that are reversible and observed at constant temperature for single component glass-forming liquids. The experimental challenges involved in nonlinear dielectric experiments, the approaches to separating and identifying the different sources of nonlinear behavior, and the current understanding of how high electric fields affect dielectric materials will be discussed. Covering studies from Debye’s initial approach to the present state-of-the-art, it will be emphasized what insight can be gained from the nonlinear responses that are not available from dielectric relaxation results obtained in the linear regime.

Chi 3 dispersion in planar tantalum pentoxide waveguides in the telecommunications window.

PubMed

Chen, Ruiqi Y; Charlton, Martin D B; Lagoudakis, Pavlos G

2009-04-01

We report on the dispersion of the third-order nonlinear susceptibility (chi(3) or "Chi 3") in planar Ta2O5 waveguides in the telecommunications spectral window. We utilize the observation of third-harmonic generation under ultrashort pulsed excitation as a reference-free characterization method of chi(3) and obtain a large nonlinear coefficient, 2x10(-13) esu, at 1550 nm. Our observation of efficient third-harmonic generation in Ta2O5 waveguides in the telecoms window reveals the potential of this material system in high-speed integrated nonlinear optical switches.

Spatial nonlinearities: Cascading effects in the earth system

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

2006-01-01

Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

PubMed

Venturi, D; Karniadakis, G E

2014-06-08

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection-reaction problems.

Nonlinear filtering techniques for noisy geophysical data: Using big data to predict the future

NASA Astrophysics Data System (ADS)

Moore, J. M.

2014-12-01

Chaos is ubiquitous in physical systems. Within the Earth sciences it is readily evident in seismology, groundwater flows and drilling data. Models and workflows have been applied successfully to understand and even to predict chaotic systems in other scientific fields, including electrical engineering, neurology and oceanography. Unfortunately, the high levels of noise characteristic of our planet's chaotic processes often render these frameworks ineffective. This contribution presents techniques for the reduction of noise associated with measurements of nonlinear systems. Our ultimate aim is to develop data assimilation techniques for forward models that describe chaotic observations, such as episodic tremor and slip (ETS) events in fault zones. A series of nonlinear filters are presented and evaluated using classical chaotic systems. To investigate whether the filters can successfully mitigate the effect of noise typical of Earth science, they are applied to sunspot data. The filtered data can be used successfully to forecast sunspot evolution for up to eight years (see figure).

Convolutionless Nakajima–Zwanzig equations for stochastic analysis in nonlinear dynamical systems

PubMed Central

Venturi, D.; Karniadakis, G. E.

2014-01-01

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g. functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima–Zwanzig–Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance and stochastic advection–reaction problems. PMID:24910519

Nonlinear time-series-based adaptive control applications

NASA Technical Reports Server (NTRS)

Mohler, R. R.; Rajkumar, V.; Zakrzewski, R. R.

1991-01-01

A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.

Modelling and control of a nonlinear magnetostrictive actuator system

NASA Astrophysics Data System (ADS)

Ramli, M. H. M.; Majeed, A. P. P. Abdul; Anuar, M. A. M.; Mohamed, Z.

2018-04-01

This paper explores the implementation of a feedforward control method to a nonlinear control system, in particular, Magnetostrictive Actuators (MA) that has excellent properties of energy conversion between the mechanical and magnetic form through magnetostriction effects which could be used in actuating and sensing application. MA is known to exhibit hysteresis behaviour and it is rate dependent (the level of hysteresis depends closely on the rate of input excitation frequency). This is, nonetheless, an undesirable behaviour and has to be eliminated in realising high precision application. The MA is modelled by a phenomenological modelling approach via Prandtl-Ishlinskii (P-I) operator to characterise the hysteresis nonlinearities. A feedforward control strategy is designed and implemented to linearize and eliminate the hysteresis by model inversion. The results show that the P-I operator has the capability to model the hysteretic nonlinearity of MA with an acceptable accuracy. Furthermore, the proposed control scheme has demonstrated to be effective in providing superior trajectory tracking.

Computational process to study the wave propagation In a non-linear medium by quasi- linearization

NASA Astrophysics Data System (ADS)

Sharath Babu, K.; Venkata Brammam, J.; Baby Rani, CH

2018-03-01

Two objects having distinct velocities come into contact an impact can occur. The impact study i.e., in the displacement of the objects after the impact, the impact force is function of time‘t’ which is behaves similar to compression force. The impact tenure is very short so impulses must be generated subsequently high stresses are generated. In this work we are examined the wave propagation inside the object after collision and measured the object non-linear behavior in the one-dimensional case. Wave transmission is studied by means of material acoustic parameter value. The objective of this paper is to present a computational study of propagating pulsation and harmonic waves in nonlinear media using quasi-linearization and subsequently utilized the central difference scheme. This study gives focus on longitudinal, one- dimensional wave propagation. In the finite difference scheme Non-linear system is reduced to a linear system by applying quasi-linearization method. The computed results exhibit good agreement on par with the selected non-liner wave propagation.

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.

THz impulse radar for biomedical sensing: nonlinear system behavior

NASA Astrophysics Data System (ADS)

Brown, E. R.; Sung, Shijun; Grundfest, W. S.; Taylor, Z. D.

2014-03-01

The THz impulse radar is an "RF-inspired" sensor system that has performed remarkably well since its initial development nearly six years ago. It was developed for ex vivo skin-burn imaging, and has since shown great promise in the sensitive detection of hydration levels in soft tissues of several types, such as in vivo corneal and burn samples. An intriguing aspect of the impulse radar is its hybrid architecture which combines the high-peak-power of photoconductive switches with the high-responsivity and -bandwidth (RF and video) of Schottky-diode rectifiers. The result is a very sensitive sensor system in which the post-detection signal-to-noise ratio depends super-linearly on average signal power up to a point where the diode is "turned on" in the forward direction, and then behaves quasi-linearly beyond that point. This paper reports the first nonlinear systems analysis done on the impulse radar using MATLAB.

High power laser workover and completion tools and systems

DOEpatents

Zediker, Mark S; Rinzler, Charles C; Faircloth, Brian O; Koblick, Yeshaya; Moxley, Joel F

2014-10-28

Workover and completion systems, devices and methods for utilizing 10 kW or more laser energy transmitted deep into the earth with the suppression of associated nonlinear phenomena. Systems and devices for the laser workover and completion of a borehole in the earth. These systems and devices can deliver high power laser energy down a deep borehole, while maintaining the high power to perform laser workover and completion operations in such boreholes deep within the earth.

Structure Computation of Quiet Spike[Trademark] Flight-Test Data During Envelope Expansion

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

System identification or mathematical modeling is used in the aerospace community for development of simulation models for robust control law design. These models are often described as linear time-invariant processes. Nevertheless, it is well known that the underlying process is often nonlinear. The reason for using a linear approach has been due to the lack of a proper set of tools for the identification of nonlinear systems. Over the past several decades, the controls and biomedical communities have made great advances in developing tools for the identification of nonlinear systems. These approaches are robust and readily applicable to aerospace systems. In this paper, we show the application of one such nonlinear system identification technique, structure detection, for the analysis of F-15B Quiet Spike(TradeMark) aeroservoelastic flight-test data. Structure detection is concerned with the selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description that may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modeling may be of critical importance for the development of robust parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion, which may save significant development time and costs. The objectives of this study are to demonstrate via analysis of F-15B Quiet Spike aeroservoelastic flight-test data for several flight conditions that 1) linear models are inefficient for modeling aeroservoelastic data, 2) nonlinear identification provides a parsimonious model description while providing a high percent fit for cross-validated data, and 3) the model structure and parameters vary as the flight condition is altered.

Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method

NASA Astrophysics Data System (ADS)

Kenderi, Gábor; Fidlin, Alexander

2014-12-01

The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master-slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.

Method and apparatus for delivering high power laser energy over long distances

DOEpatents

Zediker, Mark S; Rinzler, Charles C; Faircloth, Brian O; Koblick, Yeshaya; Moxley, Joel F

2013-08-20

Systems, devices and methods for the transmission of 1 kW or more of laser energy deep into the earth and for the suppression of associated nonlinear phenomena. Systems, devices and methods for the laser drilling of a borehole in the earth. These systems can deliver high power laser energy down a deep borehole, while maintaining the high power to advance such boreholes deep into the earth and at highly efficient advancement rates.

Further Results of Soft-Inplane Tiltrotor Aeromechanics Investigation Using Two Multibody Analyses

NASA Technical Reports Server (NTRS)

Masarati, Pierangelo; Quaranta, Giuseppe; Piatak, David J.; Singleton, Jeffrey D.

2004-01-01

This investigation focuses on the development of multibody analytical models to predict the dynamic response, aeroelastic stability, and blade loading of a soft-inplane tiltrotor wind-tunnel model. Comprehensive rotorcraft-based multibody analyses enable modeling of the rotor system to a high level of detail such that complex mechanics and nonlinear effects associated with control system geometry and joint deadband may be considered. The influence of these and other nonlinear effects on the aeromechanical behavior of the tiltrotor model are examined. A parametric study of the design parameters which may have influence on the aeromechanics of the soft-inplane rotor system are also included in this investigation.

Development of Nonlinear Flight Mechanical Model of High Aspect Ratio Light Utility Aircraft

NASA Astrophysics Data System (ADS)

Bahri, S.; Sasongko, R. A.

2018-04-01

The implementation of Flight Control Law (FCL) for Aircraft Electronic Flight Control System (EFCS) aims to reduce pilot workload, while can also enhance the control performance during missions that require long endurance flight and high accuracy maneuver. In the development of FCL, a quantitative representation of the aircraft dynamics is needed for describing the aircraft dynamics characteristic and for becoming the basis of the FCL design. Hence, a 6 Degree of Freedom nonlinear model of a light utility aircraft dynamics, also called the nonlinear Flight Mechanical Model (FMM), is constructed. This paper shows the construction of FMM from mathematical formulation, the architecture design of FMM, the trimming process and simulations. The verification of FMM is done by analysis of aircraft behaviour in selected trimmed conditions.

Stable propagation of mechanical signals in soft media using stored elastic energy.

PubMed

Raney, Jordan R; Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M; Lewis, Jennifer A; Bertoldi, Katia

2016-08-30

Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals. Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.

Stable propagation of mechanical signals in soft media using stored elastic energy

PubMed Central

Raney, Jordan R.; Nadkarni, Neel; Daraio, Chiara; Lewis, Jennifer A.; Bertoldi, Katia

2016-01-01

Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals. Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates. PMID:27519797

Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems.

PubMed

Li, Jianfeng; Huang, Zhitong; Liu, Xiaoshuang; Ji, Yuefeng

2015-01-12

A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (N-TDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings

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

Kadtke, J.B.; Bulsara, A.

These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)

Nonlinear Control of a Reusable Rocket Engine for Life Extension

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Holmes, Michael S.; Ray, Asok

1998-01-01

This paper presents the conceptual development of a life-extending control system where the objective is to achieve high performance and structural durability of the plant. A life-extending controller is designed for a reusable rocket engine via damage mitigation in both the fuel (H2) and oxidizer (O2) turbines while achieving high performance for transient responses of the combustion chamber pressure and the O2/H2 mixture ratio. The design procedure makes use of a combination of linear and nonlinear controller synthesis techniques and also allows adaptation of the life-extending controller module to augment a conventional performance controller of the rocket engine. The nonlinear aspect of the design is achieved using non-linear parameter optimization of a prescribed control structure. Fatigue damage in fuel and oxidizer turbine blades is primarily caused by stress cycling during start-up, shutdown, and transient operations of a rocket engine. Fatigue damage in the turbine blades is one of the most serious causes for engine failure.

Transient Vibration Prediction for Rotors on Ball Bearings Using Load-dependent Non-linear Bearing Stiffness

NASA Technical Reports Server (NTRS)

Fleming, David P.; Poplawski, J. V.

2002-01-01

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

Linear non-normality as the cause of nonlinear instability in LAPD

NASA Astrophysics Data System (ADS)

Friedman, Brett; Carter, Troy; Umansky, Maxim

2013-10-01

A BOUT + + simulation using a Braginskii fluid model reproduces drift-wave turbulence in LAPD with high qualitative and quantitative agreement. The turbulent fluctuations in the simulation sustain themselves through a nonlinear instability mechanism that injects energy into k|| = 0 fluctuations despite the fact that all of the linear eigenmodes at k|| = 0 are stable. The reason for this is the high non-orthogonality of the eigenmodes caused by the non-normality of the linear operator, which is common in fluid and plasma models that contain equilibrium gradients. While individual stable eigenmodes must decay when acted upon by their linear operator, the sum of the eigenmodes may grow transiently with initial algebraic time dependence. This transient growth can inject energy into the system, and the nonlinearities can remix the eigenmode amplitudes to self-sustain the growth. Such a mechanism also acts in subcritical neutral fluid turbulence, and the self-sustainment process is quite similar, indicating the universality of this nonlinear instability.

Triple tailored nonlinear dispersion of dressed four- and six-wave mixing

NASA Astrophysics Data System (ADS)

Sun, Yanyong; Wang, Zhiguo; Zhang, Zhaoyang; Gu, Bingling; Wang, Kun; Yang, Gaoguo; Zhang, Yanpeng

2018-06-01

We investigate the spectral signals and spatial images of a probe transmission signal, four-wave mixing (FWM), and six-wave mixing (SWM) under double dressing effects in an inverted Y-type system. Especially, we get the triple tailored nonlinear dispersion (about 60 MHz) of the dressed FWM and SWM through the interaction between electromagnetically induced transparency (EIT) windows and the Kerr nonlinearity. Moreover, SWM and dressed FWM with narrow linewidth are obtained through the tailoring of the three EIT windows, which is much narrower than the EIT. In addition, we first elaborate the modulation effect from the self-Kerr coefficient of FWM on the spot. We also investigate the spatial characteristics (defocusing, shifting, and splitting) of FWM and SWM induced by tailored self-Kerr and cross-Kerr effects among the relative fields. Such spatial shifting, splitting induced by the tailored nonlinear dispersion can be used for a higher contrast and high speed switch as well as a high resolution router.

Design of HIFU transducers for generating specified nonlinear ultrasound fields

PubMed Central

Rosnitskiy, Pavel B.; Yuldashev, Petr V.; Sapozhnikov, Oleg A.; Maxwell, Adam; Kreider, Wayne; Bailey, Michael R.; Khokhlova, Vera A.

2016-01-01

Various clinical applications of high intensity focused ultrasound (HIFU) have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this work was to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasilinear conditions at the focus. Multi-parametric nonlinear modeling based on the KZK equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. Results are presented in terms of the parameters of an equivalent single-element, spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full-diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields. PMID:27775904

Human systems dynamics: Toward a computational model

NASA Astrophysics Data System (ADS)

Eoyang, Glenda H.

2012-09-01

A robust and reliable computational model of complex human systems dynamics could support advancements in theory and practice for social systems at all levels, from intrapersonal experience to global politics and economics. Models of human interactions have evolved from traditional, Newtonian systems assumptions, which served a variety of practical and theoretical needs of the past. Another class of models has been inspired and informed by models and methods from nonlinear dynamics, chaos, and complexity science. None of the existing models, however, is able to represent the open, high dimension, and nonlinear self-organizing dynamics of social systems. An effective model will represent interactions at multiple levels to generate emergent patterns of social and political life of individuals and groups. Existing models and modeling methods are considered and assessed against characteristic pattern-forming processes in observed and experienced phenomena of human systems. A conceptual model, CDE Model, based on the conditions for self-organizing in human systems, is explored as an alternative to existing models and methods. While the new model overcomes the limitations of previous models, it also provides an explanatory base and foundation for prospective analysis to inform real-time meaning making and action taking in response to complex conditions in the real world. An invitation is extended to readers to engage in developing a computational model that incorporates the assumptions, meta-variables, and relationships of this open, high dimension, and nonlinear conceptual model of the complex dynamics of human systems.

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

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

Hager, Robert, E-mail: rhager@pppl.gov; Yoon, E.S., E-mail: yoone@rpi.edu; Ku, S., E-mail: sku@pppl.gov

2016-06-15

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable onmore » high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.« less

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

DOE PAGES

Hager, Robert; Yoon, E. S.; Ku, S.; ...

2016-04-04

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. The non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. Moreover, the finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computingmore » systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. As a result, the collision operator's good weak and strong scaling behavior are shown.« less

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

PubMed

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

2015-12-24

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

Asymptotic Stability of Interconnected Passive Non-Linear Systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Joshi, S. M.; Kelkar, A. G.

1999-01-01

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

Influence of unbalance on the nonlinear dynamical response and stability of flexible rotor-bearing systems

NASA Technical Reports Server (NTRS)

Gunter, E. J.; Humphris, R. R.; Springer, H.

1983-01-01

In this paper, some of the effects of unbalance on the nonlinear response and stability of flexible rotor-bearing systems is presented from both a theoretical and experimental standpoint. In a linear system, operating above its stability threshold, the amplitude of motion grows exponentially with time and the orbits become unbounded. In an actual system, this is not necessarily the case. The actual amplitudes of motion may be bounded due to various nonlinear effects in the system. These nonlinear effects cause limit cycles of motion. Nonlinear effects are inherent in fluid film bearings and seals. Other contributors to nonlinear effects are shafts, couplings and foundations. In addition to affecting the threshold of stability, the nonlinear effects can cause jump phenomena to occur at not only the critical speeds, but also at stability onset or restabilization speeds.

Reentry Vehicle Flight Controls Design Guidelines: Dynamic Inversion

NASA Technical Reports Server (NTRS)

Ito, Daigoro; Georgie, Jennifer; Valasek, John; Ward, Donald T.

