Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

Science.gov (United States)

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Fuzzy Control Model and Simulation for Nonlinear Supply Chain System with Lead Times

Directory of Open Access Journals (Sweden)

Songtao Zhang

2017-01-01

Full Text Available A new fuzzy robust control strategy for the nonlinear supply chain system in the presence of lead times is proposed. Based on Takagi-Sugeno fuzzy control system, the fuzzy control model of the nonlinear supply chain system with lead times is constructed. Additionally, we design a fuzzy robust H∞ control strategy taking the definition of maximal overlapped-rules group into consideration to restrain the impacts such as those caused by lead times, switching actions among submodels, and customers’ stochastic demands. This control strategy can not only guarantee that the nonlinear supply chain system is robustly asymptotically stable but also realize soft switching among subsystems of the nonlinear supply chain to make the less fluctuation of the system variables by introducing the membership function of fuzzy system. The comparisons between the proposed fuzzy robust H∞ control strategy and the robust H∞ control strategy are finally illustrated through numerical simulations on a two-stage nonlinear supply chain with lead times.

Nonlinear mirror mode dynamics: Simulations and modeling

Czech Academy of Sciences Publication Activity Database

Califano, F.; Hellinger, Petr; Kuznetsov, E.; Passot, T.; Sulem, P. L.; Trávníček, Pavel

2008-01-01

Roč. 113, - (2008), A08219/1-A08219/20 ISSN 0148-0227 R&D Projects: GA AV ČR IAA300420702; GA AV ČR IAA300420602 Grant - others:PECS(CZ) 98024 Institutional research plan: CEZ:AV0Z30420517 Keywords : mirror instability * nonlinear evolution * numerical simulations * magnetic holes * mirror structures * kinetic plasma instabilities Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.147, year: 2008

Neurosurgery simulation using non-linear finite element modeling and haptic interaction

Science.gov (United States)

Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet

2012-02-01

Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary element method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.

Non-linear Loudspeaker Unit Modelling

DEFF Research Database (Denmark)

Pedersen, Bo Rohde; Agerkvist, Finn T.

2008-01-01

Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of thr...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....

Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — Time simulation of a nonlinear aerodynamics model (NA) developed at Virginia Tech coupled with a nonlinear structure model (NS) is proposed as a design/analysis...

Estimation of Nonlinear DC-Motor Models Using a Sensitivity Approach

DEFF Research Database (Denmark)

Knudsen, Morten; Jensen, J.G.

1995-01-01

A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed.......A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed....

Equivalent circuit simulation of HPEM-induced transient responses at nonlinear loads

Directory of Open Access Journals (Sweden)

M. Kotzev

2017-09-01

Full Text Available In this paper the equivalent circuit modeling of a nonlinearly loaded loop antenna and its transient responses to HPEM field excitations are investigated. For the circuit modeling the general strategy to characterize the nonlinearly loaded antenna by a linear and a nonlinear circuit part is pursued. The linear circuit part can be determined by standard methods of antenna theory and numerical field computation. The modeling of the nonlinear circuit part requires realistic circuit models of the nonlinear loads that are given by Schottky diodes. Combining both parts, appropriate circuit models are obtained and analyzed by means of a standard SPICE circuit simulator. It is the main result that in this way full-wave simulation results can be reproduced. Furthermore it is clearly seen that the equivalent circuit modeling offers considerable advantages with respect to computation speed and also leads to improved physical insights regarding the coupling between HPEM field excitation and nonlinearly loaded loop antenna.

Modeling of fatigue crack induced nonlinear ultrasonics using a highly parallelized explicit local interaction simulation approach

Science.gov (United States)

Shen, Yanfeng; Cesnik, Carlos E. S.

2016-04-01

This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.

Computer Simulation of Hydraulic Systems with Typical Nonlinear Characteristics

Directory of Open Access Journals (Sweden)

D. N. Popov

2017-01-01

Full Text Available The task was to synthesise an adjustable hydraulic system structure, the mathematical model of which takes into account its inherent nonlinearity. Its solution suggests using a successive computer simulations starting with a structure of the linearized stable hydraulic system, which is then complicated by including the essentially non-linear elements. The hydraulic system thus obtained may be unable to meet the Lyapunov stability criterion and be unstable. This can be eliminated through correcting elements. Control of correction results is provided according to the form of transition processes due to stepwise variation of the control signal.Computer simulation of a throttle-controlled electrohydraulic servo drive with the rotary output element illustrates the proposed method application. A constant pressure power source provides fluid feed for the drive under pressure.For drive simulation the following models were involved: the linear model, the model taking into consideration a non-linearity of the flow-dynamic characteristics of a spool-type valve, and the non-linear models that take into account the dry friction in the spool-type valve, the backlash in the steering angle sensor of the motor shaft.The paper shows possibility of damping oscillation caused by variable hydrodynamic forces through introducing a correction device.The list of references attached contains 16 sources, which were used to justify and explain certain factors of the automatic control theory and the fluid mechanics of unsteady flows.The article presents 6 block-diagrams of the electrohydraulic servo drive and their appropriate transition processes, which have been studied.

Simulation of nonlinear wave run-up with a high-order Boussinesq model

DEFF Research Database (Denmark)

Fuhrman, David R.; Madsen, Per A.

2008-01-01

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions....... As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions...... cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability...

Computational study of nonlinear plasma waves. I. Simulation model and monochromatic wave propagation

International Nuclear Information System (INIS)

Matsuda, Y.; Crawford, F.W.

1975-01-01

An economical low-noise plasma simulation model originated by Denavit is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation. These tests serve to establish the low-noise features of the model, and to verify the theoretical linear dispersion relation at wave energy levels as low as 10 -6 of the plasma thermal energy: Better quantitative results are obtained, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories

Time-domain simulation and nonlinear analysis on ride performance of four-wheel vehicles

Energy Technology Data Exchange (ETDEWEB)

Wang, Y S; He, H; Geng, A L [School of Automobile and Traffic Engineering, Liaoning University of Technology, Jinzhou 121001 (China)], E-mail: jzwbt@163.com

2008-02-15

A nonlinear dynamic model with eight DOFs of a four-wheel vehicle is established in this paper. After detaching the nonlinear characteristics of the leaf springs and shock absorbers, the multi-step linearizing method is used to simulate the vehicle vibration in time domain, under a correlated four-wheel road roughness model. Experimental verifications suggest that the newly built vehicle model and simulation procedure are reasonable and feasible to be used in vehicle vibration analysis. Furthermore, some nonlinear factors of the leaf springs and shock absorbers, which affect the vehicle ride performance (or comfort), are investigated under different vehicle running speeds. Some substaintial rules of the nonlinear vehicle vibrations are revealed in this paper.

Time-domain simulation and nonlinear analysis on ride performance of four-wheel vehicles

International Nuclear Information System (INIS)

Wang, Y S; He, H; Geng, A L

2008-01-01

A nonlinear dynamic model with eight DOFs of a four-wheel vehicle is established in this paper. After detaching the nonlinear characteristics of the leaf springs and shock absorbers, the multi-step linearizing method is used to simulate the vehicle vibration in time domain, under a correlated four-wheel road roughness model. Experimental verifications suggest that the newly built vehicle model and simulation procedure are reasonable and feasible to be used in vehicle vibration analysis. Furthermore, some nonlinear factors of the leaf springs and shock absorbers, which affect the vehicle ride performance (or comfort), are investigated under different vehicle running speeds. Some substaintial rules of the nonlinear vehicle vibrations are revealed in this paper

Nonlinear dynamics modeling and simulation of two-wheeled self-balancing vehicle

Directory of Open Access Journals (Sweden)

Yunping Liu

2016-11-01

Full Text Available Two-wheeled self-balancing vehicle system is a kind of naturally unstable underactuated system with high-rank unstable multivariable strongly coupling complicated dynamic nonlinear property. Nonlinear dynamics modeling and simulation, as a basis of two-wheeled self-balancing vehicle dynamics research, has the guiding effect for system design of the project demonstration and design phase. Dynamics model of the two-wheeled self-balancing vehicle is established by importing a TSi ProPac package to the Mathematica software (version 8.0, which analyzes the stability and calculates the Lyapunov exponents of the system. The relationship between external force and stability of the system is analyzed by the phase trajectory. Proportional–integral–derivative control is added to the system in order to improve the stability of the two-wheeled self-balancing vehicle. From the research, Lyapunov exponent can be used to research the stability of hyperchaos system. The stability of the two-wheeled self-balancing vehicle is better by inputting the proportional–integral–derivative control. The Lyapunov exponent and phase trajectory can help us analyze the stability of a system better and lay the foundation for the analysis and control of the two-wheeled self-balancing vehicle system.