2002-01-01

This report addresses issues in developing a flight control design for vehicles operating across a broad flight regime and with highly nonlinear physical descriptions of motion. Specifically it addresses the need for reentry vehicles that could operate through reentry from space to controlled touchdown on Earth. The latter part of controlled descent is achieved by parachute or paraglider - or by all automatic or a human-controlled landing similar to that of the Orbiter. Since this report addresses the specific needs of human-carrying (not necessarily piloted) reentry vehicles, it deals with highly nonlinear equations of motion, and then-generated control systems must be robust across a very wide range of physics. Thus, this report deals almost exclusively with some form of dynamic inversion (DI). Two vital aspects of control theory - noninteracting control laws and the transformation of nonlinear systems into equivalent linear systems - are embodied in DI. Though there is no doubt that the mathematical tools and underlying theory are widely available, there are open issues as to the practicality of using DI as the only or primary design approach for reentry articles. This report provides a set of guidelines that can be used to determine the practical usefulness of the technique.

Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy

NASA Astrophysics Data System (ADS)

Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.

2018-01-01

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

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

Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

NASA Astrophysics Data System (ADS)

Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

2018-05-01

Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

Nonlinear damping based semi-active building isolation system

NASA Astrophysics Data System (ADS)

Ho, Carmen; Zhu, Yunpeng; Lang, Zi-Qiang; Billings, Stephen A.; Kohiyama, Masayuki; Wakayama, Shizuka

2018-06-01

Many buildings in Japan currently have a base-isolation system with a low stiffness that is designed to shift the natural frequency of the building below the frequencies of the ground motion due to earthquakes. However, the ground motion observed during the 2011 Tohoku earthquake contained strong long-period waves that lasted for a record length of 3 min. To provide a novel and better solution against the long-period waves while maintaining the performance of the standard isolation range, the exploitation of the characteristics of nonlinear damping is proposed in this paper. This is motivated by previous studies of the authors, which have demonstrated that nonlinear damping can achieve desired performance over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Simulation results have shown strong vibration isolation performance on a building model with identified parameters and have indicated that nonlinear damping can achieve low acceleration transmissibilities round the structural natural frequency as well as the higher ground motion frequencies that have been frequently observed during most earthquakes in Japan. In addition, physical building model based laboratory experiments are also conducted, The results demonstrate the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. In comparison with the tuned-mass damper and other active control methods, the proposed solution offers a more pragmatic, low-cost, robust and effective alternative that can be readily installed into the base-isolation system of most buildings.

Nonlinear dynamics behavior analysis of the spatial configuration of a tendril-bearing plant

NASA Astrophysics Data System (ADS)

Feng, Jingjing; Zhang, Qichang; Wang, Wei; Hao, Shuying

2017-03-01

Tendril-bearing plants appear to have a spiraling shape when tendrils climb along a support during growth. The growth characteristics of a tendril-bearer can be simplified to a model of a thin elastic rod with a cylindrical constraint. In this paper, the connection between some typical configuration characteristics of tendrils and complex nonlinear dynamic behavior are qualitatively analyzed. The space configuration problem of tendrils can be explained through the study of the nonlinear dynamic behavior of the thin elastic rod system equation. In this study, the complex non-Z2 symmetric critical orbits in the system equation under critical parameters were presented. A new function transformation method that can effectively maintain the critical orbit properties was proposed, and a new nonlinear differential equations system containing complex nonlinear terms can been obtained to describe the cross section position and direction of a rod during climbing. Numerical simulation revealed that the new system can describe the configuration of a rod with reasonable accuracy. To adequately explain the growing regulation of the rod shape, the critical orbit and configuration of rod are connected in a direct way. The high precision analytical expressions of these complex non-Z2 symmetric critical orbits are obtained by introducing a suitable analytical method, and then these expressions are used to draw the corresponding three-dimensional configuration figures of an elastic thin rod. Combined with actual tendrils on a live plant, the space configuration of the winding knots of tendril is explained by the concept of heteroclinic orbit from the perspective of nonlinear dynamics, and correctness of the theoretical analysis was verified. This theoretical analysis method could also be effectively applied to other similar slender structures.

Giant magnetic impedance of wires with a thin magnetic coating

NASA Astrophysics Data System (ADS)

Kurlyandskaya, G. V.; Bebenin, N. G.; Vas'kovsky, V. O.

2011-02-01

In this review, we analyzed and generalized the results of experimental investigations of physical processes that occur in composite wires with a thin magnetic coating under the conditions of the appearance in them of a giant magnetoimpedance (GMI) effect. Principles of the measurements of high-frequency impedance are described in short; basic definitions are given, and the differences in the linear and nonlinear GMI regimes are described. Data are systemized on the giant magnetic impedance of wires with a thin magnetic coating (composite materials) under the conditions of a strong nonlinearity of the GMI effect, which is accompanied by the appearance of higher harmonics in the output signal. The extremely high susceptibility of the harmonic parameters to external actions can be used in the technical applications for creating ultrasensitive detectors of low magnetic fields. Special attention is paid to model calculations, which confirm the fact that the experimentally observed features of a nonlinear GMI effect are connected with the high sensitivity of the magnetic system to a circular magnetic field near the spin-reorientation phase transitions. Fine features of the effective magnetic anisotropy can play the key role and therefore cannot be ignored in the general case.

The effect of system nonlinearities on system noise statistics

NASA Technical Reports Server (NTRS)

Robinson, L. H., Jr.

1971-01-01

The effects are studied of nonlinearities in a baseline communications system on the system noise amplitude statistics. So that a meaningful identification of system nonlinearities can be made, the baseline system is assumed to transmit a single biphase-modulated signal through a relay satellite to the receiving equipment. The significant nonlinearities thus identified include square-law or product devices (e.g., in the carrier reference recovery loops in the receivers), bandpass limiters, and traveling wave tube amplifiers.

Entanglement Dynamics of Linear and Nonlinear Interaction of Two Two-Level Atoms with a Quantized Phase-Damped Field in the Dispersive Regime

NASA Astrophysics Data System (ADS)

Tavassoly, M. K.; Daneshmand, R.; Rustaee, N.

2018-06-01

In this paper we study the linear and nonlinear (intensity-dependent) interactions of two two-level atoms with a single-mode quantized field far from resonance, while the phase-damping effect is also taken into account. To find the analytical solution of the atom-field state vector corresponding to the considered model, after deducing the effective Hamiltonian we evaluate the time-dependent elements of the density operator using the master equation approach and superoperator method. Consequently, we are able to study the influences of the special nonlinearity function f (n) = √ {n}, the intensity of the initial coherent state field and the phase-damping parameter on the degree of entanglement of the whole system as well as the field and atom. It is shown that in the presence of damping, by passing time, the amount of entanglement of each subsystem with the rest of system, asymptotically reaches to its stationary and maximum value. Also, the nonlinear interaction does not have any effect on the entanglement of one of the atoms with the rest of system, but it changes the amplitude and time period of entanglement oscillations of the field and the other atom. Moreover, this may cause that, the degree of entanglement which may be low (high) at some moments of time becomes high (low) by entering the intensity-dependent function in the atom-field coupling.

Application of Nonlinear Systems Inverses to Automatic Flight Control Design: System Concepts and Flight Evaluations

NASA Technical Reports Server (NTRS)

Meyer, G.; Cicolani, L.

1981-01-01

A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.

Nearly fully compressed 1053 nm pulses directly obtained from 800 nm laser-seeded photonic crystal fiber below zero dispersion point

NASA Astrophysics Data System (ADS)

Refaeli, Zaharit; Shamir, Yariv; Ofir, Atara; Marcus, Gilad

2018-02-01

We report a simple robust and broadly spectral-adjustable source generating near fully compressed 1053 nm 62 fs pulses directly out of a highly-nonlinear photonic crystal fiber. A dispersion-nonlinearity balance of 800 nm Ti:Sa 20 fs pulses was obtained initially by negative pre-chirping and then launching the pulses into the fibers' normal dispersion regime. Following a self-phase modulation spectral broadening, some energy that leaked below the zero dispersion point formed a soliton whose central wavelength could be tuned by Self-Frequency-Raman-Shift effect. Contrary to a common approach of power, or, fiber-length control over the shift, here we continuously varied the state of polarization, exploiting the Raman and Kerr nonlinearities responsivity for state of polarization. We obtained soliton pulses with central wavelength tuned over 150 nm, spanning from well below 1000 to over 1150 nm, of which we could select stable pulses around the 1 μm vicinity. With linewidth of > 20 nm FWHM Gaussian-like temporal-shape pulses with 62 fs duration and near flat phase structure we confirmed high quality pulse source. We believe such scheme can be used for high energy or high power glass lasers systems, such as Nd or Yb ion-doped amplifiers and systems.

Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

PubMed Central

Dostal, Petr

2015-01-01

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Dynamics of metastable breathers in nonlinear chains in acoustic vacuum

NASA Astrophysics Data System (ADS)

Sen, Surajit; Mohan, T. R. Krishna

2009-03-01

The study of the dynamics of one-dimensional chains with both harmonic and nonlinear interactions, as in the Fermi-Pasta-Ulam and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Nevertheless, little is known about the dynamical behavior of purely nonlinear chains where there is a complete absence of the harmonic term, and hence sound propagation is not admissible, i.e., under conditions of “acoustic vacuum.” Here we study the dynamics of highly localized excitations, or breathers, which are known to be initiated by the quasistatic stretching of the bonds between adjacent particles. We show via detailed particle-dynamics-based studies that many low-energy pulses also form in the vicinity of the perturbation, and the breathers that form are “fragile” in the sense that they can be easily delocalized by scattering events in the system. We show that the localized excitations eventually disperse, allowing the system to attain an equilibrium-like state that is realizable in acoustic vacuum. We conclude with a discussion of how the dynamics is affected by the presence of acoustic oscillations.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Application of an Ensemble Smoother to Precipitation Assimilation

NASA Technical Reports Server (NTRS)

Zhang, Sara; Zupanski, Dusanka; Hou, Arthur; Zupanski, Milija

2008-01-01

Assimilation of precipitation in a global modeling system poses a special challenge in that the observation operators for precipitation processes are highly nonlinear. In the variational approach, substantial development work and model simplifications are required to include precipitation-related physical processes in the tangent linear model and its adjoint. An ensemble based data assimilation algorithm "Maximum Likelihood Ensemble Smoother (MLES)" has been developed to explore the ensemble representation of the precipitation observation operator with nonlinear convection and large-scale moist physics. An ensemble assimilation system based on the NASA GEOS-5 GCM has been constructed to assimilate satellite precipitation data within the MLES framework. The configuration of the smoother takes the time dimension into account for the relationship between state variables and observable rainfall. The full nonlinear forward model ensembles are used to represent components involving the observation operator and its transpose. Several assimilation experiments using satellite precipitation observations have been carried out to investigate the effectiveness of the ensemble representation of the nonlinear observation operator and the data impact of assimilating rain retrievals from the TMI and SSM/I sensors. Preliminary results show that this ensemble assimilation approach is capable of extracting information from nonlinear observations to improve the analysis and forecast if ensemble size is adequate, and a suitable localization scheme is applied. In addition to a dynamically consistent precipitation analysis, the assimilation system produces a statistical estimate of the analysis uncertainty.

Investigation of a Nonlinear Control System

NASA Technical Reports Server (NTRS)

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

1958-01-01

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

Linear and nonlinear schemes applied to pitch control of wind turbines.

PubMed

Geng, Hua; Yang, Geng

2014-01-01

Linear controllers have been employed in industrial applications for many years, but sometimes they are noneffective on the system with nonlinear characteristics. This paper discusses the structure, performance, implementation cost, advantages, and disadvantages of different linear and nonlinear schemes applied to the pitch control of the wind energy conversion systems (WECSs). The linear controller has the simplest structure and is easily understood by the engineers and thus is widely accepted by the industry. In contrast, nonlinear schemes are more complicated, but they can provide better performance. Although nonlinear algorithms can be implemented in a powerful digital processor nowadays, they need time to be accepted by the industry and their reliability needs to be verified in the commercial products. More information about the system nonlinear feature is helpful to simplify the controller design. However, nonlinear schemes independent of the system model are more robust to the uncertainties or deviations of the system parameters.

Design of optimal nonlinear network controllers for Alzheimer's disease.

PubMed

Sanchez-Rodriguez, Lazaro M; Iturria-Medina, Yasser; Baines, Erica A; Mallo, Sabela C; Dousty, Mehdy; Sotero, Roberto C

2018-05-01

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer's disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients' biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer's Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks-namely, networks having low average shortest path length, high global efficiency-are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

A sub-cc nonlinear piezoelectric energy harvester for powering leadless pacemakers

PubMed Central

Ansari, MH; Karami, M Amin

2018-01-01

A miniature nonlinear piezoelectric energy harvester is developed to power state of the art leadless cardiac pacemakers from cardiac motions. The energy harvester is integrated in the leadless pacemaker and is connected to the myocardium. The energy harvester converts myocardial motions to electricity to power leadless pacemakers. The energy is stored in a battery or supercapacitor and is used for pacing. The device is composed of a bimorph piezoelectric beam confined in a gray iron frame. The system is assembled at high temperature and operated at the body temperature. The mismatch in the coefficients of thermal expansion of the beam and the frame causes the beam to buckle in body temperature. This intentional buckling makes the beam unstable and improves the power production and robustness of the device. Having high natural frequency is a major problem in microelectromechanical systems energy harvesters. Considering the small size of the energy harvester, 0.5 cm3, the natural frequency is expected to be high. In our design, the natural frequency is lowered significantly using a buckled beam and a proof mass. Since the beam is buckled, the design is bistable and nonlinear, which could increase the output power. In this article, the device is analytically modeled, and the natural frequencies and mode shapes of the energy harvester are analytically derived. The terms corresponding to geometric nonlinearities are included in the electromechanical coupled governing equations. The simulations show that the device generates sufficient electricity to power leadless pacemakers. PMID:29674842

Large Spatial and Temporal Separations of Cause and Effect in Policy Making - Dealing with Non-linear Effects

NASA Astrophysics Data System (ADS)

McCaskill, John

There can be large spatial and temporal separation of cause and effect in policy making. Determining the correct linkage between policy inputs and outcomes can be highly impractical in the complex environments faced by policy makers. In attempting to see and plan for the probable outcomes, standard linear models often overlook, ignore, or are unable to predict catastrophic events that only seem improbable due to the issue of multiple feedback loops. There are several issues with the makeup and behaviors of complex systems that explain the difficulty many mathematical models (factor analysis/structural equation modeling) have in dealing with non-linear effects in complex systems. This chapter highlights those problem issues and offers insights to the usefulness of ABM in dealing with non-linear effects in complex policy making environments.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

2014-02-01

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system

NASA Astrophysics Data System (ADS)

Avitabile, D.; Desroches, M.; Knobloch, E.; Krupa, M.

2017-11-01

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of solutions describing the possible location of stationary fronts are identified, whose origin is traced to the onset of convective and absolute instability when the system is unbounded. The former are present only for non-zero upstream boundary conditions and provide a quantitative understanding of noise-sustained structures in systems of this type. The latter correspond to the onset of a global mode and are present even with zero upstream boundary conditions. The role of canard trajectories in the nonlinear transition between these states is clarified and the stability properties of the resulting spatial structures are determined. Front location in the convective regime is highly sensitive to the upstream boundary condition, and its dependence on this boundary condition is studied using a combination of numerical continuation and Monte Carlo simulations of the partial differential equation. Statistical properties of the system subjected to random or stochastic boundary conditions at the inlet are interpreted using the deterministic slow-fast spatial dynamical system.

Nonlinear spectroscopy of trapped ions

NASA Astrophysics Data System (ADS)

Schlawin, Frank; Gessner, Manuel; Mukamel, Shaul; Buchleitner, Andreas

2014-08-01

Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and it has become a highly successful method for experiments in chemical physics. Current quantum optical experiments approach system sizes and levels of complexity that require the development of efficient techniques to assess spectral and dynamical features with scalable experimental overhead. However, established methods from optical spectroscopy of macroscopic ensembles cannot be applied straightforwardly to few-atom systems. Based on the ideas proposed in M. Gessner et al., (arXiv:1312.3365), we develop a diagrammatic approach to construct nonlinear measurement protocols for controlled quantum systems, and we discuss experimental implementations with trapped ion technology in detail. These methods, in combination with distinct features of ultracold-matter systems, allow us to monitor and analyze excitation dynamics in both the electronic and vibrational degrees of freedom. They are independent of system size, and they can therefore reliably probe systems in which, e.g., quantum state tomography becomes prohibitively expensive. We propose signals that can probe steady-state currents, detect the influence of anharmonicities on phonon transport, and identify signatures of chaotic dynamics near a quantum phase transition in an Ising-type spin chain.

Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system.

PubMed

Avitabile, D; Desroches, M; Knobloch, E; Krupa, M

2017-11-01

A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of solutions describing the possible location of stationary fronts are identified, whose origin is traced to the onset of convective and absolute instability when the system is unbounded. The former are present only for non-zero upstream boundary conditions and provide a quantitative understanding of noise-sustained structures in systems of this type. The latter correspond to the onset of a global mode and are present even with zero upstream boundary conditions. The role of canard trajectories in the nonlinear transition between these states is clarified and the stability properties of the resulting spatial structures are determined. Front location in the convective regime is highly sensitive to the upstream boundary condition, and its dependence on this boundary condition is studied using a combination of numerical continuation and Monte Carlo simulations of the partial differential equation. Statistical properties of the system subjected to random or stochastic boundary conditions at the inlet are interpreted using the deterministic slow-fast spatial dynamical system.

Design of CO2 dispersion interferometer based on the ratio of modulation amplitudes on EAST

NASA Astrophysics Data System (ADS)

Li, W. M.; Liu, H. Q.; Yang, Y.; Zeng, L.; Yao, Y.; Zou, Z. Y.; Wei, X. C.; Jie, Y. X.