A Collection of Nonlinear Aircraft Simulations in MATLAB

Science.gov (United States)

Garza, Frederico R.; Morelli, Eugene A.

2003-01-01

Nonlinear six degree-of-freedom simulations for a variety of aircraft were created using MATLAB. Data for aircraft geometry, aerodynamic characteristics, mass / inertia properties, and engine characteristics were obtained from open literature publications documenting wind tunnel experiments and flight tests. Each nonlinear simulation was implemented within a common framework in MATLAB, and includes an interface with another commercially-available program to read pilot inputs and produce a three-dimensional (3-D) display of the simulated airplane motion. Aircraft simulations include the General Dynamics F-16 Fighting Falcon, Convair F-106B Delta Dart, Grumman F-14 Tomcat, McDonnell Douglas F-4 Phantom, NASA Langley Free-Flying Aircraft for Sub-scale Experimental Research (FASER), NASA HL-20 Lifting Body, NASA / DARPA X-31 Enhanced Fighter Maneuverability Demonstrator, and the Vought A-7 Corsair II. All nonlinear simulations and 3-D displays run in real time in response to pilot inputs, using contemporary desktop personal computer hardware. The simulations can also be run in batch mode. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. Since all the nonlinear simulations are implemented entirely in MATLAB, user-defined control laws can be added in a straightforward fashion, and the simulations are portable across various computing platforms. Routines for trim, linearization, and numerical integration are included. The general nonlinear simulation framework and the specifics for each particular aircraft are documented.

A Compact Synchronous Cellular Model of Nonlinear Calcium Dynamics: Simulation and FPGA Synthesis Results.

Science.gov (United States)

Soleimani, Hamid; Drakakis, Emmanuel M

2017-06-01

Recent studies have demonstrated that calcium is a widespread intracellular ion that controls a wide range of temporal dynamics in the mammalian body. The simulation and validation of such studies using experimental data would benefit from a fast large scale simulation and modelling tool. This paper presents a compact and fully reconfigurable cellular calcium model capable of mimicking Hopf bifurcation phenomenon and various nonlinear responses of the biological calcium dynamics. The proposed cellular model is synthesized on a digital platform for a single unit and a network model. Hardware synthesis, physical implementation on FPGA, and theoretical analysis confirm that the proposed cellular model can mimic the biological calcium behaviors with considerably low hardware overhead. The approach has the potential to speed up large-scale simulations of slow intracellular dynamics by sharing more cellular units in real-time. To this end, various networks constructed by pipelining 10 k to 40 k cellular calcium units are compared with an equivalent simulation run on a standard PC workstation. Results show that the cellular hardware model is, on average, 83 times faster than the CPU version.

Forecasting with nonlinear time series models

DEFF Research Database (Denmark)

Kock, Anders Bredahl; Teräsvirta, Timo

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...... and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...

Numerical simulation of electro-osmotic consolidation coupling non-linear variation of soil parameters

Science.gov (United States)

Wu, Hui; Hu, Liming; Wen, Qingbo

2017-06-01

Electro-osmotic consolidation is an effective method for soft ground improvement. A main limitation of previous numerical models on this technique is the ignorance of the non-linear variation of soil parameters. In the present study, a multi-field numerical model is developed with the consideration of the non-linear variation of soil parameters during electro-osmotic consolidation process. The numerical simulations on an axisymmetric model indicated that the non-linear variation of soil parameters showed remarkable impact on the development of the excess pore water pressure and degree of consolidation. A field experiment with complex geometry, boundary conditions, electrode configuration and voltage application was further simulated with the developed numerical model. The comparison between field and numerical data indicated that the numerical model coupling of the non-linear variation of soil parameters gave more reasonable results. The developed numerical model is capable to analyze engineering cases with complex operating conditions.

Modeling Nonlinear Site Response Uncertainty in Broadband Ground Motion Simulations for the Los Angeles Basin

Science.gov (United States)

Assimaki, D.; Li, W.; Steidl, J. M.; Schmedes, J.

2007-12-01

The assessment of strong motion site response is of great significance, both for mitigating seismic hazard and for performing detailed analyses of earthquake source characteristics. There currently exists, however, large degree of uncertainty concerning the mathematical model to be employed for the computationally efficient evaluation of local site effects, and the site investigation program necessary to evaluate the nonlinear input model parameters and ensure cost-effective predictions; and while site response observations may provide critical constraints on interpretation methods, the lack of a statistically significant number of in-situ strong motion records prohibits statistical analyses to be conducted and uncertainties to be quantified based entirely on field data. In this paper, we combine downhole observations and broadband ground motion synthetics for characteristic site conditions the Los Angeles Basin, and investigate the variability in ground motion estimation introduced by the site response assessment methodology. In particular, site-specific regional velocity and attenuation structures are initially compiled using near-surface geotechnical data collected at downhole geotechnical arrays, inverse low-strain velocity and attenuation profiles at these sites obtained by inversion of weak motion records and the crustal velocity structure at the corresponding locations obtained from the Southern California Earthquake Centre Community Velocity Model. Successively, broadband ground motions are simulated by means of a hybrid low/high-frequency finite source model with correlated random parameters for rupture scenaria of weak, medium and large magnitude events (M =3.5-7.5). Observed estimates of site response at the stations of interest are first compared to the ensemble of approximate and incremental nonlinear site response models. Parametric studies are next conducted for each fixed magnitude (fault geometry) scenario by varying the source-to-site distance and

Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes

DEFF Research Database (Denmark)

Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan

2013-01-01

The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...

Dynamic Flight Simulation Utilizing High Fidelity CFD-Based Nonlinear Reduced Order Model, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — The Nonlinear Dynamic Flight Simulation (NL-DFS) system will be developed in the Phase II project by combining the classical nonlinear rigid-body flight dynamics...

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

Science.gov (United States)

Nguyen, Nhan; Ting, Eric

2018-01-01

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

Comparison of a nonlinear dynamic model of a piping system to test data

International Nuclear Information System (INIS)

Blakely, K.D.; Howard, G.E.; Walton, W.B.; Johnson, B.A.; Chitty, D.E.

1983-01-01

Response of a nonlinear finite element model of the Heissdampfreaktor recirculation piping loop (URL) was compared to measured data, representing the physical benchmarking of a nonlinear model. Analysis-test comparisons of piping response are presented for snapback tests that induced extreme nonlinear behavior of the URL system. Nonlinearities in the system are due to twelve swaybraces (pipe supports) that possessed nonlinear force-deflection characteristics. These nonlinearities distorted system damping estimates made by using the half-power bandwidth method on Fourier transforms of measured accelerations, with the severity of distortion increasing with increasing degree of nonlinearity. Time domain methods, which are not so severely affected by the presence of nonlinearities, were used to compute system damping ratios. Nonlinear dynamic analyses were accurately and efficiently performed using the pseudo-force technique and the finite element program MSC/NASTRAN. Measured damping was incorporated into the model for snapback simulations. Acceleration time histories, acceleration Fourier transforms, and swaybrace force time histories of the nonlinear model, plus several linear models, were compared to test measurements. The nonlinear model predicted three-fourths of the measured peak accelerations to within 50%, half of the accelerations to within 25%, and one-fifth of the accelerations to within 10%. This nonlinear model predicted accelerations (in the time and frequency domains) and swaybrace forces much better than did any of the linear models, demonstrating the increased accuracy resulting from properly simulating nonlinear support behavior. In addition, earthquake response comparisons were made between the experimentally validated nonlinear model and a linear model. Significantly lower element stresses were predicted for the nonlinear model, indicating the potential usefulness of nonlinear simulations in piping design assessments. (orig.)