2018-02-01

A dispersion interferometer (DI) system is one of the more promising density measurement methods for large, high density fusion devices as they have considerable immunity to mechanical vibration and a shorter wavelength which helps to prevent fringe jump errors. In this paper, a DI system with a photoelastic modulator (PEM) has been designed for high density measurements on the EAST tokamak with vertical double pass optical layout. The bench test of all system components was done, especially for the specific nonlinear crystal for DI system. The second hamonic power with the AgGaSe2 nonlinear crystal can reach to 22.85 μW at 20 W fundamental power of CO2 laser. The second-harmonic power based on the AgGaSe2 show a good linear relationship with the various power of the CO2 laser. Based on the bench test results, the new DI system design will be realized and utilized on EAST.

Are consistent equal-weight particle filters possible?

NASA Astrophysics Data System (ADS)

van Leeuwen, P. J.

2017-12-01

Particle filters are fully nonlinear data-assimilation methods that could potentially change the way we do data-assimilation in highly nonlinear high-dimensional geophysical systems. However, the standard particle filter in which the observations come in by changing the relative weights of the particles is degenerate. This means that one particle obtains weight one, and all other particles obtain a very small weight, effectively meaning that the ensemble of particles reduces to that one particle. For over 10 years now scientists have searched for solutions to this problem. One obvious solution seems to be localisation, in which each part of the state only sees a limited number of observations. However, for a realistic localisation radius based on physical arguments, the number of observations is typically too large, and the filter is still degenerate. Another route taken is trying to find proposal densities that lead to more similar particle weights. There is a simple proof, however, that shows that there is an optimum, the so-called optimal proposal density, and that optimum will lead to a degenerate filter. On the other hand, it is easy to come up with a counter example of a particle filter that is not degenerate in high-dimensional systems. Furthermore, several particle filters have been developed recently that claim to have equal or equivalent weights. In this presentation I will show how to construct a particle filter that is never degenerate in high-dimensional systems, and how that is still consistent with the proof that one cannot do better than the optimal proposal density. Furthermore, it will be shown how equal- and equivalent-weights particle filters fit within this framework. This insight will then lead to new ways to generate particle filters that are non-degenerate, opening up the field of nonlinear filtering in high-dimensional systems.

AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, 4th, Cleveland, OH, Sept. 21-23, 1992, Technical Papers. Pts. 1 & 2

NASA Technical Reports Server (NTRS)

1992-01-01

The papers presented at the symposium cover aerodynamics, design applications, propulsion systems, high-speed flight, structures, controls, sensitivity analysis, optimization algorithms, and space structures applications. Other topics include helicopter rotor design, artificial intelligence/neural nets, and computational aspects of optimization. Papers are included on flutter calculations for a system with interacting nonlinearities, optimization in solid rocket booster application, improving the efficiency of aerodynamic shape optimization procedures, nonlinear control theory, and probabilistic structural analysis of space truss structures for nonuniform thermal environmental effects.

Chirped self-similar waves for quadratic-cubic nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Pal, Ritu; Loomba, Shally; Kumar, C. N.

2017-12-01

We have constructed analytical self-similar wave solutions for quadratic-cubic Nonlinear Schrödinger equation (QC-NLSE) by means of similarity transformation method. Then, we have investigated the role of chirping on these self-similar waves as they propagate through the tapered graded index waveguide. We have revealed that the chirping leads to interesting features and allows us to control the propagation of self-similar waves. This has been demonstrated for two cases (i) periodically distributed system and (ii) constant choice of system parameters. We expect our results to be useful in designing high performance optical devices.

A Weighted Measurement Fusion Particle Filter for Nonlinear Multisensory Systems Based on Gauss–Hermite Approximation

PubMed Central

Li, Yun

2017-01-01

We addressed the fusion estimation problem for nonlinear multisensory systems. Based on the Gauss–Hermite approximation and weighted least square criterion, an augmented high-dimension measurement from all sensors was compressed into a lower dimension. By combining the low-dimension measurement function with the particle filter (PF), a weighted measurement fusion PF (WMF-PF) is presented. The accuracy of WMF-PF appears good and has a lower computational cost when compared to centralized fusion PF (CF-PF). An example is given to show the effectiveness of the proposed algorithms. PMID:28956862

Selected Problems in Nonlinear Dynamics and Sociophysics

NASA Astrophysics Data System (ADS)

Westley, Alexandra Renee

This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

An Energy Decaying Scheme for Nonlinear Dynamics of Shells

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.

On the Response of a Nonlinear Structure to High Kurtosis Non-Gaussian Random Loadings

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam; Turner, Travis L.

2011-01-01

This paper is a follow-on to recent work by the authors in which the response and high-cycle fatigue of a nonlinear structure subject to non-Gaussian loadings was found to vary markedly depending on the nature of the loading. There it was found that a non-Gaussian loading having a steady rate of short-duration, high-excursion peaks produced essentially the same response as would have been incurred by a Gaussian loading. In contrast, a non-Gaussian loading having the same kurtosis, but with bursts of high-excursion peaks was found to elicit a much greater response. This work is meant to answer the question of when consideration of a loading probability distribution other than Gaussian is important. The approach entailed nonlinear numerical simulation of a beam structure under Gaussian and non-Gaussian random excitations. Whether the structure responded in a Gaussian or non-Gaussian manner was determined by adherence to, or violations of, the Central Limit Theorem. Over a practical range of damping, it was found that the linear response to a non-Gaussian loading was Gaussian when the period of the system impulse response is much greater than the rate of peaks in the loading. Lower damping reduced the kurtosis, but only when the linear response was non-Gaussian. In the nonlinear regime, the response was found to be non-Gaussian for all loadings. The effect of a spring-hardening type of nonlinearity was found to limit extreme values and thereby lower the kurtosis relative to the linear response regime. In this case, lower damping gave rise to greater nonlinearity, resulting in lower kurtosis than a higher level of damping.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

A Block Iterative Finite Element Model for Nonlinear Leaky Aquifer Systems

NASA Astrophysics Data System (ADS)

Gambolati, Giuseppe; Teatini, Pietro

1996-01-01

A new quasi three-dimensional finite element model of groundwater flow is developed for highly compressible multiaquifer systems where aquitard permeability and elastic storage are dependent on hydraulic drawdown. The model is solved by a block iterative strategy, which is naturally suggested by the geological structure of the porous medium and can be shown to be mathematically equivalent to a block Gauss-Seidel procedure. As such it can be generalized into a block overrelaxation procedure and greatly accelerated by the use of the optimum overrelaxation factor. Results for both linear and nonlinear multiaquifer systems emphasize the excellent computational performance of the model and indicate that convergence in leaky systems can be improved up to as much as one order of magnitude.

Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

NASA Astrophysics Data System (ADS)

Manfredi, Sabato

2016-06-01

Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.

Localization and identification of structural nonlinearities using cascaded optimization and neural networks

NASA Astrophysics Data System (ADS)

Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.

2017-10-01

In this study, a new approach is proposed for identification of structural nonlinearities by employing cascaded optimization and neural networks. Linear finite element model of the system and frequency response functions measured at arbitrary locations of the system are used in this approach. Using the finite element model, a training data set is created, which appropriately spans the possible nonlinear configurations space of the system. A classification neural network trained on these data sets then localizes and determines the types of all nonlinearities associated with the nonlinear degrees of freedom in the system. A new training data set spanning the parametric space associated with the determined nonlinearities is created to facilitate parametric identification. Utilizing this data set, initially, a feed forward regression neural network is trained, which parametrically identifies the classified nonlinearities. Then, the results obtained are further improved by carrying out an optimization which uses network identified values as starting points. Unlike identification methods available in literature, the proposed approach does not require data collection from the degrees of freedoms where nonlinear elements are attached, and furthermore, it is sufficiently accurate even in the presence of measurement noise. The application of the proposed approach is demonstrated on an example system with nonlinear elements and on a real life experimental setup with a local nonlinearity.

Global tracking for a class of uncertain nonlinear systems with unknown sign-switching control direction by output feedback

NASA Astrophysics Data System (ADS)

Roux Oliveira, Tiago; Jacoud Peixoto, Alessandro; Hsu, Liu

2015-09-01

This paper addresses the design of a sliding mode controller for a class of high-order uncertain nonlinear plants with unmatched state-dependent nonlinearities and unknown sign of the high frequency gain, i.e., the control direction is assumed unknown. Differently from most previous studies, the control direction is allowed to switch its sign. We show that it is possible to obtain global exact tracking using only output-feedback by coupling a relay periodic switching function with a norm state observer. One significant advantage of the new scheme is its robustness and improved transient response under arbitrary changes of the control direction which have been theoretically demonstrated for jump variations and successfully tested by simulations. The proposed controller is also evaluated with a DC motor control experiment.

Adaptive non-predictor control of lower triangular uncertain nonlinear systems with an unknown time-varying delay in the input

NASA Astrophysics Data System (ADS)

Koo, Min-Sung; Choi, Ho-Lim

2018-01-01

In this paper, we consider a control problem for a class of uncertain nonlinear systems in which there exists an unknown time-varying delay in the input and lower triangular nonlinearities. Usually, in the existing results, input delays have been coupled with feedforward (or upper triangular) nonlinearities; in other words, the combination of lower triangular nonlinearities and input delay has been rare. Motivated by the existing controller for input-delayed chain of integrators with nonlinearity, we show that the control of input-delayed nonlinear systems with two particular types of lower triangular nonlinearities can be done. As a control solution, we propose a newly designed feedback controller whose main features are its dynamic gain and non-predictor approach. Three examples are given for illustration.

A high-precision instrument for analyzing nonlinear dynamic behavior of bearing cage.

PubMed

Yang, Z; Chen, H; Yu, T; Li, B

2016-08-01

The high-precision ball bearing is fundamental to the performance of complex mechanical systems. As the speed increases, the cage behavior becomes a key factor in influencing the bearing performance, especially life and reliability. This paper develops a high-precision instrument for analyzing nonlinear dynamic behavior of the bearing cage. The trajectory of the rotational center and non-repetitive run-out (NRRO) of the cage are used to evaluate the instability of cage motion. This instrument applied an aerostatic spindle to support and spin test the bearing to decrease the influence of system error. Then, a high-speed camera is used to capture images when the bearing works at high speeds. A 3D trajectory tracking software tema Motion is used to track the spot which marked the cage surface. Finally, by developing the matlab program, a Lissajous' figure was used to evaluate the nonlinear dynamic behavior of the cage with different speeds. The trajectory of rotational center and NRRO of the cage with various speeds are analyzed. The results can be used to predict the initial failure and optimize cage structural parameters. In addition, the repeatability precision of instrument is also validated. In the future, the motorized spindle will be applied to increase testing speed and image processing algorithms will be developed to analyze the trajectory of the cage.

A high-precision instrument for analyzing nonlinear dynamic behavior of bearing cage

NASA Astrophysics Data System (ADS)

Yang, Z.; Chen, H.; Yu, T.; Li, B.

2016-08-01

The high-precision ball bearing is fundamental to the performance of complex mechanical systems. As the speed increases, the cage behavior becomes a key factor in influencing the bearing performance, especially life and reliability. This paper develops a high-precision instrument for analyzing nonlinear dynamic behavior of the bearing cage. The trajectory of the rotational center and non-repetitive run-out (NRRO) of the cage are used to evaluate the instability of cage motion. This instrument applied an aerostatic spindle to support and spin test the bearing to decrease the influence of system error. Then, a high-speed camera is used to capture images when the bearing works at high speeds. A 3D trajectory tracking software tema Motion is used to track the spot which marked the cage surface. Finally, by developing the matlab program, a Lissajous' figure was used to evaluate the nonlinear dynamic behavior of the cage with different speeds. The trajectory of rotational center and NRRO of the cage with various speeds are analyzed. The results can be used to predict the initial failure and optimize cage structural parameters. In addition, the repeatability precision of instrument is also validated. In the future, the motorized spindle will be applied to increase testing speed and image processing algorithms will be developed to analyze the trajectory of the cage.

A high-precision instrument for analyzing nonlinear dynamic behavior of bearing cage

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

Yang, Z., E-mail: zhaohui@nwpu.edu.cn; Yu, T.; Chen, H.

2016-08-15

The high-precision ball bearing is fundamental to the performance of complex mechanical systems. As the speed increases, the cage behavior becomes a key factor in influencing the bearing performance, especially life and reliability. This paper develops a high-precision instrument for analyzing nonlinear dynamic behavior of the bearing cage. The trajectory of the rotational center and non-repetitive run-out (NRRO) of the cage are used to evaluate the instability of cage motion. This instrument applied an aerostatic spindle to support and spin test the bearing to decrease the influence of system error. Then, a high-speed camera is used to capture images whenmore » the bearing works at high speeds. A 3D trajectory tracking software TEMA Motion is used to track the spot which marked the cage surface. Finally, by developing the MATLAB program, a Lissajous’ figure was used to evaluate the nonlinear dynamic behavior of the cage with different speeds. The trajectory of rotational center and NRRO of the cage with various speeds are analyzed. The results can be used to predict the initial failure and optimize cage structural parameters. In addition, the repeatability precision of instrument is also validated. In the future, the motorized spindle will be applied to increase testing speed and image processing algorithms will be developed to analyze the trajectory of the cage.« less

High-pulse energy Q-switched Tm3+:YAG laser for nonlinear frequency conversion to the mid-IR

NASA Astrophysics Data System (ADS)

Stöppler, Georg; Kieleck, Christelle; Eichhorn, Marc

2010-10-01

For some medical fields in laser surgery and as a pump source for nonlinear materials to generate mid-IR radiation, e.g. for countermeasure applications, it is very useful to have a solid-state laser with high pulse energy at 2 μm. The rare earth ion Thulium offers a cross relaxation and can thus be directly diode pumped with common laser diodes around 800 nm for an efficient pumping. However, it was not considered for high pulse energy operation due to the high saturation fluence of around 62 J/cm2 at 2 μm. A limiting factor has always been the damage threshold of the optical elements inside the cavity. One of the reasons is the strong thermal lens of YAG, which affects a change of the beam radius inside the resonator and additionally degrades the beam quality with increasing pump power. Using a new pump geometry of the Tm3+:YAG laser system, it is now possible to reach pulse energies > 13 mJ at a diffraction limited beam quality of M2 < 1.1. The Q-switched Tm3+:YAG laser system uses an AOM operating at 100 Hz and will be described in detail. Due to the high pulse energy and very good beam quality, this laser is very interesting for nonlinear parametric frequency conversion.

Nonlinear dispersion effects in elastic plates: numerical modelling and validation

NASA Astrophysics Data System (ADS)

Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

Control design and robustness analysis of a ball and plate system by using polynomial chaos

NASA Astrophysics Data System (ADS)

Colón, Diego; Balthazar, José M.; dos Reis, Célia A.; Bueno, Átila M.; Diniz, Ivando S.; de S. R. F. Rosa, Suelia

2014-12-01

In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.

Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses

NASA Astrophysics Data System (ADS)

Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin

2016-08-01

This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS

PubMed Central

Bessonova, O.V.; Khokhlova, V.A.; Bailey, M.R.; Canney, M.S.; Crum, L.A.

2009-01-01

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post- shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions. PMID:20161349

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS.

PubMed

Bessonova, O V; Khokhlova, V A; Bailey, M R; Canney, M S; Crum, L A

2009-07-21

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post- shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

Focusing of high power ultrasound beams and limiting values of shock wave parameters

NASA Astrophysics Data System (ADS)

Bessonova, O. V.; Khokhlova, V. A.; Bailey, M. R.; Canney, M. S.; Crum, L. A.

2009-10-01

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post-shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.

PubMed

Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A

2016-04-29

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

Properties and Frequency Conversion of High-Brightness Diode-Laser Systems

NASA Astrophysics Data System (ADS)

Boller, Klaus-Jochen; Beier, Bernard; Wallenstein, Richard

An overview of recent developments in the field of high-power, high-brightness diode-lasers, and the optically nonlinear conversion of their output into other wavelength ranges, is given. We describe the generation of continuous-wave (CW) laser beams at power levels of several hundreds of milliwatts to several watts with near-perfect spatial and spectral properties using Master-Oscillator Power-Amplifier (MOPA) systems. With single- or double-stage systems, using amplifiers of tapered or rectangular geometry, up to 2.85 W high-brightness radiation is generated at wavelengths around 810nm with AlGaAs diodes. Even higher powers, up to 5.2W of single-frequency and high spatial quality beams at 925nm, are obtained with InGaAs diodes. We describe the basic properties of the oscillators and amplifiers used. A strict proof-of-quality for the diode radiation is provided by direct and efficient nonlinear optical conversion of the diode MOPA output into other wavelength ranges. We review recent experiments with the highest power levels obtained so far by direct frequency doubling of diode radiation. In these experiments, 100mW single-frequency ultraviolet light at 403nm was generated, as well as 1W of single-frequency blue radiation at 465nm. Nonlinear conversion of diode radiation into widely tunable infrared radiation has recently yielded record values. We review the efficient generation of widely tunable single-frequency radiation in the infrared with diode-pumped Optical Parametric Oscillators (OPOs). With this system, single-frequency output radiation with powers of more than 0.5W was generated, widely tunable around wavelengths of 2.1,m and 1.65,m and with excellent spectral and spatial quality. These developments are clear indicators of recent advances in the field of high-brightness diode-MOPA systems, and may emphasize their future central importance for applications within a vast range of optical wavelengths.

Dynamics and control simulation of the Spacelab Experiment Pointing Mount

NASA Technical Reports Server (NTRS)

Marsh, E. L.; Ward, R. S.

1977-01-01

Computer simulations were developed to evaluate the performance of four Experiment Pointing Mounts (EPM) being considered for Spacelab experiments in the 1980-1990 time frame. The system modeled compromises a multibody system consisting of the shuttle, a mechanical isolation device, the EPM, celestial and inertial sensors, bearings, gimbal torque motors and associated nonlinearities, the experiment payload, and control and estimator algorithms. Each mount was subjected to a common disturbance (shuttle vernier thruster firing and man push off) and command (stellar pointing or solar raster scan) input. The fundamental limitation common to all mounts was found to be sensor noise. System dynamics and hardware nonlinearities have secondary effects on pointing performance for sufficiently high bandwidth.

Modern methods and systems for precise control of the quality of agricultural and food production

NASA Astrophysics Data System (ADS)

Bednarjevsky, Sergey S.; Veryasov, Yuri V.; Akinina, Evgeniya V.; Smirnov, Gennady I.

1999-01-01

The results on the modeling of non-linear dynamics of strong continuous and impulse radiation in the laser nephelometry of polydisperse biological systems, important from the viewpoint of applications in biotechnologies, are presented. The processes of nonlinear self-action of the laser radiation by the multiple scattering in the disperse biological agro-media are considered. The simplified algorithms of the calculation of the parameters of the biological media under investigation are indicated and the estimates of the errors of the laser-nephelometric measurements are given. The universal high-informative optical analyzers and the standard etalon specimens of agro- objects make the technological foundation of the considered methods and systems.

Semi-physical Simulation Platform of a Parafoil Nonlinear Dynamic System

NASA Astrophysics Data System (ADS)

Gao, Hai-Tao; Yang, Sheng-Bo; Zhu, Er-Lin; Sun, Qing-Lin; Chen, Zeng-Qiang; Kang, Xiao-Feng

2013-11-01

Focusing on the problems in the process of simulation and experiment on a parafoil nonlinear dynamic system, such as limited methods, high cost and low efficiency we present a semi-physical simulation platform. It is designed by connecting parts of physical objects to a computer, and remedies the defect that a computer simulation is divorced from a real environment absolutely. The main components of the platform and its functions, as well as simulation flows, are introduced. The feasibility and validity are verified through a simulation experiment. The experimental results show that the platform has significance for improving the quality of the parafoil fixed-point airdrop system, shortening the development cycle and saving cost.

A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes

NASA Astrophysics Data System (ADS)

Ferhatoglu, Erhan; Cigeroglu, Ender; Özgüven, H. Nevzat

2018-07-01

In this paper, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the nonlinear system is bounded by the confinement of these linear systems. In this study, a modal superposition method utilizing novel hybrid mode shapes which are defined as linear combinations of the modal vectors of the limiting linear systems is proposed to determine periodic response of nonlinear systems. In this method the response of the nonlinear system is written in terms of hybrid modes instead of the modes of the underlying linear system. This provides decrease of the number of modes that should be retained for an accurate solution, which in turn reduces the number of nonlinear equations to be solved. In this way, computational time for response calculation is directly curtailed. In the solution, the equations of motion are converted to a set of nonlinear algebraic equations by using describing function approach, and the numerical solution is obtained by using Newton's method with arc-length continuation. The method developed is applied on two different systems: a lumped parameter model and a finite element model. Several case studies are performed and the accuracy and computational efficiency of the proposed modal superposition method with hybrid mode shapes are compared with those of the classical modal superposition method which utilizes the mode shapes of the underlying linear system.

Robust adaptive uniform exact tracking control for uncertain Euler-Lagrange system

NASA Astrophysics Data System (ADS)

Yang, Yana; Hua, Changchun; Li, Junpeng; Guan, Xinping

2017-12-01

This paper offers a solution to the robust adaptive uniform exact tracking control for uncertain nonlinear Euler-Lagrange (EL) system. An adaptive finite-time tracking control algorithm is designed by proposing a novel nonsingular integral terminal sliding-mode surface. Moreover, a new adaptive parameter tuning law is also developed by making good use of the system tracking errors and the adaptive parameter estimation errors. Thus, both the trajectory tracking and the parameter estimation can be achieved in a guaranteed time adjusted arbitrarily based on practical demands, simultaneously. Additionally, the control result for the EL system proposed in this paper can be extended to high-order nonlinear systems easily. Finally, a test-bed 2-DOF robot arm is set-up to demonstrate the performance of the new control algorithm.

The effects of control field detuning on the modulation instability in a three-level quantum well system

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

Borgohain, Nitu, E-mail: nituborgohain.ism@gmail.com; Konar, S.

The paper presents a theoretical study of the modulation instability of a continuous or quasi-continuous optical probe in a three level quantum well system under electromagnetically induced transparency. The modulation instability is affected by the control field detuning, as well as even-order dispersion and by the strength of Kerr (third-order) and quintic (fifth-order) nonlinearities. The fourth-order dispersion reduces the bandwidth over which modulation instability occurs, whereas the quintic nonlinearity saturates the growth of the modulation instability. Detuning the control field from resonance can significantly reduce the growth of the modulation instability at both low and high power levels. At lowmore » powers, the system becomes stable against modulation instability for small detuning of the control field and at high powers modulation instability disappears for larger detuning.« less

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Nonlinear dynamics and control of a vibrating rectangular plate

NASA Technical Reports Server (NTRS)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems

EPA Science Inventory

Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

Modal analysis and nonlinear characterization of an airborne power ultrasonic transducer with rectangular plate radiator.

PubMed

Andrés, R R; Acosta, V M; Lucas, M; Riera, E

2018-01-01

Some industrial processes like particle agglomeration or food dehydration among others can be enhanced by the use of power ultrasonic technologies. These technologies are based on an airborne power ultrasonic transducer (APUT) constituted by a pre-stressed Langevin-type transducer, a mechanical amplifier and an extensive plate radiator. In order to produce the desired effects in industrial processing, the transducer has to vibrate in an extensional mode driving an extensive radiator in the desired flexural mode with high amplitude displacements. Due to the generation of these high amplitude displacements in the radiator surfaces, non-linear effects like frequency shifts, hysteresis or modal interactions, among others, may be produced in the transducer behavior. When any nonlinear effect appears, when applying power, the stability and efficiency of this ultrasonic technology decreases, and the transducer may be damaged depending on the excitation power level and the nature of the nonlinearity. In this paper, an APUT with flat rectangular radiator is presented, as the active part of an innovative system with stepped reflectors. The nonlinear behavior of the APUT has been characterized numerically and experimentally in case of the modal analysis and experimentally in the case of dynamic analysis. According to the results obtained after the experiments, no modal interactions are expected, nor do other nonlinear effects. Copyright © 2017 Elsevier B.V. All rights reserved.

Center for Parallel Optimization.

DTIC Science & Technology

1996-03-19

A NEW OPTIMIZATION BASED APPROACH TO IMPROVING GENERALIZATION IN MACHINE LEARNING HAS BEEN PROPOSED AND COMPUTATIONALLY VALIDATED ON SIMPLE LINEAR MODELS AS WELL AS ON HIGHLY NONLINEAR SYSTEMS SUCH AS NEURAL NETWORKS.

High power pumped mid-IR wavelength systems using nonlinear frequency mixing (NFM) devices

NASA Technical Reports Server (NTRS)

Sanders, Steven (Inventor); Lang, Robert J. (Inventor); Waarts, Robert G. (Inventor)

1999-01-01

Laser diode pumped mid-IR wavelength systems include at least one high power, near-IR wavelength, injection and/or sources wherein one or both of such sources may be tunable providing a pump wave output beam to a quasi-phase matched (QPM) nonlinear frequency mixing (NFM) device. The NFM device may be a difference frequency mixing (DFM) device or an optical parametric oscillation (OPO) device. Wavelength tuning of at least one of the sources advantageously provides the ability for optimizing pump or injection wavelengths to match the QPM properties of the NFM device enabling a broad range of mid-IR wavelength selectivity. Also, pump powers are gain enhanced by the addition of a rare earth amplifier or oscillator, or a Raman/Brillouin amplifier or oscillator between the high power source and the NFM device. Further, polarization conversion using Raman or Brillouin wavelength shifting is provided to optimize frequency conversion efficiency in the NFM device.

Advanced optical fiber communication systems

NASA Astrophysics Data System (ADS)

Kazovsky, Leonid G.

1994-03-01

Our research is focused on three major aspects of advanced optical fiber communication systems: dynamic wavelength division multiplexing (WDM) networks, fiber nonlinearities, and high dynamic range coherent analog optical links. In the area of WDM networks, we have designed and implemented two high-speed interface boards and measured their throughput and latency. Furthermore, we designed and constructed an experimental PSK/ASK transceiver that simultaneously transmits packet-switched ASK data and circuit-switched PSK data on the same optical carrier. In the area of fiber nonlinearities, we investigated the theoretical impact of modulation frequency on cross-phase modulation (XPM) in dispersive fibers. In the area of high dynamic range coherent analog optical links, we developed theoretical expressions for the RF power transfer ratio (or RF power gain) and the noise figure (NF) of angle-modulated links. We then compared the RF power gains and noise figures of these links to that of an intensity modulated direct detection (DD) link.

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

NASA Astrophysics Data System (ADS)

Triki, Houria; Porsezian, K.; Choudhuri, Amitava; Dinda, P. Tchofo

2016-06-01

A class of derivative nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinear terms describing the propagation of ultrashort optical pulses through a nonlinear medium with higher-order Kerr responses is investigated. An intensity-dependent chirp ansatz is adopted for solving the two coupled amplitude-phase nonlinear equations of the propagating wave. We find that the dynamics of field amplitude in this system is governed by a first-order nonlinear ordinary differential equation with a tenth-degree nonlinear term. We demonstrate that this system allows the propagation of a very rich variety of solitary waves (kink, dark, bright, and gray solitary pulses) which do not coexist in the conventional nonlinear systems that have appeared so far in the literature. The stability of the solitary wave solution under some violation on the parametric conditions is investigated. Moreover, we show that, unlike conventional systems, the nonlinear Schrödinger equation considered here meets the special requirements for the propagation of a chirped solitary wave on a continuous-wave background, involving a balance among group velocity dispersion, self-steepening, and higher-order nonlinearities of different nature.

Nonlinear normal modes in electrodynamic systems: A nonperturbative approach

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

Kudrin, A. V., E-mail: kud@rf.unn.ru; Kudrina, O. A.; Petrov, E. Yu.

2016-06-15

We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known tomore » hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.« less

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Dynamic Range Enhancement of High-Speed Electrical Signal Data via Non-Linear Compression

NASA Technical Reports Server (NTRS)

Laun, Matthew C. (Inventor)

2016-01-01

Systems and methods for high-speed compression of dynamic electrical signal waveforms to extend the measuring capabilities of conventional measuring devices such as oscilloscopes and high-speed data acquisition systems are discussed. Transfer function components and algorithmic transfer functions can be used to accurately measure signals that are within the frequency bandwidth but beyond the voltage range and voltage resolution capabilities of the measuring device.

An Adaptive Moving Target Imaging Method for Bistatic Forward-Looking SAR Using Keystone Transform and Optimization NLCS.

PubMed

Li, Zhongyu; Wu, Junjie; Huang, Yulin; Yang, Haiguang; Yang, Jianyu

2017-01-23

Bistatic forward-looking SAR (BFSAR) is a kind of bistatic synthetic aperture radar (SAR) system that can image forward-looking terrain in the flight direction of an aircraft. Until now, BFSAR imaging theories and methods for a stationary scene have been researched thoroughly. However, for moving-target imaging with BFSAR, the non-cooperative movement of the moving target induces some new issues: (I) large and unknown range cell migration (RCM) (including range walk and high-order RCM); (II) the spatial-variances of the Doppler parameters (including the Doppler centroid and high-order Doppler) are not only unknown, but also nonlinear for different point-scatterers. In this paper, we put forward an adaptive moving-target imaging method for BFSAR. First, the large and unknown range walk is corrected by applying keystone transform over the whole received echo, and then, the relationships among the unknown high-order RCM, the nonlinear spatial-variances of the Doppler parameters, and the speed of the mover, are established. After that, using an optimization nonlinear chirp scaling (NLCS) technique, not only can the unknown high-order RCM be accurately corrected, but also the nonlinear spatial-variances of the Doppler parameters can be balanced. At last, a high-order polynomial filter is applied to compress the whole azimuth data of the moving target. Numerical simulations verify the effectiveness of the proposed method.

Nonlinear aeroacoustic characterization of Helmholtz resonators with a local-linear neuro-fuzzy network model

NASA Astrophysics Data System (ADS)

Förner, K.; Polifke, W.

2017-10-01

The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.

Linear and nonlinear trending and prediction for AVHRR time series data

NASA Technical Reports Server (NTRS)

Smid, J.; Volf, P.; Slama, M.; Palus, M.

1995-01-01

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.

An optimization model for the US Air-Traffic System

NASA Technical Reports Server (NTRS)

Mulvey, J. M.

1986-01-01

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

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

Robust nonlinear variable selective control for networked systems

NASA Astrophysics Data System (ADS)

Rahmani, Behrooz

2016-10-01

This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.

Efficient, nonlinear phase estimation with the nonmodulated pyramid wavefront sensor

NASA Astrophysics Data System (ADS)

Frazin, Richard A.

2018-04-01

The sensitivity of the the pyramid wavefront sensor (PyWFS) has made it a popular choice for astronomical adaptive optics (AAO) systems, and it is at its most sensitive when it is used without modulation of the input beam. In non-modulated mode, the device is highly nonlinear. Hence, all PyWFS implementations on current AAO systems employ modulation to make the device more linear. The upcoming era of 30-m class telescopes and the demand for ultra-precise wavefront control stemming from science objectives that include direct imaging of exoplanets make using the PyWFS without modulation desirable. This article argues that nonlinear estimation based on Newton's method for nonlinear optimization can be useful for mitigating the effects of nonlinearity in the non-modulated PyWFS. The proposed approach requires all optical modeling to be pre-computed, which has the advantage of avoiding real-time simulations of beam propagation. Further, the required real-time calculations are amenable to massively parallel computation. Numerical experiments simulate a currently operational PyWFS. A singular value analysis shows that the common practice of calculating two "slope" images from the four PyWFS pupil images discards critical information and is unsuitable for the non-modulated PyWFS simulated here. Instead, this article advocates estimators that use the raw pixel values not only from the four geometrical images of the pupil, but from surrounding pixels as well. The simulations indicate that nonlinear estimation can be effective when the Strehl ratio of the input beam is greater than 0.3, and the improvement relative to linear estimation tends to increase at larger Strehl ratios. At Strehl ratios less than about 0.5, the performances of both the nonlinear and linear estimators are relatively insensitive to noise, since they are dominated by nonlinearity error.

Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

PubMed

Steinacher, Arno; Bates, Declan G; Akman, Ozgur E; Soyer, Orkun S

2016-01-01

Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for the ubiquity of nonlinear dynamics in gene expression networks, and generate useful guidelines for the design of synthetic gene circuits.

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields.

PubMed

Rosnitskiy, Pavel B; Yuldashev, Petr V; Sapozhnikov, Oleg A; Maxwell, Adam D; Kreider, Wayne; Bailey, Michael R; Khokhlova, Vera A

2017-02-01

Various clinical applications of high-intensity focused ultrasound have different requirements for the pressure levels and degree of nonlinear waveform distortion at the focus. The goal of this paper is to determine transducer design parameters that produce either a specified shock amplitude in the focal waveform or specified peak pressures while still maintaining quasi-linear conditions at the focus. Multiparametric nonlinear modeling based on the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with an equivalent source boundary condition was employed. Peak pressures, shock amplitudes at the focus, and corresponding source outputs were determined for different transducer geometries and levels of nonlinear distortion. The results are presented in terms of the parameters of an equivalent single-element spherically shaped transducer. The accuracy of the method and its applicability to cases of strongly focused transducers were validated by comparing the KZK modeling data with measurements and nonlinear full diffraction simulations for a single-element source and arrays with 7 and 256 elements. The results provide look-up data for evaluating nonlinear distortions at the focus of existing therapeutic systems as well as for guiding the design of new transducers that generate specified nonlinear fields.

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.

Pre-chirp managed nonlinear amplification in fibers delivering 100  W, 60  fs pulses.

PubMed

Liu, Wei; Schimpf, Damian N; Eidam, Tino; Limpert, Jens; Tünnermann, Andreas; Kärtner, Franz X; Chang, Guoqing

2015-01-15

We demonstrate a pre-chirp managed Yb-doped fiber laser system that outputs 75 MHz, 130 W spectrally broadened pulses, which are compressed by a diffraction-grating pair to 60 fs with average powers as high as 100 W. Fine tuning the pulse chirp prior to amplification leads to high-quality compressed pulses. Detailed experiments and numerical simulation reveal that the optimum pre-chirp group-delay dispersion increases from negative to positive with increasing output power for rod-type high-power fiber amplifiers. The resulting laser parameters are suitable for extreme nonlinear optics applications such as frequency conversion in femtosecond enhancement cavities.

Effect of nonlinearity saturation on hot-image formation in cascaded saturable nonlinear medium slabs

NASA Astrophysics Data System (ADS)

Wang, Youwen; Dai, Zhiping; Ling, Xiaohui; Chen, Liezun; Lu, Shizhuan; You, Kaiming

2016-11-01

In high-power laser system such as Petawatt lasers, the laser beam can be intense enough to result in saturation of nonlinear refraction index of medium. Based on the standard linearization method of small-scale self-focusing and the split-step Fourier numerical calculation method, we present analytical and simulative investigations on the hot-image formation in cascaded saturable nonlinear medium slabs, to disclose the effect of nonlinearity saturation on the distribution and intensity of hot images. The analytical and simulative results are found in good agreement. It is shown that, saturable nonlinearity does not change the distribution of hot images, while may greatly affect the intensity of hot images, i.e., for a given saturation light intensity, with the intensity of the incident laser beam, the intensity of hot images firstly increases monotonously and eventually reaches a saturation; for the incident laser beam of a given intensity, with the saturation light intensity lowering, the intensity of hot images decreases rapidly, even resulting in a few hot images too weak to be visible.