Nonlinear Model Predictive Control with Constraint Satisfactions for a Quadcopter

Science.gov (United States)

Wang, Ye; Ramirez-Jaime, Andres; Xu, Feng; Puig, Vicenç

2017-01-01

This paper presents a nonlinear model predictive control (NMPC) strategy combined with constraint satisfactions for a quadcopter. The full dynamics of the quadcopter describing the attitude and position are nonlinear, which are quite sensitive to changes of inputs and disturbances. By means of constraint satisfactions, partial nonlinearities and modeling errors of the control-oriented model of full dynamics can be transformed into the inequality constraints. Subsequently, the quadcopter can be controlled by an NMPC controller with the updated constraints generated by constraint satisfactions. Finally, the simulation results applied to a quadcopter simulator are provided to show the effectiveness of the proposed strategy.

Nonlinear vs. linear biasing in Trp-cage folding simulations

Energy Technology Data Exchange (ETDEWEB)

Spiwok, Vojtěch, E-mail: spiwokv@vscht.cz; Oborský, Pavel; Králová, Blanka [Department of Biochemistry and Microbiology, University of Chemistry and Technology, Prague, Technická 3, Prague 6 166 28 (Czech Republic); Pazúriková, Jana [Institute of Computer Science, Masaryk University, Botanická 554/68a, 602 00 Brno (Czech Republic); Křenek, Aleš [Institute of Computer Science, Masaryk University, Botanická 554/68a, 602 00 Brno (Czech Republic); Center CERIT-SC, Masaryk Univerzity, Šumavská 416/15, 602 00 Brno (Czech Republic)

2015-03-21

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energy minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.

Nonlinear flow model for well production in an underground formation

Directory of Open Access Journals (Sweden)

J. C. Guo

2013-05-01

Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

Simulation of nonlinear transient elastography: finite element model for the propagation of shear waves in homogeneous soft tissues.

Science.gov (United States)

Ye, W; Bel-Brunon, A; Catheline, S; Combescure, A; Rochette, M

2018-01-01

In this study, visco-hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non-linear elastic parameter of Landau's model, which provides a practical guideline to identify the non-linearity of homogeneous tissues using elastography experiment. Copyright © 2017 John Wiley & Sons, Ltd.

Nonlinear Prediction Model for Hydrologic Time Series Based on Wavelet Decomposition

Science.gov (United States)

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.

Nonlinear simulation of edge-localized mode in spherical tokamak

International Nuclear Information System (INIS)

Mizuguchi, N.; Hayashi, T.; Nakajima, N.; Khan, R.

2006-10-01

A numerical modeling for the dynamics of an edge-localized mode (ELM) crash in the spherical tokamak is proposed with a consecutive scenario which is initiated by the spontaneous growth of the ballooning mode instability by means of a three-dimensional nonlinear magnetohydrodynamic simulation. The simulation result shows a two-step relaxation process which is induced by the intermediate-n ballooning instability followed by the m/n=1/1 internal kink mode, where m and n represent the poloidal and toroidal mode numbers, respectively. By comparing with the experimental observations, we have found that the simulation result can reproduce several characteristic features of the so-called type-I ELM in an appropriate time scale: (1) relation to the ballooning instability, (2) intermediate-n precursors, (3) low-n structure on the crash, (4) formation and separation of the filament, and (5) considerable amount of loss of plasma. Furthermore, the model is verified by examining the effect of diamagnetic stabilization and comparing the nonlinear behavior with that of the peeling modes. The ion diamagnetic drift terms are found to stabilize some specific components linearly; nevertheless they are not so effective in the nonlinear dynamics such as the filament formation and the amount of loss. For the peeling mode case, no prominent filament structure is formed in contrast to the ballooning case. (author)

From spiking neuron models to linear-nonlinear models.

Science.gov (United States)

Ostojic, Srdjan; Brunel, Nicolas

2011-01-20

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

NUMERICAL MODELING AND DYNAMIC SIMULATIONS OF NONLINEAR AEROTHERMOELASTIC OF A DOUBLE-WEDGE LIFTING SURFACE

Directory of Open Access Journals (Sweden)

ARIF A. EBRAHEEM AL-QASSAR

2008-12-01

Full Text Available The design of the re-entry space vehicles and high-speed aircrafts requires special attention to the nonlinear thermoelastic and aerodynamic instabilities of their structural components. The thermal effects are important since temperature environment influences significantly the static and dynamic behaviors of flight structures in supersonic/hypersonic regimes. To contribute to the understanding of dynamic behavior of these “hot” structures, a double-wedge lifting surface with combined freeplay and cubic stiffening structural nonlinearities in both plunging and pitching degrees-of-freedom operating in supersonic/hypersonic flight speed regimes has been analyzed. A third order Piston Theory Aerodynamics is used to evaluate the applied nonlinear unsteady aerodynamic loads. The loss of torsional stiffness that may be incurred by lifting surfaces subjected to axial stresses induced by aerodynamic heating is also considered. The aerodynamic heating effect is estimated based on the adiabatic wall temperature due to high speed airstreams. Modelling issues as well as simulation results have been presented and pertinent conclusions outlined. It is highlighted that a serious loss of torsional stiffness may induce the dynamic instability of the lifting surfaces. The influence of various parameters such as flight condition, thickness ratio, freeplays and pitching stiffness nonlinearity are also discussed.

Real-time simulation of the nonlinear visco-elastic deformations of soft tissues.

Science.gov (United States)

Basafa, Ehsan; Farahmand, Farzam

2011-05-01

Mass-spring-damper (MSD) models are often used for real-time surgery simulation due to their fast response and fairly realistic deformation replication. An improved real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was developed and tested. The mechanical realization of conventional MSD models was improved using nonlinear springs and nodal dampers, while their high computational efficiency was maintained using an adapted implicit integration algorithm. New practical algorithms for model parameter tuning, collision detection, and simulation were incorporated. The model was able to replicate complex biological soft tissue mechanical properties under large deformations, i.e., the nonlinear and viscoelastic behaviors. The simulated response of the model after tuning of its parameters to the experimental data of a deer liver sample, closely tracked the reference data with high correlation and maximum relative differences of less than 5 and 10%, for the tuning and testing data sets respectively. Finally, implementation of the proposed model and algorithms in a graphical environment resulted in a real-time simulation with update rates of 150 Hz for interactive deformation and haptic manipulation, and 30 Hz for visual rendering. The proposed real time simulation model of soft tissue deformation due to a laparoscopic surgical indenter was efficient, realistic, and accurate in ex vivo testing. This model is a suitable candidate for testing in vivo during laparoscopic surgery.

Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.

Science.gov (United States)

Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang

2016-10-31

Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.

Quality of computerized blast load simulation for non-linear dynamic ...

African Journals Online (AJOL)

Quality of computerized blast load simulation for non-linear dynamic response ... commercial software system and a special-purpose, blast-specific software product to ... depend both on the analysis model of choice and the stand-off distances.

Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

Science.gov (United States)

Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

2018-04-01

We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

Nonlinear dynamic simulation of optimal depletion of crude oil in the lower 48 United States

International Nuclear Information System (INIS)

Ruth, M.; Cleveland, C.J.

1993-01-01

This study combines the economic theory of optimal resource use with econometric estimates of demand and supply parameters to develop a nonlinear dynamic model of crude oil exploration, development, and production in the lower 48 United States. The model is simulated with the graphical programming language STELLA, for the years 1985 to 2020. The procedure encourages use of economic theory and econometrics in combination with nonlinear dynamic simulation to enhance our understanding of complex interactions present in models of optimal resource use. (author)

A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations

International Nuclear Information System (INIS)

Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q

2013-01-01

Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field

Fuzzy robust nonlinear control approach for electro-hydraulic flight motion simulator

Directory of Open Access Journals (Sweden)

Han Songshan

2015-02-01

Full Text Available A fuzzy robust nonlinear controller for hydraulic rotary actuators in flight motion simulators is proposed. Compared with other three-order models of hydraulic rotary actuators, the proposed controller based on first-order nonlinear model is more easily applied in practice, whose control law is relatively simple. It not only does not need high-order derivative of desired command, but also does not require the feedback signals of velocity, acceleration and jerk of hydraulic rotary actuators. Another advantage is that it does not rely on any information of friction, inertia force and external disturbing force/torque, which are always difficult to resolve in flight motion simulators. Due to the special composite vane seals of rectangular cross-section and goalpost shape used in hydraulic rotary actuators, the leakage model is more complicated than that of traditional linear hydraulic cylinders. Adaptive multi-input single-output (MISO fuzzy compensators are introduced to estimate nonlinear uncertain functions about leakage and bulk modulus. Meanwhile, the decomposition of the uncertainties is used to reduce the total number of fuzzy rules. Different from other adaptive fuzzy compensators, a discontinuous projection mapping is employed to guarantee the estimation process to be bounded. Furthermore, with a sufficient number of fuzzy rules, the controller theoretically can guarantee asymptotic tracking performance in the presence of the above uncertainties, which is very important for high-accuracy tracking control of flight motion simulators. Comparative experimental results demonstrate the effectiveness of the proposed algorithm, which can guarantee transient performance and better final accurate tracking in the presence of uncertain nonlinearities and parametric uncertainties.

Non-linear modeling of 1H NMR metabonomic data using kernel-based orthogonal projections to latent structures optimized by simulated annealing

International Nuclear Information System (INIS)

Fonville, Judith M.; Bylesjoe, Max; Coen, Muireann; Nicholson, Jeremy K.; Holmes, Elaine; Lindon, John C.; Rantalainen, Mattias

2011-01-01

Highlights: → Non-linear modeling of metabonomic data using K-OPLS. → automated optimization of the kernel parameter by simulated annealing. → K-OPLS provides improved prediction performance for exemplar spectral data sets. → software implementation available for R and Matlab under GPL v2 license. - Abstract: Linear multivariate projection methods are frequently applied for predictive modeling of spectroscopic data in metabonomic studies. The OPLS method is a commonly used computational procedure for characterizing spectral metabonomic data, largely due to its favorable model interpretation properties providing separate descriptions of predictive variation and response-orthogonal structured noise. However, when the relationship between descriptor variables and the response is non-linear, conventional linear models will perform sub-optimally. In this study we have evaluated to what extent a non-linear model, kernel-based orthogonal projections to latent structures (K-OPLS), can provide enhanced predictive performance compared to the linear OPLS model. Just like its linear counterpart, K-OPLS provides separate model components for predictive variation and response-orthogonal structured noise. The improved model interpretation by this separate modeling is a property unique to K-OPLS in comparison to other kernel-based models. Simulated annealing (SA) was used for effective and automated optimization of the kernel-function parameter in K-OPLS (SA-K-OPLS). Our results reveal that the non-linear K-OPLS model provides improved prediction performance in three separate metabonomic data sets compared to the linear OPLS model. We also demonstrate how response-orthogonal K-OPLS components provide valuable biological interpretation of model and data. The metabonomic data sets were acquired using proton Nuclear Magnetic Resonance (NMR) spectroscopy, and include a study of the liver toxin galactosamine, a study of the nephrotoxin mercuric chloride and a study of

Comparison of simulated and measured response of load rejection on A hydro power plant model with mixed mode nonlinear controller

Energy Technology Data Exchange (ETDEWEB)

Babunski, Darko; Tuneski, Atanasko; Zaev, Emil [Faculty of Mechanical Engineering, ' Ss. Cyril and Methodius' University, Skopje (Macedonia, The Former Yugoslav Republic of)

2014-07-01

Revised Hydro Power Plant model of the IEEE working group recommended converted to state space model is used for simulation of transient response of hydro turbine, and verification was made using measurements of transients from real Hydro Power Plant (HPP). Nonlinear mixed model controller was designed and implemented into complete HPP simulation model and compared with PID with real parameters used in HPP, and with adjusted PID parameters with consideration of smallest frequency error. Verification of performance of the model was made comparing model response with measured load rejection, which is worst case of HPP operation. (Author)

Non-Linear Metamodeling Extensions to the Robust Parameter Design of Computer Simulations

Science.gov (United States)

2016-09-15

The combined-array RSM approach has been applied to a piston simulation [11] and an economic order quantity inventory model [12, 13]. A textbook ...are limited when applied to simulations. In the former case, the mean and variance models can be inadequate due to a high level of non-linearity...highly non-linear nature of typical simulations. In the multi-response RPD problem, the objective is to find the optimal control parameter levels

Computational study of nonlinear plasma waves. I. Simulation model and monochromatic wave propagtion

International Nuclear Information System (INIS)

Matda, Y.; Crawford, F.W.

1974-12-01

An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described. (auth)

On the nonlinear modeling of ring oscillators

KAUST Repository

Elwakil, Ahmed S.

2009-06-01

We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.

On the nonlinear modeling of ring oscillators

KAUST Repository

Elwakil, Ahmed S.; Salama, Khaled N.

2009-01-01

We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.

Nonlinear time-domain cochlear model for transient stimulation and human otoacoustic emission

DEFF Research Database (Denmark)

Verhulst, Sarah; Dau, Torsten; Shera, Christopher A.

2012-01-01

This paper describes the implementation and performance of a nonlinear time-domain model of the cochlea for transient stimulation and human otoacoustic emission generation. The nonlinearity simulates compressive growth of measured basilar-membrane impulse responses. The model accounts...... for reflection and distortion-source otoacoustic emissions (OAEs) and simulates spontaneous OAEs through manipulation of the middle-ear reflectance. The model was calibrated using human psychoacoustical and otoacoustic tuning parameters. It can be used to investigate time-dependent properties of cochlear...

Nonlinear adaptive robust back stepping force control of hydraulic load simulator: Theory and experiments

International Nuclear Information System (INIS)

Yao, Jianyong; Jiao, Zongxia; Yao, Bin

2014-01-01

High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.

Nonlinear adaptive robust back stepping force control of hydraulic load simulator: Theory and experiments

Energy Technology Data Exchange (ETDEWEB)

Yao, Jianyong [Nanjing University of Science and Technology, Nanjing (China); Jiao, Zongxia [Beihang University, Beijing (China); Yao, Bin [Purdue University, West Lafayette (United States)

2014-04-15

High performance robust force control of hydraulic load simulator with constant but unknown hydraulic parameters is considered. In contrast to the linear control based on hydraulic linearization equations, hydraulic inherent nonlinear properties and uncertainties make the conventional feedback proportional-integral-derivative (PID) control not yield to high performance requirements. Furthermore, the hydraulic system may be subjected to non-smooth and discontinuous nonlinearities due to the directional change of valve opening. In this paper, based on a nonlinear system model of hydraulic load simulator, a discontinuous projection-based nonlinear adaptive robust back stepping controller is developed with servo valve dynamics. The proposed controller constructs a novel stable adaptive controller and adaptation laws with additional pressure dynamic related unknown parameters, which can compensate for the system nonlinearities and uncertain parameters, meanwhile a well-designed robust controller is also synthesized to dominate the model uncertainties coming from both parametric uncertainties and uncertain nonlinearities including unmodeled and ignored system dynamics. The controller theoretically guarantee a prescribed transient performance and final tracking accuracy in presence of both parametric uncertainties and uncertain nonlinearities; while achieving asymptotic output tracking in the absence of unstructured uncertainties. The implementation issues are also discussed for controller simplification. Some comparative results are obtained to verify the high-performance nature of the proposed controller.

Numerical studies on the electromagnetic properties of the nonlinear Lorentz Computational model for the dielectric media

International Nuclear Information System (INIS)

Abe, H.; Okuda, H.