Modelling of a bridge-shaped nonlinear piezoelectric energy harvester

NASA Astrophysics Data System (ADS)

Gafforelli, G.; Xu, R.; Corigliano, A.; Kim, S. G.

2013-12-01

Piezoelectric MicroElectroMechanical Systems (MEMS) energy harvesting is an attractive technology for harvesting small magnitudes of energy from ambient vibrations. Increasing the operating frequency bandwidth of such devices is one of the major issues for real world applications. A MEMS-scale doubly clamped nonlinear beam resonator is designed and developed to demonstrate very wide bandwidth and high power density. In this paper a first complete theoretical discussion of nonlinear resonating piezoelectric energy harvesting is provided. The sectional behaviour of the beam is studied through the Classical Lamination Theory (CLT) specifically modified to introduce the piezoelectric coupling and nonlinear Green-Lagrange strain tensor. A lumped parameter model is built through Rayleigh-Ritz Method and the resulting nonlinear coupled equations are solved in the frequency domain through the Harmonic Balance Method (HBM). Finally, the influence of external load resistance on the dynamic behaviour is studied. The theoretical model shows that nonlinear resonant harvesters have much wider power bandwidth than that of linear resonators but their maximum power is still bounded by the mechanical damping as is the case for linear resonating harvesters.

Leaderless consensus for the fractional-order nonlinear multi-agent systems under directed interaction topology

NASA Astrophysics Data System (ADS)

Bai, Jing; Wen, Guoguang; Rahmani, Ahmed

2018-04-01

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems' convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems' stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results.

Short-Time Nonlinear Effects in the Exciton-Polariton System

NASA Astrophysics Data System (ADS)

Guevara, Cristi D.; Shipman, Stephen P.

2018-04-01

In the exciton-polariton system, a linear dispersive photon field is coupled to a nonlinear exciton field. Short-time analysis of the lossless system shows that, when the photon field is excited, the time required for that field to exhibit nonlinear effects is longer than the time required for the nonlinear Schrödinger equation, in which the photon field itself is nonlinear. When the initial condition is scaled by ɛ ^α , it is found that the relative error committed by omitting the nonlinear term in the exciton-polariton system remains within ɛ for all times up to t=Cɛ ^β , where β =(1-α (p-1))/(p+2). This is in contrast to β =1-α (p-1) for the nonlinear Schrödinger equation. The result is proved for solutions in H^s(R^n) for s>n/2. Numerical computations indicate that the results are sharp and also hold in L^2(R^n).

Artificial Neural Networks

NASA Technical Reports Server (NTRS)

Niebur, Dagmar

1995-01-01

Electric power systems represent complex systems involving many electrical components whoseoperation has to be planned, analyzed, monitored and controlled. The time-scale of tasks in electricpower systems extends from long term planning years ahead to milliseconds in the area of control. The behavior of power systems is highly non-linear. Monitoring and control involves several hundred variables which are only partly available by measurements.

Nonlinear Conductive Behaviour of Silver Nanowires/Silicone Rubber Composites

NASA Astrophysics Data System (ADS)

Lu, Pin; Qu, Zhaoming; Wang, Qingguo; Bai, Liyun; Zhao, Shiyang

2018-01-01

Silver nanowires with an average length of 10 μm and diameter of about 90 nm have been synthesized by polyol reduction of silver nitrate in the presence of polyvinylpyrrolidone(PVP). Silver nanowires (AgNWs)/silicone rubber (SR) composites have been made by mixing silver nanowires into silicone rubber. The nonlinear response of AgNWs/SR composites under high electric field is investigated. The nonlinear Conductive behavior of composites is considered as a competitive process of several effects. From the perspective of the microstructure of composites, the conductive path is established by the quantum tunnel effect between silver nanowires. The influence factors on the conductivity of composites are discussed and analyzed. The results show that the AgNWs/SR composites with nonlinear conductive properties are of great potential application in electromagnetic protection of electron device and system.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

Intelligent adaptive nonlinear flight control for a high performance aircraft with neural networks.

PubMed

Savran, Aydogan; Tasaltin, Ramazan; Becerikli, Yasar

2006-04-01

This paper describes the development of a neural network (NN) based adaptive flight control system for a high performance aircraft. The main contribution of this work is that the proposed control system is able to compensate the system uncertainties, adapt to the changes in flight conditions, and accommodate the system failures. The underlying study can be considered in two phases. The objective of the first phase is to model the dynamic behavior of a nonlinear F-16 model using NNs. Therefore a NN-based adaptive identification model is developed for three angular rates of the aircraft. An on-line training procedure is developed to adapt the changes in the system dynamics and improve the identification accuracy. In this procedure, a first-in first-out stack is used to store a certain history of the input-output data. The training is performed over the whole data in the stack at every stage. To speed up the convergence rate and enhance the accuracy for achieving the on-line learning, the Levenberg-Marquardt optimization method with a trust region approach is adapted to train the NNs. The objective of the second phase is to develop intelligent flight controllers. A NN-based adaptive PID control scheme that is composed of an emulator NN, an estimator NN, and a discrete time PID controller is developed. The emulator NN is used to calculate the system Jacobian required to train the estimator NN. The estimator NN, which is trained on-line by propagating the output error through the emulator, is used to adjust the PID gains. The NN-based adaptive PID control system is applied to control three angular rates of the nonlinear F-16 model. The body-axis pitch, roll, and yaw rates are fed back via the PID controllers to the elevator, aileron, and rudder actuators, respectively. The resulting control system has learning, adaptation, and fault-tolerant abilities. It avoids the storage and interpolation requirements for the too many controller parameters of a typical flight control system. Performance of the control system is successfully tested by performing several six-degrees-of-freedom nonlinear simulations.

Parameter Design and Optimal Control of an Open Core Flywheel Energy Storage System

NASA Technical Reports Server (NTRS)

Pang, D.; Anand, D. K.; Kirk, J. A.

1996-01-01

In low earth orbit (LEO) satellite applications spacecraft power is provided by photovoltaic cells and batteries. To overcome battery shortcomings the University of Maryland, working in cooperation with NASA/GSFC and NASA/LeRC, has developed a magnetically suspended flywheel for energy storage applications. The system is referred to as an Open Core Composite Flywheel (OCCF) energy storage system. Successful application of flywheel energy storage requires integration of several technologies, viz. bearings, rotor design, motor/generator, power conditioning, and system control. In this paper we present a parameter design method which has been developed for analyzing the linear SISO model of the magnetic bearing controller for the OCCF. The objective of this continued research is to principally analyze the magnetic bearing system for nonlinear effects in order to increase the region of stability, as determined by high speed and large air gap control. This is achieved by four tasks: (1) physical modeling, design, prototyping, and testing of an improved magnetically suspended flywheel energy storage system, (2) identification of problems that limit performance and their corresponding solutions, (3) development of a design methodology for magnetic bearings, and (4) design of an optimal controller for future high speed applications. Both nonlinear SISO and MIMO models of the magnetic system were built to study limit cycle oscillations and power amplifier saturation phenomenon observed in experiments. The nonlinear models include the inductance of EM coils, the power amplifier saturation, and the physical limitation of the flywheel movement as discussed earlier. The control program EASY5 is used to study the nonlinear SISO and MIMO models. Our results have shown that the characteristics and frequency responses of the magnetic bearing system obtained from modeling are comparable to those obtained experimentally. Although magnetic saturation is shown in the bearings, there are good correlations between the theoretical model and experimental data. Both simulation and experiment confirm large variations of the magnetic bearing characteristics due to air gap growth. Therefore, the gap growth effect should be considered in the magnetic bearing system design. Additionally, the magnetic bearing control system will be compared to other design methods using not only parameter design but H-infinity optimal control and mu synthesis.

Introduction to Focus Issue: nonlinear and stochastic physics in biology.

PubMed

Bahar, Sonya; Neiman, Alexander B; Jung, Peter; Kurths, Jürgen; Schimansky-Geier, Lutz; Showalter, Kenneth

2011-12-01

Frank Moss was a leading figure in the study of nonlinear and stochastic processes in biological systems. His work, particularly in the area of stochastic resonance, has been highly influential to the interdisciplinary scientific community. This Focus Issue pays tribute to Moss with articles that describe the most recent advances in the field he helped to create. In this Introduction, we review Moss's seminal scientific contributions and introduce the articles that make up this Focus Issue.

Catch-Disperse-Release Readout for Superconducting Qubits

DTIC Science & Technology

2013-03-01

adiabatic, a fast high-fidelity qubit readout is possible even in the strongly nonlinear dispersive regime. Interestingly, the Jaynes - Cummings nonlinearity...will be included later) and describe the system by the Jaynes - Cummings (JC) Hamiltonian [7] with a microwave drive (we use ~ = 1) H = ωq(t)σ+σ− + ωra...λeff,0 rotates on the phase plane faster than in the two-level approximation , while λeff,1 rotates slower (some- times even in the opposite

Model Development and Model-Based Control Design for High Performance Nonlinear Smart Systems

DTIC Science & Technology

2007-11-20

potentially impact a broad range of flow control problems of interest to the Air Force and Boeing. Point of contact: James Mabe , Boeing Phantom Works...rotorcraft blades. In both cases, models and control designs will be validated using data from Boeing experiments and flight tests. Point of contact: James ... Mabe , Boeing Phantom Works, Seattle, WA, 206-655-0091. 3. PZT Unimorphs – Boeing: Nonlinear structural models developed through AFOSR support are being

Full spectrum optical safeguard

DOEpatents

Ackerman, Mark R.

2008-12-02

An optical safeguard device with two linear variable Fabry-Perot filters aligned relative to a light source with at least one of the filters having a nonlinear dielectric constant material such that, when a light source produces a sufficiently high intensity light, the light alters the characteristics of the nonlinear dielectric constant material to reduce the intensity of light impacting a connected optical sensor. The device can be incorporated into an imaging system on a moving platform, such as an aircraft or satellite.

Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points

NASA Astrophysics Data System (ADS)

Choi, Youngsun; Hahn, Choloong; Yoon, Jae Woong; Song, Seok Ho; Berini, Pierre

2017-01-01

Time-asymmetric state-evolution properties while encircling an exceptional point are presently of great interest in search of new principles for controlling atomic and optical systems. Here, we show that encircling-an-exceptional-point interactions that are essentially reciprocal in the linear interaction regime make a plausible nonlinear integrated optical device architecture highly nonreciprocal over an extremely broad spectrum. In the proposed strategy, we describe an experimentally realizable coupled-waveguide structure that supports an encircling-an-exceptional-point parametric evolution under the influence of a gain saturation nonlinearity. Using an intuitive time-dependent Hamiltonian and rigorous numerical computations, we demonstrate strictly nonreciprocal optical transmission with a forward-to-backward transmission ratio exceeding 10 dB and high forward transmission efficiency (~100%) persisting over an extremely broad bandwidth approaching 100 THz. This predicted performance strongly encourages experimental realization of the proposed concept to establish a practical on-chip optical nonreciprocal element for ultra-short laser pulses and broadband high-density optical signal processing.

Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation.

PubMed

Mustafa, M; Mushtaq, A; Hayat, T; Alsaedi, A

2016-01-01

Present study explores the MHD three-dimensional rotating flow and heat transfer of ferrofluid induced by a radiative surface. The base fluid is considered as water with magnetite-Fe3O4 nanoparticles. Novel concept of non-linear radiative heat flux is considered which produces a non-linear energy equation in temperature field. Conventional transformations are employed to obtain the self-similar form of the governing differential system. The arising system involves an interesting temperature ratio parameter which is an indicator of small/large temperature differences in the flow. Numerical simulations with high precision are determined by well-known shooting approach. Both uniform stretching and rotation have significant impact on the solutions. The variation in velocity components with the nanoparticle volume fraction is non-monotonic. Local Nusselt number in Fe3O4-water ferrofluid is larger in comparison to the pure fluid even at low particle concentration.

Stepwise photochromism of bisnaphthopyrans exhibiting an excitation intensity-dependent color change.

PubMed

Inagaki, Yuki; Mutoh, Katsuya; Abe, Jiro

2018-06-07

Non-linear photoresponses against excitation light intensity are important for the development of attractive photofunctional materials exhibiting high spatial selective photoswitching that is not affected by weak background light. Biphotochromic systems composed of two fast photochromic units have the potential to show a stepwise two-photon absorption process in which the optical properties can be non-linearly controlled by changing the excitation light conditions. Herein, we designed and synthesized novel bisnaphthopyran derivatives containing fast photoswitchable naphthopyran units. The bisnaphthopyran derivatives show a stepwise two-photon-induced photochromic reaction upon UV light irradiation accompanied by a drastic color change due to a large change in the molecular structure between the one-photon product and the two-photon product. Consequently, the color of the bisnaphthopyran derivatives can be non-linearly controlled by changing the excitation intensity. This characteristic photochromic property of the biphotochromic system provides important insight into advanced photoresponsive materials.

Static DC to DC Power Conditioning-Active Ripple Filter, 1 MHZ DC to DC Conversion, and Nonlinear Analysis. Ph.D. Thesis; [voltage regulation and conversion circuitry for spacecraft power supplies

NASA Technical Reports Server (NTRS)

Sander, W. A., III

1973-01-01

Dc to dc static power conditioning systems on unmanned spacecraft have as their inputs highly fluctuating dc voltages which they condition to regulated dc voltages. These input voltages may be less than or greater than the desired regulated voltages. The design of two circuits which address specific problems in the design of these power conditioning systems and a nonlinear analysis of one of the circuits are discussed. The first circuit design is for a nondissipative active ripple filter which uses an operational amplifier to amplify and cancel the sensed ripple voltage. A dc to dc converter operating at a switching frequency of 1 MHz is the second circuit discussed. A nonlinear analysis of the type of dc to dc converter utilized in designing the 1 MHz converter is included.

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.

Conversion of the high-mode solitons in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Zhang, Xiaping

2017-01-01

The conversion of high-mode solitons propagating in Strongly Nonlocal Nonlinear Media (SNNM) in three coordinate systems, namely, the elliptic coordinate system, the rectangular coordinate system and the cylindrical coordinate system, based on the Snyder-Mitchell Model that describes the paraxial beam propagating in SNNM, is discussed. Through constituting the trial solution with modulating the Gaussian beam by Ince polynomials, the closed-solution of Gaussian beams in elliptic coordinate is accessed. The Ince-Gaussian (IG) beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian (LG) beams, which is controlled by the elliptic parameter. The conditions of conversion in the three types of solitons are given in relation to the Gouy phase invariability in stable propagation. The profiles of the IG breather at a different propagating distance are numerically obtained, and the conversions of a few IG solitons are illustrated. The difference between the IG soliton and the corresponding LG soliton is remarkable from the Poynting vector and phase plots at their profiles along the propagating axis.

Discrete-time nonlinear damping backstepping control with observers for rejection of low and high frequency disturbances

NASA Astrophysics Data System (ADS)

Kim, Wonhee; Chen, Xu; Lee, Youngwoo; Chung, Chung Choo; Tomizuka, Masayoshi

2018-05-01

A discrete-time backstepping control algorithm is proposed for reference tracking of systems affected by both broadband disturbances at low frequencies and narrow band disturbances at high frequencies. A discrete time DOB, which is constructed based on infinite impulse response filters is applied to compensate for narrow band disturbances at high frequencies. A discrete-time nonlinear damping backstepping controller with an augmented observer is proposed to track the desired output and to compensate for low frequency broadband disturbances along with a disturbance observer, for rejecting narrow band high frequency disturbances. This combination has the merit of simultaneously compensating both broadband disturbances at low frequencies and narrow band disturbances at high frequencies. The performance of the proposed method is validated via experiments.

A novel methodology for non-linear system identification of battery cells used in non-road hybrid electric vehicles

NASA Astrophysics Data System (ADS)

Unger, Johannes; Hametner, Christoph; Jakubek, Stefan; Quasthoff, Marcus

2014-12-01

An accurate state of charge (SoC) estimation of a traction battery in hybrid electric non-road vehicles, which possess higher dynamics and power densities than on-road vehicles, requires a precise battery cell terminal voltage model. This paper presents a novel methodology for non-linear system identification of battery cells to obtain precise battery models. The methodology comprises the architecture of local model networks (LMN) and optimal model based design of experiments (DoE). Three main novelties are proposed: 1) Optimal model based DoE, which aims to high dynamically excite the battery cells at load ranges frequently used in operation. 2) The integration of corresponding inputs in the LMN to regard the non-linearities SoC, relaxation, hysteresis as well as temperature effects. 3) Enhancements to the local linear model tree (LOLIMOT) construction algorithm, to achieve a physical appropriate interpretation of the LMN. The framework is applicable for different battery cell chemistries and different temperatures, and is real time capable, which is shown on an industrial PC. The accuracy of the obtained non-linear battery model is demonstrated on cells with different chemistries and temperatures. The results show significant improvement due to optimal experiment design and integration of the battery non-linearities within the LMN structure.