1994-06-01

We study linear and nonlinear properties of a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. It is shown that the model may be useful for studying linear and nonlinear wave propagation in the dielectric media

Design of a non-linear power take-off simulator for model testing of rotating wave energy devices

Energy Technology Data Exchange (ETDEWEB)

Lopes, M.F.P.; Henriques, J.C.C.; Lopes, Miguel C.; Gato, L.M.C. [IDMEC - Instituto de Engenharia Mecanica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Lisboa (Portugal); Dente Antonio [CIE3 - Center for Innovation in Electrical and Energy Engineering, Lisboa (Portugal)

2009-07-01

Eddy current brakes provide a versatile way of simulating the power take-off system (PTO) in the model testing of wave energy converters at small scale. These are based on the principle that a conductive material moving perpendicularly to a magnetic field generates a braking force proportional to its velocity. This was applied in the design of the PTO simulator of a bottom-hinged flap wave energy converter model, at 1/16 scale. The efforts put into the accurate dynamic simulation of the device led to the development of a controllable PTO simulator, which can be applied to other small scale rotating wave energy device models. A special power source was built to provide the required controllable current intensity to feed the magnetic field generating coils. Different non-linear damping PTO characteristic curves can be simulated by basing the current control on real-time velocity measurement. The calibration of the system was done by connecting the device to a constant rotating speed motor and measuring the resistent torque produced by the PTO with a torquemeter for different values of current intensity through the coils.

Non-linear belt transient analysis. A hybrid model for numerical belt conveyor simulation

Energy Technology Data Exchange (ETDEWEB)

Harrison, A. [Scientific Solutions, Inc., Aurora, CO (United States)

2008-07-01

Frictional and rolling losses along a running conveyor are discussed due to their important influence on wave propagation during starting and stopping. Hybrid friction models allow belt rubber losses and material flexing to be included in the initial tension calculations prior to any dynamic analysis. Once running tensions are defined, a numerical integration method using non-linear stiffness gradients is used to generate transient forces during starting and stopping. A modified Euler integration technique is used to simulate the entire starting and stopping cycle in less than 0.1 seconds. The procedure enables a faster scrutiny of unforeseen conveyor design issues such as low belt tension zones and high forces at drives. (orig.)

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

Science.gov (United States)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Landau fluid model for weakly nonlinear dispersive magnetohydrodynamics

International Nuclear Information System (INIS)

Passot, T.; Sulem, P. L.

2005-01-01

In may astrophysical plasmas such as the solar wind, the terrestrial magnetosphere, or in the interstellar medium at small enough scales, collisions are negligible. When interested in the large-scale dynamics, a hydrodynamic approach is advantageous not only because its numerical simulations is easier than of the full Vlasov-Maxwell equations, but also because it provides a deep understanding of cross-scale nonlinear couplings. It is thus of great interest to construct fluid models that extended the classical magnetohydrodynamic (MHD) equations to collisionless situations. Two ingredients need to be included in such a model to capture the main kinetic effects: finite Larmor radius (FLR) corrections and Landau damping, the only fluid-particle resonance that can affect large scales and can be modeled in a relatively simple way. The Modelization of Landau damping in a fluid formalism is hardly possible in the framework of a systematic asymptotic expansion and was addressed mainly by means of parameter fitting in a linearized setting. We introduced a similar Landau fluid model but, that has the advantage of taking dispersive effects into account. This model properly describes dispersive MHD waves in quasi-parallel propagation. Since, by construction, the system correctly reproduces their linear dynamics, appropriate tests should address the nonlinear regime. In a first case, we show analytically that the weakly nonlinear modulational dynamics of quasi-parallel propagating Alfven waves is well captured. As a second test we consider the parametric decay instability of parallel Alfven waves and show that numerical simulations of the dispersive Landau fluid model lead to results that closely match the outcome of hybrid simulations. (Author)

Likelihood-Based Inference in Nonlinear Error-Correction Models

DEFF Research Database (Denmark)

Kristensen, Dennis; Rahbæk, Anders

We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...

Nonlinear Fuzzy Model Predictive Control for a PWR Nuclear Power Plant

Directory of Open Access Journals (Sweden)

Xiangjie Liu

2014-01-01

Full Text Available Reliable power and temperature control in pressurized water reactor (PWR nuclear power plant is necessary to guarantee high efficiency and plant safety. Since the nuclear plants are quite nonlinear, the paper presents nonlinear fuzzy model predictive control (MPC, by incorporating the realistic constraints, to realize the plant optimization. T-S fuzzy modeling on nuclear power plant is utilized to approximate the nonlinear plant, based on which the nonlinear MPC controller is devised via parallel distributed compensation (PDC scheme in order to solve the nonlinear constraint optimization problem. Improved performance compared to the traditional PID controller for a TMI-type PWR is obtained in the simulation.

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

Science.gov (United States)

Sebastian, Resmi; Sitharam, T. G.

2018-01-01

Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.

Parallel processing for nonlinear dynamics simulations of structures including rotating bladed-disk assemblies

Science.gov (United States)

Hsieh, Shang-Hsien

1993-01-01

The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system.

Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

International Nuclear Information System (INIS)

Adcock, T. A. A.; Taylor, P. H.

2016-01-01

The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum

Radio Evolution of Supernova Remnants Including Nonlinear Particle Acceleration: Insights from Hydrodynamic Simulations

Science.gov (United States)

Pavlović, Marko Z.; Urošević, Dejan; Arbutina, Bojan; Orlando, Salvatore; Maxted, Nigel; Filipović, Miroslav D.

2018-01-01

We present a model for the radio evolution of supernova remnants (SNRs) obtained by using three-dimensional hydrodynamic simulations coupled with nonlinear kinetic theory of cosmic-ray (CR) acceleration in SNRs. We model the radio evolution of SNRs on a global level by performing simulations for a wide range of the relevant physical parameters, such as the ambient density, supernova (SN) explosion energy, acceleration efficiency, and magnetic field amplification (MFA) efficiency. We attribute the observed spread of radio surface brightnesses for corresponding SNR diameters to the spread of these parameters. In addition to our simulations of Type Ia SNRs, we also considered SNR radio evolution in denser, nonuniform circumstellar environments modified by the progenitor star wind. These simulations start with the mass of the ejecta substantially higher than in the case of a Type Ia SN and presumably lower shock speed. The magnetic field is understandably seen as very important for the radio evolution of SNRs. In terms of MFA, we include both resonant and nonresonant modes in our large-scale simulations by implementing models obtained from first-principles, particle-in-cell simulations and nonlinear magnetohydrodynamical simulations. We test the quality and reliability of our models on a sample consisting of Galactic and extragalactic SNRs. Our simulations give Σ ‑ D slopes between ‑4 and ‑6 for the full Sedov regime. Recent empirical slopes obtained for the Galactic samples are around ‑5, while those for the extragalactic samples are around ‑4.

Nonlinear simulation of magnetic reconnection with a drift kinetic electron model

International Nuclear Information System (INIS)

Zwingmann, W.; Ottaviani, M.

2004-01-01

The process of reconnection allows for a change of magnetic topology inside a plasma. It is an important process for eruptive phenomena in astrophysical plasma, and the sawtooth relaxation in laboratory plasma close to thermonuclear conditions. The sawtooth relaxation is associated with the collisionless electron tearing instability, caused by the electron inertia. A thorough treatment therefore requires a kinetic model for the electron dynamics. In this contribution, we report on the numerical simulation of the electron tearing instability by solving the Vlasov equation directly. The results confirm results of an early paper on the same subject, and extends them to smaller values of the collision skin depth d e = 0.25. Our results suggest a faster than exponential growth in the early nonlinear phase of the instability. We observe as well an asymmetry of the resulting fields. It seems, however, that the field structure becomes closer to the fluid case for small values of d e

Nonlinear behavior analysis of split-winding dry-type transformer using a new star model and a coupled field-circuit approach

Directory of Open Access Journals (Sweden)

Azizian Davood

2016-12-01

Full Text Available Regarding the importance of short circuit and inrush current simulations in the split-winding transformer, a novel nonlinear equivalent circuit is introduced in this paper for nonlinear simulation of this transformer. The equivalent circuit is extended using the nonlinear inductances. Employing a numerical method, leakage and magnetizing inductances in the split-winding transformer are extracted and the nonlinear model inductances are estimated using these inductances. The introduced model is validated and using this nonlinear model, inrush and short-circuit currents are calculated. It has been seen that the introduced model is valid and suitable for simulations of the split-winding transformer due to various loading conditions. Finally, the effects of nonlinearity of the model inductances are discussed in the following.

Nonlinear PIC simulation in a Penning trap

International Nuclear Information System (INIS)

Lapenta, G.; Delzanno, G.L.; Finn, J. M.

2002-01-01

We study the nonlinear dynamics of a Penning trap plasma, including the effect of the finite length and end curvature of the plasma column. A new cylindrical PIC code, called KANDINSKY, has been implemented by using a new interpolation scheme. The principal idea is to calculate the volume of each cell from a particle volume, in the same manner as it is done for the cell charge. With this new method, the density is conserved along streamlines and artificial sources of compressibility are avoided. The code has been validated with a reference Eulerian fluid code. We compare the dynamics of three different models: a model with compression effects, the standard Euler model and a geophysical fluid dynamics model. The results of our investigation prove that Penning traps can really be used to simulate geophysical fluids

Nonlinear Modeling and Simulation of Thermal Effects in Microcantilever Resonators Dynamic

International Nuclear Information System (INIS)

Tadayon, M A; Sayyaadi, H; Jazar, G Nakhaie

2006-01-01

Thermal dependency of material characteristics in micro electromechanical systems strongly affects their performance, design, and control. Hence, it is essential to understand and model that in MEMS devices to optimize their designs. A thermal phenomenon introduces two main effects: damping due to internal friction, and softening due to Young modulus temperature relation. Based on some reported theoretical and experimental results, we model the thermal phenomena and use two Lorentzian functions to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal effects, a nonlinear model of the MEMS, by considering capacitor nonlinearity, have been used. The response of the system is developed by employing multiple time scales perturbation method on nondimensionalized form of equations. Frequency response, resonant frequency and peak amplitude are examined for variation of dynamic parameters involved

Identification of stochastic interactions in nonlinear models of structural mechanics

Science.gov (United States)

Kala, Zdeněk

2017-07-01

In the paper, the polynomial approximation is presented by which the Sobol sensitivity analysis can be evaluated with all sensitivity indices. The nonlinear FEM model is approximated. The input area is mapped using simulations runs of Latin Hypercube Sampling method. The domain of the approximation polynomial is chosen so that it were possible to apply large number of simulation runs of Latin Hypercube Sampling method. The method presented also makes possible to evaluate higher-order sensitivity indices, which could not be identified in case of nonlinear FEM.

Nonlinear instabilities induced by the F coil power amplifier at FTU: Modeling and control

International Nuclear Information System (INIS)

Zaccarian, L.; Boncagni, L.; Cascone, D.; Centioli, C.; Cerino, S.; Gravanti, F.; Iannone, F.; Mecocci, F.; Pangione, L.; Podda, S.; Vitale, V.; Vitelli, R.

2009-01-01

In this paper we focus on the instabilities caused by the nonlinear behavior of the F coil current amplifier at FTU. This behavior induces closed-loop instability of the horizontal position stabilizing loop whenever the requested current is below the circulating current level. In the paper we first illustrate a modeling phase where nonlinear dynamics are derived and identified to reproduce the open-loop responses measured by the F coil current amplifier. The derived model is shown to successfully reproduce the experimental behavior by direct comparison with experimental data. Based on this dynamic model, we then reproduce the closed-loop scenario of the experiment and show that the proposed nonlinear model successfully reproduces the nonlinear instabilities experienced in the experimental sessions. Given the simulation setup, we next propose a nonlinear control solution to this instability problem. The proposed solution is shown to recover stability in closed-loop simulations. Experimental tests are scheduled for the next experimental campaign after the FTU restart.

Simulation Analysis of Helicopter Ground Resonance Nonlinear Dynamics

Science.gov (United States)

Zhu, Yan; Lu, Yu-hui; Ling, Ai-min

2017-07-01

In order to accurately predict the dynamic instability of helicopter ground resonance, a modeling and simulation method of helicopter ground resonance considering nonlinear dynamic characteristics of components (rotor lead-lag damper, landing gear wheel and absorber) is presented. The numerical integral method is used to calculate the transient responses of the body and rotor, simulating some disturbance. To obtain quantitative instabilities, Fast Fourier Transform (FFT) is conducted to estimate the modal frequencies, and the mobile rectangular window method is employed in the predictions of the modal damping in terms of the response time history. Simulation results show that ground resonance simulation test can exactly lead up the blade lead-lag regressing mode frequency, and the modal damping obtained according to attenuation curves are close to the test results. The simulation test results are in accordance with the actual accident situation, and prove the correctness of the simulation method. This analysis method used for ground resonance simulation test can give out the results according with real helicopter engineering tests.

A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors

Science.gov (United States)

Shi, H.; Yang, B.; Thomson, M.; Fang, H.

2011-01-01

This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.

A framework for simulating ultrasound imaging based on first order nonlinear pressure–velocity relations

DEFF Research Database (Denmark)

Du, Yigang; Fan, Rui; Li, Yong

2016-01-01

An ultrasound imaging framework modeled with the first order nonlinear pressure–velocity relations (NPVR) based simulation and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound...... propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework......, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA...

Stochastic Simulation of Integrated Circuits with Nonlinear Black-Box Components via Augmented Deterministic Equivalents

Directory of Open Access Journals (Sweden)

MANFREDI, P.

2014-11-01

Full Text Available This paper extends recent literature results concerning the statistical simulation of circuits affected by random electrical parameters by means of the polynomial chaos framework. With respect to previous implementations, based on the generation and simulation of augmented and deterministic circuit equivalents, the modeling is extended to generic and ?black-box? multi-terminal nonlinear subcircuits describing complex devices, like those found in integrated circuits. Moreover, based on recently-published works in this field, a more effective approach to generate the deterministic circuit equivalents is implemented, thus yielding more compact and efficient models for nonlinear components. The approach is fully compatible with commercial (e.g., SPICE-type circuit simulators and is thoroughly validated through the statistical analysis of a realistic interconnect structure with a 16-bit memory chip. The accuracy and the comparison against previous approaches are also carefully established.

Nonlinear turbulence theory and simulation of Buneman instability

International Nuclear Information System (INIS)

Yoon, P. H.; Umeda, T.

2010-01-01

In the present paper, the weak turbulence theory for reactive instabilities, formulated in a companion paper [P. H. Yoon, Phys. Plasmas 17, 112316 (2010)], is applied to the strong electron-ion two-stream (or Buneman) instability. The self-consistent theory involves quasilinear velocity space diffusion equation for the particles and nonlinear wave kinetic equation that includes quasilinear (or induced emission) term as well as nonlinear wave-particle interaction term (or a term that represents an induced scattering off ions). We have also performed one-dimensional electrostatic Vlasov simulation in order to benchmark the theoretical analysis. Under the assumption of self-similar drifting Gaussian distribution function for the electrons it is shown that the current reduction and the accompanying electron heating as well as electric field turbulence generation can be discussed in a self-consistent manner. Upon comparison with the Vlasov simulation result it is found that quasilinear wave kinetic equation alone is insufficient to account for the final saturation amplitude. Upon including the nonlinear scattering term in the wave kinetic equation, however, we find that a qualitative agreement with the simulation is recovered. From this, we conclude that the combined quasilinear particle diffusion plus induced emission and scattering (off ions) processes adequately account for the nonlinear development of the Buneman instability.

Numerical simulation of ultrasound-thermotherapy combining nonlinear wave propagation with broadband soft-tissue absorption.

Science.gov (United States)

Ginter, S

2000-07-01

Ultrasound (US) thermotherapy is used to treat tumours, located deep in human tissue, by heat. It features by the application of high intensity focused ultrasound (HIFU), high local temperatures of about 90 degrees C and short treating time of a few seconds. Dosage of the therapy remains a problem. To get it under control, one has to know the heat source, i.e. the amount of absorbed US power, which shows nonlinear influences. Therefore, accurate simulations are essential. In this paper, an improved simulation model is introduced which enables accurate investigations of US thermotherapy. It combines nonlinear US propagation effects, which lead to generation of higher harmonics, with a broadband frequency-power law absorption typical for soft tissue. Only the combination of both provides a reliable calculation of the generated heat. Simulations show the influence of nonlinearities and broadband damping for different source signals on the absorbed US power density distribution.