A string of Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential

NASA Astrophysics Data System (ADS)

Gupta, Samit Kumar

2018-03-01

Dynamic wave localization phenomena draw fundamental and technological interests in optics and photonics. Based on the recently proposed (Ablowitz and Musslimani, 2013) continuous nonlocal nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for two first order Peregrine solitons as the initial ansatz. Peregrine soliton, as an exact solution to the PTNLSE, evokes a very potent question: what effects does the interaction of two first order Peregrine solitons have on the overall optical field dynamics. Upon numerical computation, we observe the appearance of Kuznetsov-Ma (KM) soliton trains in the unbroken PT-phase when the initial Peregrine solitons are in phase. In the out of phase condition, it shows repulsive nonlinear waves. Quite interestingly, our study shows that within a specific range of the interval factor in the transverse co-ordinate there exists a string of high intensity well-localized Peregrine rogue waves in the PT unbroken phase. We note that the interval factor as well as the transverse shift parameter play important roles in the nonlinear interaction and evolution dynamics of the optical fields. This could be important in developing fundamental understanding of nonlocal non-Hermitian NLSE systems and dynamic wave localization behaviors.

Performance of thermal deposition and mass flux condition on bioconvection nanoparticles containing gyrotactic microorganisms

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Ahmad, Bilal

2017-11-01

This is an attempt to investigate the influence of thermal radiation on the movement of motile gyrotactic microorganisms submerged in a water-based nanofluid flow over a nonlinear stretching sheet. The mathematical modeling of this physical problem leads to a system of nonlinear coupled partial differential equations. The problem is tackled by converting nonlinear partial differential equations into the system of highly nonlinear ordinary differential equations. The resulting nonlinear equations of momentum, energy, concentration of nanoparticles and motile gyrotactic microorganisms along with the mass flux condition are solved numerically by means of a shooting algorithm. The effects of the involved physical parameters of interest are discussed graphically. The values of the skin friction coefficient, Nusselt number, Sherwood number and local density number of motile microorganisms are tabulated for detailed analysis on the flow pattern at the stretching surface. It is concluded that the nanofluid temperature is an increasing function of the thermal radiation and the Biot number parameter. An opposite trend is observed for the local Nusselt number. The association with the preceding results in limiting sense is shown as well. A tremendous agreement of the current study in a restrictive manner is achieved as well. In addition, flow configurations through stream functions are presented and deliberated significantly.

CMOS-compatible 2-bit optical spectral quantization scheme using a silicon-nanocrystal-based horizontal slot waveguide

PubMed Central

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Wu, Qiang; Sang, Xinzhu; Farrell, Gerald; Yu, Chongxiu; Li, Feng; Tam, Hwa Yaw; Wai, P. K. A.

2014-01-01

All-optical analog-to-digital converters based on the third-order nonlinear effects in silicon waveguide are a promising candidate to overcome the limitation of electronic devices and are suitable for photonic integration. In this paper, a 2-bit optical spectral quantization scheme for on-chip all-optical analog-to-digital conversion is proposed. The proposed scheme is realized by filtering the broadened and split spectrum induced by the self-phase modulation effect in a silicon horizontal slot waveguide filled with silicon-nanocrystal. Nonlinear coefficient as high as 8708 W−1/m is obtained because of the tight mode confinement of the horizontal slot waveguide and the high nonlinear refractive index of the silicon-nanocrystal, which provides the enhanced nonlinear interaction and accordingly low power threshold. The results show that a required input peak power level less than 0.4 W can be achieved, along with the 1.98-bit effective-number-of-bit and Gray code output. The proposed scheme can find important applications in on-chip all-optical digital signal processing systems. PMID:25417847

CMOS-compatible 2-bit optical spectral quantization scheme using a silicon-nanocrystal-based horizontal slot waveguide.

PubMed

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Wu, Qiang; Sang, Xinzhu; Farrell, Gerald; Yu, Chongxiu; Li, Feng; Tam, Hwa Yaw; Wai, P K A

2014-11-24

All-optical analog-to-digital converters based on the third-order nonlinear effects in silicon waveguide are a promising candidate to overcome the limitation of electronic devices and are suitable for photonic integration. In this paper, a 2-bit optical spectral quantization scheme for on-chip all-optical analog-to-digital conversion is proposed. The proposed scheme is realized by filtering the broadened and split spectrum induced by the self-phase modulation effect in a silicon horizontal slot waveguide filled with silicon-nanocrystal. Nonlinear coefficient as high as 8708 W(-1)/m is obtained because of the tight mode confinement of the horizontal slot waveguide and the high nonlinear refractive index of the silicon-nanocrystal, which provides the enhanced nonlinear interaction and accordingly low power threshold. The results show that a required input peak power level less than 0.4 W can be achieved, along with the 1.98-bit effective-number-of-bit and Gray code output. The proposed scheme can find important applications in on-chip all-optical digital signal processing systems.

Robust/optimal temperature profile control of a high-speed aerospace vehicle using neural networks.

PubMed

Yadav, Vivek; Padhi, Radhakant; Balakrishnan, S N

2007-07-01

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A 1-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

The nonlinear chemo-mechanic coupled dynamics of the F 1 -ATPase molecular motor.

PubMed

Xu, Lizhong; Liu, Fang

2012-03-01

The ATP synthase consists of two opposing rotary motors, F0 and F1, coupled to each other. When the F1 motor is not coupled to the F0 motor, it can work in the direction hydrolyzing ATP, as a nanomotor called F1-ATPase. It has been reported that the stiffness of the protein varies nonlinearly with increasing load. The nonlinearity has an important effect on the rotating rate of the F1-ATPase. Here, considering the nonlinearity of the γ shaft stiffness for the F1-ATPase, a nonlinear chemo-mechanical coupled dynamic model of F1 motor is proposed. Nonlinear vibration frequencies of the γ shaft and their changes along with the system parameters are investigated. The nonlinear stochastic response of the elastic γ shaft to thermal excitation is analyzed. The results show that the stiffness nonlinearity of the γ shaft causes an increase of the vibration frequency for the F1 motor, which increases the motor's rotation rate. When the concentration of ATP is relatively high and the load torque is small, the effects of the stiffness nonlinearity on the rotating rates of the F1 motor are obvious and should be considered. These results are useful for improving calculation of the rotating rate for the F1 motor and provide insight about the stochastic wave mechanics of F1-ATPase.

General implementation of arbitrary nonlinear quadrature phase gates

NASA Astrophysics Data System (ADS)

Marek, Petr; Filip, Radim; Ogawa, Hisashi; Sakaguchi, Atsushi; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.

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

PubMed Central

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

2015-01-01

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

Nonlinear effects in the time measurement device based on surface acoustic wave filter excitation.

PubMed

Prochazka, Ivan; Panek, Petr

2009-07-01

A transversal surface acoustic wave filter has been used as a time interpolator in a time interval measurement device. We are presenting the experiments and results of an analysis of the nonlinear effects in such a time interpolator. The analysis shows that the nonlinear distortion in the time interpolator circuits causes a deterministic measurement error which can be understood as the time interpolation nonlinearity. The dependence of this error on time of the measured events can be expressed as a sparse Fourier series thus it usually oscillates very quickly in comparison to the clock period. The theoretical model is in good agreement with experiments carried out on an experimental two-channel timing system. Using highly linear amplifiers in the time interpolator and adjusting the filter excitation level to the optimum, we have achieved the interpolation nonlinearity below 0.2 ps. The overall single-shot precision of the experimental timing device is 0.9 ps rms in each channel.

Relativistic laser-plasma interactions in the quantum regime.

PubMed

Eliasson, Bengt; Shukla, P K

2011-04-01

We consider nonlinear interactions between a relativistically strong laser beam and a plasma in the quantum regime. The collective behavior of electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the electromagnetic wave through the Maxwell and Poisson equations. This allows us to study nonlinear interactions between arbitrarily large-amplitude electromagnetic waves and a quantum plasma. We have used our system of nonlinear equations to study theoretically the parametric instabilities involving stimulated Raman scattering and modulational instabilities. A model for quasi-steady-state propagating electromagnetic wave packets is also derived, and which shows possibility of localized solitary structures in a quantum plasma. Numerical simulations demonstrate collapse and acceleration of electrons in the nonlinear stage of the modulational instability, as well as possibility of the wake-field acceleration of electrons to relativistic speeds by short laser pulses at nanometer length scales. Our study is relevant for understanding the localization of intense electromagnetic pulses in a quantum plasma with extremely high electron densities and relatively low temperature.

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

NASA Astrophysics Data System (ADS)

Wu, R. Q.; Zhang, W.; Yao, M. H.

2018-02-01

In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton's second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.

Scaling and characterisation of a 2-DoF velocity amplified electromagnetic vibration energy harvester

NASA Astrophysics Data System (ADS)

O’Donoghue, D.; Frizzell, R.; Punch, J.

2018-07-01

Vibration energy harvesters (VEHs) offer an alternative to batteries for the autonomous operation of low-power electronics. Understanding the influence of scaling on VEHs is of great importance in the design of reduced scale harvesters. The nonlinear harvesters investigated here employ velocity amplification, a technique used to increase velocity through impacts, to improve the power output of multiple-degree-of-freedom VEHs, compared to linear resonators. Such harvesters, employing electromagnetic induction, are referred to as velocity amplified electromagnetic generators (VAEGs), with gains in power achieved by increasing the relative velocity between the magnet and coil in the transducer. The influence of scaling on a nonlinear 2-DoF VAEG is presented. Due to the increased complexity of VAEGs, compared to linear systems, linear scaling theory cannot be directly applied to VAEGs. Therefore, a detailed nonlinear scaling method is utilised. Experimental and numerical methods are employed. This nonlinear scaling method can be used for analysing the scaling behaviour of all nonlinear electromagnetic VEHs. It is demonstrated that the electromagnetic coupling coefficient degrades more rapidly with scale for systems with larger displacement amplitudes, meaning that systems operating at low frequencies will scale poorly compared to those operating at higher frequencies. The load power of the 2-DoF VAEG is predicted to scale as {P}L\\propto {s}5.51 (s = volume1/3), suggesting that achieving high power densities in a VAEG with low device volume is extremely challenging.

An enhanced nonlinear damping approach accounting for system constraints in active mass dampers

NASA Astrophysics Data System (ADS)

Venanzi, Ilaria; Ierimonti, Laura; Ubertini, Filippo

2015-11-01

Active mass dampers are a viable solution for mitigating wind-induced vibrations in high-rise buildings and improve occupants' comfort. Such devices suffer particularly when they reach force saturation of the actuators and maximum extension of their stroke, which may occur in case of severe loading conditions (e.g. wind gust and earthquake). Exceeding actuators' physical limits can impair the control performance of the system or even lead to devices damage, with consequent need for repair or substitution of part of the control system. Controllers for active mass dampers should account for their technological limits. Prior work of the authors was devoted to stroke issues and led to the definition of a nonlinear damping approach, very easy to implement in practice. It consisted of a modified skyhook algorithm complemented with a nonlinear braking force to reverse the direction of the mass before reaching the stroke limit. This paper presents an enhanced version of this approach, also accounting for force saturation of the actuator and keeping the simplicity of implementation. This is achieved by modulating the control force by a nonlinear smooth function depending on the ratio between actuator's force and saturation limit. Results of a numerical investigation show that the proposed approach provides similar results to the method of the State Dependent Riccati Equation, a well-established technique for designing optimal controllers for constrained systems, yet very difficult to apply in practice.

Nonlinear analysis of a rotor-bearing system using describing functions

NASA Astrophysics Data System (ADS)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Solutions of the cylindrical nonlinear Maxwell equations.

PubMed

Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying

2012-01-01

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.

Transition-metal dichalcogenides heterostructure saturable absorbers for ultrafast photonics.

PubMed

Chen, Hao; Yin, Jinde; Yang, Jingwei; Zhang, Xuejun; Liu, Mengli; Jiang, Zike; Wang, Jinzhang; Sun, Zhipei; Guo, Tuan; Liu, Wenjun; Yan, Peiguang

2017-11-01

In this Letter, high-quality WS 2 film and MoS 2 film were vertically stacked on the tip of a single-mode fiber in turns to form heterostructure (WS 2 -MoS 2 -WS 2 )-based saturable absorbers with all-fiber integrated features. Their nonlinear saturable absorption properties were remarkable, such as a large modulation depth (∼16.99%) and a small saturable intensity (6.23  MW·cm -2 ). Stable pulses at 1.55 μm with duration as short as 296 fs and average power as high as 25 mW were obtained in an erbium-doped fiber laser system. The results demonstrate that the proposed heterostructures own remarkable nonlinear optical properties and offer a platform for adjusting nonlinear optical properties by stacking different transition-metal dichalcogenides or modifying the thickness of each layer, paving the way for engineering functional ultrafast photonics devices with desirable properties.

Molecular structure, chemical reactivity, nonlinear optical activity and vibrational spectroscopic studies on 6-(4-n-heptyloxybenzyoloxy)-2-hydroxybenzylidene)amino)-2H-chromen-2-one: A combined density functional theory and experimental approach

NASA Astrophysics Data System (ADS)

Pegu, David; Deb, Jyotirmoy; Saha, Sandip Kumar; Paul, Manoj Kumar; Sarkar, Utpal

2018-05-01

In this work, we have synthesized new coumarin Schiff base molecule, viz., 6-(4-n-heptyloxybenzyoloxy)-2-hydroxybenzylidene)amino)-2H-chromen-2-one and characterized its structural, electronic and spectroscopic properties experimentally and theoretically. The theoretical analysis of UV-visible absorption spectra reflects a red shift in the absorption maximum in comparison to the experimental results. Most of the vibrational assignments of infrared and Raman spectra predicted using density functional theory approach match well with the experimental findings. Further, the chemical reactivity analysis confirms that solvent highly affects the reactivity of the studied compound. The large hyperpolarizability value of the compound concludes that the system exhibits significant nonlinear optical features and thus, points out their possibility in designing material with high nonlinear activity.

Exact modelling of the optical bistability in ferroelectics via two-wave mixing: A system with full nonlinearity

NASA Astrophysics Data System (ADS)

Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.

2018-05-01

In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.

A single-degree-of-freedom model for non-linear soil amplification

USGS Publications Warehouse

Erdik, Mustafa Ozder

1979-01-01

For proper understanding of soil behavior during earthquakes and assessment of a realistic surface motion, studies of the large-strain dynamic response of non-linear hysteretic soil systems are indispensable. Most of the presently available studies are based on the assumption that the response of a soil deposit is mainly due to the upward propagation of horizontally polarized shear waves from the underlying bedrock. Equivalent-linear procedures, currently in common use in non-linear soil response analysis, provide a simple approach and have been favorably compared with the actual recorded motions in some particular cases. Strain compatibility in these equivalent-linear approaches is maintained by selecting values of shear moduli and damping ratios in accordance with the average soil strains, in an iterative manner. Truly non-linear constitutive models with complete strain compatibility have also been employed. The equivalent-linear approaches often raise some doubt as to the reliability of their results concerning the system response in high frequency regions. In these frequency regions the equivalent-linear methods may underestimate the surface motion by as much as a factor of two or more. Although studies are complete in their methods of analysis, they inevitably provide applications pertaining only to a few specific soil systems, and do not lead to general conclusions about soil behavior. This report attempts to provide a general picture of the soil response through the use of a single-degree-of-freedom non-linear-hysteretic model. Although the investigation is based on a specific type of nonlinearity and a set of dynamic soil properties, the method described does not limit itself to these assumptions and is equally applicable to other types of nonlinearity and soil parameters.

Direct numerical simulations of premixed autoignition in compressible uniformly-sheared turbulence

NASA Astrophysics Data System (ADS)

Towery, Colin; Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter

2017-11-01

High-speed combustion systems, such as scramjet engines, operate at high temperatures and pressures, extremely short combustor residence times, very high rates of shear stress, and intense turbulent mixing. As a result, the reacting flow can be premixed and have highly-compressible turbulence fluctuations. We investigate the effects of compressible turbulence on the ignition delay time, heat-release-rate (HRR) intermittency, and mode of autoignition of premixed Hydrogen-air fuel in uniformly-sheared turbulence using new three-dimensional direct numerical simulations with a multi-step chemistry mechanism. We analyze autoignition in both the Eulerian and Lagrangian reference frames at eight different turbulence Mach numbers, Mat , spanning the quasi-isentropic, linear thermodynamic, and nonlinear compressibility regimes, with eddy shocklets appearing in the nonlinear regime. Results are compared to our previous study of premixed autoignition in isotropic turbulence at the same Mat and with a single-step reaction mechanism. This previous study found large decreases in delay times and large increases in HRR intermittency between the linear and nonlinear compressibility regimes and that detonation waves could form in both regimes.

F-15B QuietSpike(TradeMark) Aeroservoelastic Flight Test Data Analysis

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2007-01-01

System identification or mathematical modelling is utilised in the aerospace community for the development of simulation models for robust control law design. These models are often described as linear, time-invariant processes and assumed to be uniform throughout the flight envelope. Nevertheless, it is well known that the underlying process is inherently nonlinear. The reason for utilising a linear approach has been due to the lack of a proper set of tools for the identification of nonlinear systems. Over the past several decades the controls and biomedical communities have made great advances in developing tools for the identification of nonlinear systems. These approaches are robust and readily applicable to aerospace systems. In this paper, we show the application of one such nonlinear system identification technique, structure detection, for the analysis of F-15B QuietSpike(TradeMark) aeroservoelastic flight test data. Structure detection is concerned with the selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modelling may be of critical importance for the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion which may save significant development time and costs. The objectives of this study are to demonstrate via analysis of F-15B QuietSpike(TradeMark) aeroservoelastic flight test data for several flight conditions (Mach number) that (i) linear models are inefficient for modelling aeroservoelastic data, (ii) nonlinear identification provides a parsimonious model description whilst providing a high percent fit for cross-validated data and (iii) the model structure and parameters vary as the flight condition is altered.

Nonlinear consolidation in randomly heterogeneous highly compressible aquitards

NASA Astrophysics Data System (ADS)

Zapata-Norberto, Berenice; Morales-Casique, Eric; Herrera, Graciela S.