A Detailed Analytical Study of Non-Linear Semiconductor Device Modelling

Directory of Open Access Journals (Sweden)

Umesh Kumar

1995-01-01

junction diode have been developed. The results of computer simulated examples have been presented in each case. The non-linear lumped model for Gunn is a unified model as it describes the diffusion effects as the-domain traves from cathode to anode. An additional feature of this model is that it describes the domain extinction and nucleation phenomena in Gunn dioder with the help of a simple timing circuit. The non-linear lumped model for SCR is general and is valid under any mode of operation in any circuit environment. The memristive circuit model for p-n junction diodes is capable of simulating realistically the diode’s dynamic behavior under reverse, forward and sinusiodal operating modes. The model uses memristor, the charge-controlled resistor to mimic various second-order effects due to conductivity modulation. It is found that both storage time and fall time of the diode can be accurately predicted.

Monte Carlo simulation of nonlinear reactive contaminant transport in unsaturated porous media

International Nuclear Information System (INIS)

Giacobbo, F.; Patelli, E.

2007-01-01

In the current proposed solutions of radioactive waste repositories, the protective function against the radionuclide water-driven transport back to the biosphere is to be provided by an integrated system of engineered and natural geologic barriers. The occurrence of several nonlinear interactions during the radionuclide migration process may render burdensome the classical analytical-numerical approaches. Moreover, the heterogeneity of the barriers' media forces approximations to the classical analytical-numerical models, thus reducing their fidelity to reality. In an attempt to overcome these difficulties, in the present paper we adopt a Monte Carlo simulation approach, previously developed on the basis of the Kolmogorov-Dmitriev theory of branching stochastic processes. The approach is here extended for describing transport through unsaturated porous media under transient flow conditions and in presence of nonlinear interchange phenomena between the liquid and solid phases. This generalization entails the determination of the functional dependence of the parameters of the proposed transport model from the water content and from the contaminant concentration, which change in space and time during the water infiltration process. The corresponding Monte Carlo simulation approach is verified with respect to a case of nonreactive transport under transient unsaturated flow and to a case of nonlinear reactive transport under stationary saturated flow. Numerical applications regarding linear and nonlinear reactive transport under transient unsaturated flow are reported

Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control

KAUST Repository

Domínguez, Luis F.

2011-01-19

In this paper we present recent advances in multiparametric nonlinear programming (mp-NLP) algorithms for explicit nonlinear model predictive control (mp-NMPC). Three mp-NLP algorithms for NMPC are discussed, based on which novel mp-NMPC controllers are derived. The performance of the explicit controllers are then tested and compared in a simulation example involving the operation of a continuous stirred-tank reactor (CSTR). © 2010 American Chemical Society.

Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers

Directory of Open Access Journals (Sweden)

Nicolás Peréz Alvarez

2015-11-01

Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.

forecasting with nonlinear time series model: a monte-carlo

African Journals Online (AJOL)

PUBLICATIONS1

Carlo method of forecasting using a special nonlinear time series model, called logistic smooth transition ... We illustrate this new method using some simulation ..... in MATLAB 7.5.0. ... process (DGP) using the logistic smooth transi-.

Simulation of nonlinear propagation of biomedical ultrasound using PZFlex and the KZK Texas code

Science.gov (United States)

Qiao, Shan; Jackson, Edward; Coussios, Constantin-C.; Cleveland, Robin

2015-10-01

In biomedical ultrasound nonlinear acoustics can be important in both diagnostic and therapeutic applications and robust simulations tools are needed in the design process but also for day-to-day use such as treatment planning. For most biomedical application the ultrasound sources generate focused sound beams of finite amplitude. The KZK equation is a common model as it accounts for nonlinearity, absorption and paraxial diffraction and there are a number of solvers available, primarily developed by research groups. We compare the predictions of the KZK Texas code (a finite-difference time-domain algorithm) to an FEM-based commercial software, PZFlex. PZFlex solves the continuity equation and momentum conservation equation with a correction for nonlinearity in the equation of state incorporated using an incrementally linear, 2nd order accurate, explicit algorithm in time domain. Nonlinear ultrasound beams from two transducers driven at 1 MHz and 3.3 MHz respectively were simulated by both the KZK Texas code and PZFlex, and the pressure field was also measured by a fibre-optic hydrophone to validate the models. Further simulations were carried out a wide range of frequencies. The comparisons showed good agreement for the fundamental frequency for PZFlex, the KZK Texas code and the experiments. For the harmonic components, the KZK Texas code was in good agreement with measurements but PZFlex underestimated the amplitude: 32% for the 2nd harmonic and 66% for the 3rd harmonic. The underestimation of harmonics by PZFlex was more significant when the fundamental frequency increased. Furthermore non-physical oscillations in the axial profile of harmonics occurred in the PZFlex results when the amplitudes were relatively low. These results suggest that careful benchmarking of nonlinear simulations is important.

Simulation of nonlinear propagation of biomedical ultrasound using PZFlex and the KZK Texas code

Energy Technology Data Exchange (ETDEWEB)

Qiao, Shan, E-mail: shan.qiao@eng.ox.ac.uk; Jackson, Edward; Coussios, Constantin-C; Cleveland, Robin [Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford, Oxford (United Kingdom)

2015-10-28

In biomedical ultrasound nonlinear acoustics can be important in both diagnostic and therapeutic applications and robust simulations tools are needed in the design process but also for day-to-day use such as treatment planning. For most biomedical application the ultrasound sources generate focused sound beams of finite amplitude. The KZK equation is a common model as it accounts for nonlinearity, absorption and paraxial diffraction and there are a number of solvers available, primarily developed by research groups. We compare the predictions of the KZK Texas code (a finite-difference time-domain algorithm) to an FEM-based commercial software, PZFlex. PZFlex solves the continuity equation and momentum conservation equation with a correction for nonlinearity in the equation of state incorporated using an incrementally linear, 2nd order accurate, explicit algorithm in time domain. Nonlinear ultrasound beams from two transducers driven at 1 MHz and 3.3 MHz respectively were simulated by both the KZK Texas code and PZFlex, and the pressure field was also measured by a fibre-optic hydrophone to validate the models. Further simulations were carried out a wide range of frequencies. The comparisons showed good agreement for the fundamental frequency for PZFlex, the KZK Texas code and the experiments. For the harmonic components, the KZK Texas code was in good agreement with measurements but PZFlex underestimated the amplitude: 32% for the 2nd harmonic and 66% for the 3rd harmonic. The underestimation of harmonics by PZFlex was more significant when the fundamental frequency increased. Furthermore non-physical oscillations in the axial profile of harmonics occurred in the PZFlex results when the amplitudes were relatively low. These results suggest that careful benchmarking of nonlinear simulations is important.

Simulation of nonlinear propagation of biomedical ultrasound using PZFlex and the KZK Texas code

International Nuclear Information System (INIS)

Qiao, Shan; Jackson, Edward; Coussios, Constantin-C; Cleveland, Robin

2015-01-01

In biomedical ultrasound nonlinear acoustics can be important in both diagnostic and therapeutic applications and robust simulations tools are needed in the design process but also for day-to-day use such as treatment planning. For most biomedical application the ultrasound sources generate focused sound beams of finite amplitude. The KZK equation is a common model as it accounts for nonlinearity, absorption and paraxial diffraction and there are a number of solvers available, primarily developed by research groups. We compare the predictions of the KZK Texas code (a finite-difference time-domain algorithm) to an FEM-based commercial software, PZFlex. PZFlex solves the continuity equation and momentum conservation equation with a correction for nonlinearity in the equation of state incorporated using an incrementally linear, 2nd order accurate, explicit algorithm in time domain. Nonlinear ultrasound beams from two transducers driven at 1 MHz and 3.3 MHz respectively were simulated by both the KZK Texas code and PZFlex, and the pressure field was also measured by a fibre-optic hydrophone to validate the models. Further simulations were carried out a wide range of frequencies. The comparisons showed good agreement for the fundamental frequency for PZFlex, the KZK Texas code and the experiments. For the harmonic components, the KZK Texas code was in good agreement with measurements but PZFlex underestimated the amplitude: 32% for the 2nd harmonic and 66% for the 3rd harmonic. The underestimation of harmonics by PZFlex was more significant when the fundamental frequency increased. Furthermore non-physical oscillations in the axial profile of harmonics occurred in the PZFlex results when the amplitudes were relatively low. These results suggest that careful benchmarking of nonlinear simulations is important