2018-05-01

Severe land subsidence due to groundwater extraction may occur in multiaquifer systems where highly compressible aquitards are present. The highly compressible nature of the aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. The effect of realistic vertical heterogeneity of hydrogeologic and geotechnical parameters on the consolidation of highly compressible aquitards is investigated by means of one-dimensional Monte Carlo numerical simulations where the lower boundary represents the effect of an instant drop in hydraulic head due to groundwater pumping. Two thousand realizations are generated for each of the following parameters: hydraulic conductivity ( K), compression index ( C c), void ratio ( e) and m (an empirical parameter relating hydraulic conductivity and void ratio). The correlation structure, the mean and the variance for each parameter were obtained from a literature review about field studies in the lacustrine sediments of Mexico City. The results indicate that among the parameters considered, random K has the largest effect on the ensemble average behavior of the system when compared to a nonlinear consolidation model with deterministic initial parameters. The deterministic solution underestimates the ensemble average of total settlement when initial K is random. In addition, random K leads to the largest variance (and therefore largest uncertainty) of total settlement, groundwater flux and time to reach steady-state conditions.

Real-Time linux dynamic clamp: a fast and flexible way to construct virtual ion channels in living cells.

PubMed

Dorval, A D; Christini, D J; White, J A

2001-10-01

We describe a system for real-time control of biological and other experiments. This device, based around the Real-Time Linux operating system, was tested specifically in the context of dynamic clamping, a demanding real-time task in which a computational system mimics the effects of nonlinear membrane conductances in living cells. The system is fast enough to represent dozens of nonlinear conductances in real time at clock rates well above 10 kHz. Conductances can be represented in deterministic form, or more accurately as discrete collections of stochastically gating ion channels. Tests were performed using a variety of complex models of nonlinear membrane mechanisms in excitable cells, including simulations of spatially extended excitable structures, and multiple interacting cells. Only in extreme cases does the computational load interfere with high-speed "hard" real-time processing (i.e., real-time processing that never falters). Freely available on the worldwide web, this experimental control system combines good performance. immense flexibility, low cost, and reasonable ease of use. It is easily adapted to any task involving real-time control, and excels in particular for applications requiring complex control algorithms that must operate at speeds over 1 kHz.

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.

Model tests and numerical analyses on horizontal impedance functions of inclined single piles embedded in cohesionless soil

NASA Astrophysics Data System (ADS)

Goit, Chandra Shekhar; Saitoh, Masato

2013-03-01

Horizontal impedance functions of inclined single piles are measured experimentally for model soil-pile systems with both the effects of local soil nonlinearity and resonant characteristics. Two practical pile inclinations of 5° and 10° in addition to a vertical pile embedded in cohesionless soil and subjected to lateral harmonic pile head loadings for a wide range of frequencies are considered. Results obtained with low-to-high amplitude of lateral loadings on model soil-pile systems encased in a laminar shear box show that the local nonlinearities have a profound impact on the horizontal impedance functions of piles. Horizontal impedance functions of inclined piles are found to be smaller than the vertical pile and the values decrease as the angle of pile inclination increases. Distinct values of horizontal impedance functions are obtained for the `positive' and `negative' cycles of harmonic loadings, leading to asymmetric force-displacement relationships for the inclined piles. Validation of these experimental results is carried out through three-dimensional nonlinear finite element analyses, and the results from the numerical models are in good agreement with the experimental data. Sensitivity analyses conducted on the numerical models suggest that the consideration of local nonlinearity at the vicinity of the soil-pile interface influence the response of the soil-pile systems.

Chaos and simple determinism in reversed field pinch plasmas: Nonlinear analysis of numerical simulation and experimental data

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

Watts, Christopher A.

In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulatemore » the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.« less

A robust in-situ warp-correction algorithm for VISAR streak camera data at the National Ignition Facility

NASA Astrophysics Data System (ADS)

Labaria, George R.; Warrick, Abbie L.; Celliers, Peter M.; Kalantar, Daniel H.

2015-02-01

The National Ignition Facility (NIF) at the Lawrence Livermore National Laboratory is a 192-beam pulsed laser system for high energy density physics experiments. Sophisticated diagnostics have been designed around key performance metrics to achieve ignition. The Velocity Interferometer System for Any Reflector (VISAR) is the primary diagnostic for measuring the timing of shocks induced into an ignition capsule. The VISAR system utilizes three streak cameras; these streak cameras are inherently nonlinear and require warp corrections to remove these nonlinear effects. A detailed calibration procedure has been developed with National Security Technologies (NSTec) and applied to the camera correction analysis in production. However, the camera nonlinearities drift over time affecting the performance of this method. An in-situ fiber array is used to inject a comb of pulses to generate a calibration correction in order to meet the timing accuracy requirements of VISAR. We develop a robust algorithm for the analysis of the comb calibration images to generate the warp correction that is then applied to the data images. Our algorithm utilizes the method of thin-plate splines (TPS) to model the complex nonlinear distortions in the streak camera data. In this paper, we focus on the theory and implementation of the TPS warp-correction algorithm for the use in a production environment.

Oscillating plasma bubble and its associated nonlinear studies in presence of low magnetic field

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

Megalingam, Mariammal; Sarma, Bornali; Mitra, Vramori

Oscillating plasma bubbles have been created around a cylindrical mesh grid of 75% optical transparency in a DC plasma system with a low magnetic field. Plasma bubbles are created by developing ion density gradient around a cylindrical grid of 20 cm in diameter and 25 cm in height, inserted into the plasma. Relaxation and contraction of the plasma bubbles in the presence of external conditions, such as magnetic field and pressure, have been studied. A Langmuir probe has been used to detect the plasma floating potential fluctuations at different imposed experimental conditions. Nonlinear behavior of the system has been characterized by adoptingmore » nonlinear techniques such as Fast Fourier Transform, Phase Space Plot, and Recurrence Plot. It shows that the system creates highly nonlinear phenomena associated with the plasma bubble under the imposed experimental conditions. A theoretical and numerical model has also been developed to satisfy the observed experimental analysis. Moreover, observations are extended further to study the growth of instability associated with the plasma bubbles. The intention of the present work is to correlate the findings about plasma bubbles and their related instability with the one existing in the equatorial F-region of the ionosphere.« less

An experimental study of nonlinear dynamic system identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1990-01-01

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

A methodology for designing robust multivariable nonlinear control systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Grunberg, D. B.

1986-01-01

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

NASA Astrophysics Data System (ADS)

Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

2018-03-01

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

Controllability in nonlinear systems

NASA Technical Reports Server (NTRS)

Hirschorn, R. M.

1975-01-01

An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems

ERIC Educational Resources Information Center

Stavrou, D.; Duit, R.; Komorek, M.

2008-01-01

A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…

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.

The influence of and the identification of nonlinearity in flexible structures

NASA Technical Reports Server (NTRS)

Zavodney, Lawrence D.

1988-01-01

Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

Nonlinear stability research on the hydraulic system of double-side rolling shear.

PubMed

Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

2015-10-01

This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

Nonlinear stability research on the hydraulic system of double-side rolling shear

NASA Astrophysics Data System (ADS)

Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

2015-10-01

This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

Dispersion and nonlinear effects in OFDM-RoF system

NASA Astrophysics Data System (ADS)

Alhasson, Bader H.; Bloul, Albe M.; Matin, M.

2010-08-01

The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.

Nonlinear and adaptive control

NASA Technical Reports Server (NTRS)

Athans, Michael

1989-01-01

The primary thrust of the research was to conduct fundamental research in the theories and methodologies for designing complex high-performance multivariable feedback control systems; and to conduct feasibiltiy studies in application areas of interest to NASA sponsors that point out advantages and shortcomings of available control system design methodologies.

Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

NASA Astrophysics Data System (ADS)

Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

2017-05-01

We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.

Robust approximation-free prescribed performance control for nonlinear systems and its application

NASA Astrophysics Data System (ADS)

Sun, Ruisheng; Na, Jing; Zhu, Bin

2018-02-01

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.

[Spectral quantitative analysis by nonlinear partial least squares based on neural network internal model for flue gas of thermal power plant].

PubMed

Cao, Hui; Li, Yao-Jiang; Zhou, Yan; Wang, Yan-Xia

2014-11-01

To deal with nonlinear characteristics of spectra data for the thermal power plant flue, a nonlinear partial least square (PLS) analysis method with internal model based on neural network is adopted in the paper. The latent variables of the independent variables and the dependent variables are extracted by PLS regression firstly, and then they are used as the inputs and outputs of neural network respectively to build the nonlinear internal model by train process. For spectra data of flue gases of the thermal power plant, PLS, the nonlinear PLS with the internal model of back propagation neural network (BP-NPLS), the non-linear PLS with the internal model of radial basis function neural network (RBF-NPLS) and the nonlinear PLS with the internal model of adaptive fuzzy inference system (ANFIS-NPLS) are compared. The root mean square error of prediction (RMSEP) of sulfur dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 16.96%, 16.60% and 19.55% than that of PLS, respectively. The RMSEP of nitric oxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 8.60%, 8.47% and 10.09% than that of PLS, respectively. The RMSEP of nitrogen dioxide of BP-NPLS, RBF-NPLS and ANFIS-NPLS are reduced by 2.11%, 3.91% and 3.97% than that of PLS, respectively. Experimental results show that the nonlinear PLS is more suitable for the quantitative analysis of glue gas than PLS. Moreover, by using neural network function which can realize high approximation of nonlinear characteristics, the nonlinear partial least squares method with internal model mentioned in this paper have well predictive capabilities and robustness, and could deal with the limitations of nonlinear partial least squares method with other internal model such as polynomial and spline functions themselves under a certain extent. ANFIS-NPLS has the best performance with the internal model of adaptive fuzzy inference system having ability to learn more and reduce the residuals effectively. Hence, ANFIS-NPLS is an accurate and useful quantitative thermal power plant flue gas analysis method.

Rapid solution of large-scale systems of equations

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.

1994-01-01

The analysis and design of complex aerospace structures requires the rapid solution of large systems of linear and nonlinear equations, eigenvalue extraction for buckling, vibration and flutter modes, structural optimization and design sensitivity calculation. Computers with multiple processors and vector capabilities can offer substantial computational advantages over traditional scalar computer for these analyses. These computers fall into two categories: shared memory computers and distributed memory computers. This presentation covers general-purpose, highly efficient algorithms for generation/assembly or element matrices, solution of systems of linear and nonlinear equations, eigenvalue and design sensitivity analysis and optimization. All algorithms are coded in FORTRAN for shared memory computers and many are adapted to distributed memory computers. The capability and numerical performance of these algorithms will be addressed.

Self-Organized Lattices of Nonlinear Optochemical Waves in Photopolymerizable Fluids: The Spontaneous Emergence of 3-D Order in a Weakly Correlated System.

PubMed

Ponte, Matthew R; Hudson, Alexander D; Saravanamuttu, Kalaichelvi

2018-03-01

Many of the extraordinary three-dimensional architectures that pattern our physical world emerge from complex nonlinear systems or dynamic populations whose individual constituents are only weakly correlated to each other. Shoals of fish, murmuration behaviors in birds, congestion patterns in traffic, and even networks of social conventions are examples of spontaneous pattern formation, which cannot be predicted from the properties of individual elements alone. Pattern formation at a different scale has been observed or predicted in weakly correlated systems including superconductors, atomic gases near Bose Einstein condensation, and incoherent optical fields. Understanding pattern formation in nonlinear weakly correlated systems, which are often unified through mathematical expression, could pave intelligent self-organizing pathways to functional materials, architectures, and computing technologies. However, it is experimentally difficult to directly visualize the nonlinear dynamics of pattern formation in most populations-especially in three dimensions. Here, we describe the collective behavior of large populations of nonlinear optochemical waves, which are poorly correlated in both space and time. The optochemical waves-microscopic filaments of white light entrapped within polymer channels-originate from the modulation instability of incandescent light traveling in photopolymerizable fluids. By tracing the three-dimensional distribution of optical intensity in the nascent polymerizing system, we find that populations of randomly distributed, optochemical waves synergistically and collectively shift in space to form highly ordered lattices of specific symmetries. These, to our knowledge, are the first three-dimensionally periodic structures to emerge from a system of weakly correlated waves. Their spontaneous formation in an incoherent and effectively chaotic field is counterintuitive, but the apparent contradiction of known behaviors of light including the laws of optical interference can be explained through the soliton-like interactions of optochemical waves with nearest neighbors. Critically, this work casts fundamentally new insight into the collective behaviors of poorly correlated nonlinear waves in higher dimensions and provides a rare, accessible platform for further experimental studies of these previously unexplored behaviors. Furthermore, it defines a self-organization paradigm that, unlike conventional counterparts, could generate polymer microstructures with symmetries spanning all the Bravais lattices.

Role of annealing temperatures on structure polymorphism, linear and nonlinear optical properties of nanostructure lead dioxide thin films

NASA Astrophysics Data System (ADS)

Zeyada, H. M.; Makhlouf, M. M.

2016-04-01

The powder of as synthesized lead dioxide (PbO2) has polycrystalline structure β-PbO2 phase of tetragonal crystal system. It becomes nanocrystallites α-PbO2 phase with orthorhombic crystal system upon thermal deposition to form thin films. Annealing temperatures increase nanocrystallites size from 28 to 46 nm. The optical properties of α-PbO2 phase were calculated from absolute values of transmittance and reflectance at nearly normal incidence of light by spectrophotometer measurements. The refractive and extinction indices were determined and showed a response to annealing temperatures. The absorption coefficient of α-PbO2 films is >106 cm-1 in UV region of spectra. Analysis of the absorption coefficient spectra near optical edge showed indirect allowed transition. Annealing temperature decreases the value of indirect energy gap for α-PbO2 films. The dispersion parameters such as single oscillator energy, dispersion energy, dielectric constant at high frequency and lattice dielectric constant were calculated and its variations with annealing temperatures are reported. The nonlinear refractive index (n2), third-order nonlinear susceptibility (χ(3)) and nonlinear absorption coefficient (βc) were determined. It was found that χ(3), n2 and β increase with increasing photon energy and decrease with increasing annealing temperature. The pristine film of α-PbO2 has higher values of nonlinear optical constants than for annealed films; therefore it is suitable for applications in manufacturing nonlinear optical devices.

Mathematical model for prediction of efficiency indicators of educational activity in high school

NASA Astrophysics Data System (ADS)

Tikhonova, O. M.; Kushnikov, V. A.; Fominykh, D. S.; Rezchikov, A. F.; Ivashchenko, V. A.; Bogomolov, A. S.; Filimonyuk, L. Yu; Dolinina, O. N.; Kushnikov, O. V.; Shulga, T. E.; Tverdokhlebov, V. A.

2018-05-01

The quality of high school is a current problem all over the world. The paper presents the system dedicated to predicting the accreditation indicators of technical universities based on J. Forrester mechanism of system dynamics. The mathematical model is developed for prediction of efficiency indicators of the educational activity and is based on the apparatus of nonlinear differential equations.

Single-photon nonlinearities in the propagation of focused beams through dense atomic clouds

NASA Astrophysics Data System (ADS)

Wang, Yidan; Gorshkov, Alexey; Gullans, Michael

2017-04-01

We theoretically study single-photon nonlinearities realized when a highly focused Gaussian beam passes through a dense atomic cloud. In this system, strong dipole-dipole interactions arise between closely spaced atoms and significantly affect light propagation. We find that the highly focused Gaussian beam can be treated as an effective one-dimensional waveguide, which simplifies the calculation of photon transmission and correlation functions. The formalism we develop is also applicable to the case where additional atom-atom interactions, such as interactions between Rydberg atoms, are involved. This work was supported by the ARL, NSF PFC at the JQI, AFOSR, NSF PIF, ARO, and AFOSR MURI.

Task oriented nonlinear control laws for telerobotic assembly operations

NASA Technical Reports Server (NTRS)

Walker, R. A.; Ward, L. S.; Elia, C. F.

1987-01-01

The goal of this research is to achieve very intelligent telerobotic controllers which are capable of receiving high-level commands from the human operator and implementing them in an adaptive manner in the object/task/manipulator workspace. Initiatives by the authors at Integrated Systems, Inc. to identify and develop the key technologies necessary to create such a flexible, highly programmable, telerobotic controller are presented. The focus of the discussion is on the modeling of insertion tasks in three dimensions and nonlinear implicit force feedback control laws which incorporate tool/workspace constraints. Preliminary experiments with dual arm beam assembly in 2-D are presented.

Resonance and Chaotic Trajectories in Magnetic Field Reversed Configuration

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

A.S. Landsman; S.A. Cohen; M. Edelman

The nonlinear dynamics of a single ion in a field-reversed configuration (FRC) were investigated. FRC is a toroidal fusion device which uses a specific type of magnetic field to confine ions. As a result of angular invariance, the full three-dimensional Hamiltonian system can be expressed as two coupled, highly nonlinear oscillators. Due to the high nonlinearity in the equations of motion, the behavior of the system is extremely complex, showing different regimes, depending on the values of the conserved canonical angular momentum and the geometry of the fusion vessel. Perturbation theory and averaging were used to derive the unperturbed Hamiltonianmore » and frequencies of the two degrees of freedom. The derived equations were then used to find resonances and compare to Poincar{copyright} surface-of-section plots. A regime was found where the nonlinear resonances were clearly separated by KAM [Kolmogorov-Arnold-Mosher] curves. The structure of the observed island chains was explained. The condition for the destruction of KAM curves and the onset of strong chaos was derived, using Chirikov island overlap criterion, and shown qualitatively to depend both on the canonical angular momentum and geometry of the device. After a brief discussion of the adiabatic regime the paper goes on to explore the degenerate regime that sets in at higher values of angular momenta. In this regime, the unperturbed Hamiltonian can be approximated as two uncoupled linear oscillators. In this case, the system is near-integrable, except in cases of a universal resonance, which results in large island structures, due to the smallness of nonlinear terms, which bound the resonance. The linear force constants, dominant in this regime, were derived and the geometry for a large one-to-one resonance identified. The above analysis showed good agreement with numerical simulations and was able to explain characteristic features of the dynamics.« less

Computational strategy for the solution of large strain nonlinear problems using the Wilkins explicit finite-difference approach

NASA Technical Reports Server (NTRS)

Hofmann, R.

1980-01-01

The STEALTH code system, which solves large strain, nonlinear continuum mechanics problems, was rigorously structured in both overall design and programming standards. The design is based on the theoretical elements of analysis while the programming standards attempt to establish a parallelism between physical theory, programming structure, and documentation. These features have made it easy to maintain, modify, and transport the codes. It has also guaranteed users a high level of quality control and quality assurance.

Matrix-Free Polynomial-Based Nonlinear Least Squares Optimized Preconditioning and its Application to Discontinuous Galerkin Discretizations of the Euler Equations

DTIC Science & Technology

2015-06-01

cient parallel code for applying the operator. Our method constructs a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show...apply the underlying operator. Such a preconditioner can be very attractive in scenarios where one has a highly efficient parallel code for applying...repeatedly solve a large system of linear equations where one has an extremely fast parallel code for applying an underlying fixed linear operator

Tunneling induced absorption with competing Nonlinearities.

PubMed

Peng, Yandong; Yang, Aihong; Xu, Yan; Wang, Peng; Yu, Yang; Guo, Hongju; Ren, Tingqi

2016-12-13

We investigate tunneling induced nonlinear absorption phenomena in a coupled quantum-dot system. Resonant tunneling causes constructive interference in the nonlinear absorption that leads to an increase of more than an order of magnitude over the maximum absorption in a coupled quantum dot system without tunneling. Resonant tunneling also leads to a narrowing of the linewidth of the absorption peak to a sublinewidth level. Analytical expressions show that the enhanced nonlinear absorption is largely due to the fifth-order nonlinear term. Competition between third- and fifth-order nonlinearities leads to an anomalous dispersion of the total susceptibility.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Optics and Nonlinear Buckling Mechanics in Large-Area, Highly Stretchable Arrays of Plasmonic Nanostructures.

PubMed

Gao, Li; Zhang, Yihui; Zhang, Hui; Doshay, Sage; Xie, Xu; Luo, Hongying; Shah, Deesha; Shi, Yan; Xu, Siyi; Fang, Hui; Fan, Jonathan A; Nordlander, Peter; Huang, Yonggang; Rogers, John A

2015-06-23

Large-scale, dense arrays of plasmonic nanodisks on low-modulus, high-elongation elastomeric substrates represent a class of tunable optical systems, with reversible ability to shift key optical resonances over a range of nearly 600 nm at near-infrared wavelengths. At the most extreme levels of mechanical deformation (strains >100%), nonlinear buckling processes transform initially planar arrays into three-dimensional configurations, in which the nanodisks rotate out of the plane to form linear arrays with "wavy" geometries. Analytical, finite-element, and finite-difference time-domain models capture not only the physics of these buckling processes, including all of the observed modes, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, particularly to soft optical sensors that integrate on or in the human body.

A comparative study of the effects of cone-plate and parallel-plate geometries on rheological properties under oscillatory shear flow

NASA Astrophysics Data System (ADS)

Song, Hyeong Yong; Salehiyan, Reza; Li, Xiaolei; Lee, Seung Hak; Hyun, Kyu

2017-11-01

In this study, the effects of cone-plate (C/P) and parallel-plate (P/P) geometries were investigated on the rheological properties of various complex fluids, e.g. single-phase (polymer melts and solutions) and multiphase systems (polymer blend and nanocomposite, and suspension). Small amplitude oscillatory shear (SAOS) tests were carried out to compare linear rheological responses while nonlinear responses were compared using large amplitude oscillatory shear (LAOS) tests at different frequencies. Moreover, Fourier-transform (FT)-rheology method was used to analyze the nonlinear responses under LAOS flow. Experimental results were compared with predictions obtained by single-point correction and shear rate correction. For all systems, SAOS data measured by C/P and P/P coincide with each other, but results showed discordance between C/P and P/P measurements in the nonlinear regime. For all systems except xanthan gum solutions, first-harmonic moduli were corrected using a single horizontal shift factor, whereas FT rheology-based nonlinear parameters ( I 3/1, I 5/1, Q 3, and Q 5) were corrected using vertical shift factors that are well predicted by single-point correction. Xanthan gum solutions exhibited anomalous corrections. Their first-harmonic Fourier moduli were superposed using a horizontal shift factor predicted by shear rate correction applicable to highly shear thinning fluids. The distinguished corrections were observed for FT rheology-based nonlinear parameters. I 3/1 and I 5/1 were superposed by horizontal shifts, while the other systems displayed vertical shifts of I 3/1 and I 5/1. Q 3 and Q 5 of xanthan gum solutions were corrected using both horizontal and vertical shift factors. In particular, the obtained vertical shift factors for Q 3 and Q 5 were twice as large as predictions made by single-point correction. Such larger values are rationalized by the definitions of Q 3 and Q 5. These results highlight the significance of horizontal shift corrections in nonlinear oscillatory shear data.

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

NASA Astrophysics Data System (ADS)

Huang, Rui; Hu, Haiyan; Zhao, Yonghui

2013-10-01

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.

Non-linear vibrating systems excited by a nonideal energy source with a large slope characteristic

NASA Astrophysics Data System (ADS)

González-Carbajal, Javier; Domínguez, Jaime

2017-11-01

This paper revisits the problem of an unbalanced motor attached to a fixed frame by means of a nonlinear spring and a linear damper. The excitation provided by the motor is, in general, nonideal, which means it is affected by the vibratory response. Since the system behaviour is highly dependent on the order of magnitude of the motor characteristic slope, the case of large slope is considered herein. Some Perturbation Methods are applied to the system of equations, which allows transforming the original 4D system into a much simpler 2D system. The fixed points of this reduced system and their stability are carefully studied. We find the existence of a Hopf bifurcation which, to the authors' knowledge, has not been addressed before in the literature. These analytical results are supported by numerical simulations. We also compare our approach and results with those published by other authors.

Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input.

PubMed

Yu, Jinpeng; Shi, Peng; Dong, Wenjie; Lin, Chong

2017-09-01

In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

An experimental nonlinear low dynamic stiffness device for shock isolation

NASA Astrophysics Data System (ADS)

Francisco Ledezma-Ramirez, Diego; Ferguson, Neil S.; Brennan, Michael J.; Tang, Bin

2015-07-01

The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements.

Trajectory tracking in quadrotor platform by using PD controller and LQR control approach

NASA Astrophysics Data System (ADS)

Islam, Maidul; Okasha, Mohamed; Idres, Moumen Mohammad

2017-11-01

The purpose of the paper is to discuss a comparative evaluation of performance of two different controllers i.e. Proportional-Derivative Controller (PD) and Linear Quadratic Regulation (LQR) in Quadrotor dynamic system that is under-actuated with high nonlinearity. As only four states can be controlled at the same time in the Quadrotor, the trajectories are designed on the basis of the four states whereas three dimensional position and rotation along an axis, known as yaw movement are considered. In this work, both the PD controller and LQR control approach are used for Quadrotor nonlinear model to track the trajectories. LQR control approach for nonlinear model is designed on the basis of a linear model of the Quadrotor because the performance of linear model and nonlinear model around certain nominal point is almost similar. Simulink and MATLAB software is used to design the controllers and to evaluate the performance of both the controllers.

Rail vehicle dynamic response to a nonlinear physical 'in-service' model of its secondary suspension hydraulic dampers

NASA Astrophysics Data System (ADS)

Wang, W. L.; Zhou, Z. R.; Yu, D. S.; Qin, Q. H.; Iwnicki, S.

2017-10-01

A full nonlinear physical 'in-service' model was built for a rail vehicle secondary suspension hydraulic damper with shim-pack-type valves. In the modelling process, a shim pack deflection theory with an equivalent-pressure correction factor was proposed, and a Finite Element Analysis (FEA) approach was applied. Bench test results validated the damper model over its full velocity range and thus also proved that the proposed shim pack deflection theory and the FEA-based parameter identification approach are effective. The validated full damper model was subsequently incorporated into a detailed vehicle dynamics simulation to study how its key in-service parameter variations influence the secondary-suspension-related vehicle system dynamics. The obtained nonlinear physical in-service damper model and the vehicle dynamic response characteristics in this study could be used in the product design optimization and nonlinear optimal specifications of high-speed rail hydraulic dampers.

Large predispersion for reduction of intrachannel nonlinear impairments in strongly dispersion-managed transmissions

NASA Astrophysics Data System (ADS)

Cao, Wenhua

2016-05-01

Predispersion for reduction of intrachannel nonlinear impairments in quasi-linear strongly dispersion-managed transmission system is analyzed in detail by numerical simulations. We show that for moderate amount of predispersion there is an optimal value at which reduction of the nonlinear impairments can be obtained, which is consistent with previous well-known predictions. However, we found that much better transmission performance than that of the previous predictions can be obtained if predispersion is increased to some extent. For large predispersion, the nonlinear impairments reduce monotonically with increasing predispersion and then they tend to be stabilized when predispersion is further increased. Thus, transmission performance can be efficiently improved by inserting a high-dispersive element, such as a chirped fiber bragg grating (CFBG), at the input end of the transmission link to broaden the signal pulses while, at the output end, using another CFBG with the opposite dispersion to recompress the signal.

Optical super-resolution effect induced by nonlinear characteristics of graphene oxide films

NASA Astrophysics Data System (ADS)

Zhao, Yong-chuang; Nie, Zhong-quan; Zhai, Ai-ping; Tian, Yan-ting; Liu, Chao; Shi, Chang-kun; Jia, Bao-hua

2018-01-01

In this work, we focus on the optical super-resolution effect induced by strong nonlinear saturation absorption (NSA) of graphene oxide (GO) membranes. The third-order optical nonlinearities are characterized by the canonical Z-scan technique under femtosecond laser (wavelength: 800 nm, pulse width: 100 fs) excitation. Through controlling the applied femtosecond laser energy, NSA of the GO films can be tuned continuously. The GO film is placed at the focal plane as a unique amplitude filter to improve the resolution of the focused field. A multi-layer system model is proposed to present the generation of a deep sub-wavelength spot associated with the nonlinearity of GO films. Moreover, the parameter conditions to achieve the best resolution (˜λ/6) are determined entirely. The demonstrated results here are useful for high density optical recoding and storage, nanolithography, and super-resolution optical imaging.

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.

Non-linear dynamical classification of short time series of the rössler system in high noise regimes.

PubMed

Lainscsek, Claudia; Weyhenmeyer, Jonathan; Hernandez, Manuel E; Poizner, Howard; Sejnowski, Terrence J

2013-01-01

Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson's disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to -30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A' under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.

Non-Linear Dynamical Classification of Short Time Series of the Rössler System in High Noise Regimes

PubMed Central

Lainscsek, Claudia; Weyhenmeyer, Jonathan; Hernandez, Manuel E.; Poizner, Howard; Sejnowski, Terrence J.

2013-01-01

Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson’s disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to −30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A′ under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data. PMID:24379798

Variable-Structure Control of a Model Glider Airplane

NASA Technical Reports Server (NTRS)

Waszak, Martin R.; Anderson, Mark R.

2008-01-01

A variable-structure control system designed to enable a fuselage-heavy airplane to recover from spin has been demonstrated in a hand-launched, instrumented model glider airplane. Variable-structure control is a high-speed switching feedback control technique that has been developed for control of nonlinear dynamic systems.

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

NASA Astrophysics Data System (ADS)

Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.

2015-04-01

In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized by the cantilever-surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the system's robustness to parasitic damping.

Design and implementation of non-linear image processing functions for CMOS image sensor

NASA Astrophysics Data System (ADS)

Musa, Purnawarman; Sudiro, Sunny A.; Wibowo, Eri P.; Harmanto, Suryadi; Paindavoine, Michel

2012-11-01

Today, solid state image sensors are used in many applications like in mobile phones, video surveillance systems, embedded medical imaging and industrial vision systems. These image sensors require the integration in the focal plane (or near the focal plane) of complex image processing algorithms. Such devices must meet the constraints related to the quality of acquired images, speed and performance of embedded processing, as well as low power consumption. To achieve these objectives, low-level analog processing allows extracting the useful information in the scene directly. For example, edge detection step followed by a local maxima extraction will facilitate the high-level processing like objects pattern recognition in a visual scene. Our goal was to design an intelligent image sensor prototype achieving high-speed image acquisition and non-linear image processing (like local minima and maxima calculations). For this purpose, we present in this article the design and test of a 64×64 pixels image sensor built in a standard CMOS Technology 0.35 μm including non-linear image processing. The architecture of our sensor, named nLiRIC (non-Linear Rapid Image Capture), is based on the implementation of an analog Minima/Maxima Unit. This MMU calculates the minimum and maximum values (non-linear functions), in real time, in a 2×2 pixels neighbourhood. Each MMU needs 52 transistors and the pitch of one pixel is 40×40 mu m. The total area of the 64×64 pixels is 12.5mm2. Our tests have shown the validity of the main functions of our new image sensor like fast image acquisition (10K frames per second), minima/maxima calculations in less then one ms.

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

NASA Astrophysics Data System (ADS)

Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

2018-02-01

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

Heterodyne lock-in thermography of early demineralized in dental tissues

NASA Astrophysics Data System (ADS)

Wang, Fei; Liu, Jun-yan; Mohummad, Oliullah; Wang, Xiao-chun; Wang, Yang

2017-12-01

Heterodyne lock-in thermography (HeLIT) is a highly sensitive method to detect early demineralized in dental tissues, which is based on nonlinear photothermal phenomena of dental tissues. In this paper, the nonlinear photothermal phenomena of dental tissues was introduced, and then the system of HeLIT was developed. The relationship between laser modulated parameters (modulated frequency and laser intensity) and heterodyne lock-in thermal wave signal was investigated. The comparison between HeLIT and homodyne lock-in thermography (HoLIT) for detecting the different types of dental caries (smooth surface caries, proximal surface caries and occlusal surface caries) were carried out. Experimental results illustrate that the HeLIT has the merits of high sensitivity and high specificity in detecting different types of early caries.

Electromagnetic diode based on photonic crystal cavity with embedded highly dispersive meta-interface

NASA Astrophysics Data System (ADS)

Chen, Yongqiang; Dong, Lijuan; Xu, Xiaohu; Jiang, Jun; Shi, Yunlong

2017-12-01

In this paper, we propose a scheme for subwavelength electromagnetic diodes by employing a photonic crystal (PC) cavity with embedded electromagnetically induced-transparency (EIT)-like highly dispersive meta-interface. A nonreciprocal response, with 21.5 dB transmission light contrast and 12.3 dBm working power, is conceptually demonstrated in a microstrip transmission line system with asymmetric absorption and nonlinear medium inclusion. Such high-contrast transmission and relatively low-threshold diode action stem from the composite PC-EIT mechanism. This mechanism not only possesses a large quality factor and strong localization of fields but also does not enlarge the device volume and drastically reduce transmittance. Our findings should be beneficial for the design of new and practical metamaterial-enabled nonlinear devices.

Nonlinear modelling of high-speed catenary based on analytical expressions of cable and truss elements

NASA Astrophysics Data System (ADS)

Song, Yang; Liu, Zhigang; Wang, Hongrui; Lu, Xiaobing; Zhang, Jing

2015-10-01

Due to the intrinsic nonlinear characteristics and complex structure of the high-speed catenary system, a modelling method is proposed based on the analytical expressions of nonlinear cable and truss elements. The calculation procedure for solving the initial equilibrium state is proposed based on the Newton-Raphson iteration method. The deformed configuration of the catenary system as well as the initial length of each wire can be calculated. Its accuracy and validity of computing the initial equilibrium state are verified by comparison with the separate model method, absolute nodal coordinate formulation and other methods in the previous literatures. Then, the proposed model is combined with a lumped pantograph model and a dynamic simulation procedure is proposed. The accuracy is guaranteed by the multiple iterative calculations in each time step. The dynamic performance of the proposed model is validated by comparison with EN 50318, the results of the finite element method software and SIEMENS simulation report, respectively. At last, the influence of the catenary design parameters (such as the reserved sag and pre-tension) on the dynamic performance is preliminarily analysed by using the proposed model.

Two-step sensitivity testing of parametrized and regionalized life cycle assessments: methodology and case study.

PubMed

Mutel, Christopher L; de Baan, Laura; Hellweg, Stefanie

2013-06-04

Comprehensive sensitivity analysis is a significant tool to interpret and improve life cycle assessment (LCA) models, but is rarely performed. Sensitivity analysis will increase in importance as inventory databases become regionalized, increasing the number of system parameters, and parametrized, adding complexity through variables and nonlinear formulas. We propose and implement a new two-step approach to sensitivity analysis. First, we identify parameters with high global sensitivities for further examination and analysis with a screening step, the method of elementary effects. Second, the more computationally intensive contribution to variance test is used to quantify the relative importance of these parameters. The two-step sensitivity test is illustrated on a regionalized, nonlinear case study of the biodiversity impacts from land use of cocoa production, including a worldwide cocoa products trade model. Our simplified trade model can be used for transformable commodities where one is assessing market shares that vary over time. In the case study, the highly uncertain characterization factors for the Ivory Coast and Ghana contributed more than 50% of variance for almost all countries and years examined. The two-step sensitivity test allows for the interpretation, understanding, and improvement of large, complex, and nonlinear LCA systems.