Modeling of Nonlinear Hydrodynamics of the Coastal Areas of the Black Sea by the Chain of the Proprietary and Open Source Models

Science.gov (United States)

Kantardgi, Igor; Zheleznyak, Mark; Demchenko, Raisa; Dykyi, Pavlo; Kivva, Sergei; Kolomiets, Pavlo; Sorokin, Maxim

2014-05-01

The nearshore hydrodynamic fields are produced by the nonlinear interactions of the shoaling waves of different time scales and currents. To simulate the wind wave and swells propagated to the coasts, wave generated near shore currents, nonlinear-dispersive wave transformation and wave diffraction in interaction with coastal and port structure, sediment transport and coastal erosion the chains of the models should be used. The objective of this presentation is to provide an overview of the results of the application of the model chains for the assessment of the wave impacts on new construction designed at the Black Sea coasts and the impacts of these constructions on the coastal erosion/ accretion processes to demonstrate needs for further development of the nonlinear models for the coastal engineering applications. The open source models Wave Watch III and SWAN has been used to simulate wave statistics of the dedicated areas of the Black Sea in high resolution to calculated the statistical parameters of the extreme wave approaching coastal zone construction in accordance with coastal engineering standards. As the main tool for the costal hydrodynamic simulations the modeling system COASTOX-MORPHO has been used, that includes the following models. HWAVE -code based on hyperbolic version of mild slope equations., HWAVE-S - spectral version of HWAVE., BOUSS-FNL - fully nonlinear system of Boussinesq equations for simulation wave nonlinear -dispersive wave transformation in coastal areas. COASTOX-CUR - the code provided the numerical solution of the Nonlinear Shallow Water Equations (NLSWE) by finite-volume methods on the unstructured grid describing the long wave transformation in the coastal zone with the efficient drying -wetting algorithms to simulate the inundation of the coastal areas including tsunami wave runup. Coastox -Cur equations with the radiation stress term calculated via near shore wave fields simulate the wave generated nearhore currents. COASTOX

Brownian dynamics simulations with stiff finitely extensible nonlinear elastic-Fraenkel springs as approximations to rods in bead-rod models.

Science.gov (United States)

Hsieh, Chih-Chen; Jain, Semant; Larson, Ronald G

2006-01-28

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.

An Improved Nonlinear Five-Point Model for Photovoltaic Modules

Directory of Open Access Journals (Sweden)

Sakaros Bogning Dongue

2013-01-01

Full Text Available This paper presents an improved nonlinear five-point model capable of analytically describing the electrical behaviors of a photovoltaic module for each generic operating condition of temperature and solar irradiance. The models used to replicate the electrical behaviors of operating PV modules are usually based on some simplified assumptions which provide convenient mathematical model which can be used in conventional simulation tools. Unfortunately, these assumptions cause some inaccuracies, and hence unrealistic economic returns are predicted. As an alternative, we used the advantages of a nonlinear analytical five-point model to take into account the nonideal diode effects and nonlinear effects generally ignored, which PV modules operation depends on. To verify the capability of our method to fit PV panel characteristics, the procedure was tested on three different panels. Results were compared with the data issued by manufacturers and with the results obtained using the five-parameter model proposed by other authors.

Nonlinear Dynamic Models in Advanced Life Support

Science.gov (United States)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Numerical studies on soliton propagation in the dielectric media by the nonlinear Lorentz computational model

International Nuclear Information System (INIS)

Abe, H.; Okuda, H.

1994-06-01

Soliton propagation in the dielectric media has been simulated by using the nonlinear Lorentz computational model, which was recently developed to study the propagation of electromagnetic waves in a linear and a nonlinear dielectric. The model is constructed by combining a microscopic model used in the semi-classical approximation for dielectric media and the particle model developed for the plasma simulations. The carrier wave frequency is retained in the simulation so that not only the envelope of the soliton but also its phase can be followed in time. It is shown that the model may be useful for studying pulse propagation in the dielectric media

Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models

NARCIS (Netherlands)

Koopman, S.J.; Lucas, A.; Scharth, M.

2015-01-01

We propose a general likelihood evaluation method for nonlinear non-Gaussian state-space models using the simulation-based method of efficient importance sampling. We minimize the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer

Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

Science.gov (United States)

Li, Guang

2017-01-01

This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

Feedback control systems for non-linear simulation of operational transients in LMFBRs

International Nuclear Information System (INIS)

Khatib-Rahbar, M.; Agrawal, A.K.; Srinivasan, E.S.

1979-01-01

Feedback control systems for non-linear simulation of operational transients in LMFBRs are developed. The models include (1) the reactor power control and rod drive mechanism, (2) sodium flow control and pump drive system, (3) steam generator flow control and valve actuator dynamics, and (4) the supervisory control. These models have been incorporated into the SSC code using a flexible approach, in order to accommodate some design dependent variations. The impact of system nonlinearity on the control dynamics is shown to be significant for severe perturbations. Representative result for a 10 cent and 25 cent step insertion of reactivity and a 10% ramp change in load in 40 seconds demonstrate the suitability of this model for study of operational transients without scram in LMFBRs

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li

2009-01-01

A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))

Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.

Science.gov (United States)

Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad

2016-02-01

In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.

A non-linear model of economic production processes

Science.gov (United States)

Ponzi, A.; Yasutomi, A.; Kaneko, K.

2003-06-01

We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.

Modeling of nonlinear responses for reciprocal transducers involving polarization switching

DEFF Research Database (Denmark)

Willatzen, Morten; Wang, Linxiang

2007-01-01

Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...

A new modified resource budget model for nonlinear dynamics in citrus production

International Nuclear Information System (INIS)

Ye, Xujun; Sakai, Kenshi

2016-01-01

Highlights: • A theoretical modeling and simulation study of the nonlinear dynamics in citrus is conducted. • New leaf growth is incorporated into the model as a major factor responsible for the yield oscillations. • A Ricker-type equation for the relationship between costs for flowering and fruiting is proposed. • A generic form of the resource budget model for the nonlinear dynamics in citrus is obtained. • The new model is tested with experimental data for two citrus trees. - Abstract : Alternate bearing or masting is a general yield variability phenomenon in perennial tree crops. This paper first presents a theoretical modeling and simulation study of the mechanism for this dynamics in citrus, and then provides a test of the proposed models using data from a previous 16-year experiment in a citrus orchard. Our previous studies suggest that the mutual effects between vegetative and reproductive growths caused by resource allocation and budgeting in plant body might be considered as a major factor responsible for the yield oscillations in citrus. Based on the resource budget model proposed by Isagi et al. (J Theor Biol. 1997;187:231-9), we first introduce the new leaf growth as a major energy consumption component into the model. Further, we introduce a nonlinear Ricker-type equation to replace the linear relationship between costs for flowering and fruiting used in Isagi's model. Model simulations demonstrate that the proposed new models can successfully simulate the reproductive behaviors of citrus trees with different fruiting dynamics. These results may enrich the mechanical dynamics in tree crop reproductive models and help us to better understand the dynamics of vegetative-reproductive growth interactions in a real environment.

Generalized Nonlinear Yule Models

OpenAIRE

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-01-01

With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth...

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

Science.gov (United States)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Identification of a Class of Non-linear State Space Models using RPE Techniques

DEFF Research Database (Denmark)

Zhou, Wei-Wu; Blanke, Mogens

1989-01-01

The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions...... of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator...

Nonlinear Dynamic Model of PMBLDC Motor Considering Core Losses

DEFF Research Database (Denmark)

Fasil, Muhammed; Mijatovic, Nenad; Jensen, Bogi Bech

2017-01-01

The phase variable model is used commonly when simulating a motor drive system with a three-phase permanent magnet brushless DC (PMBLDC) motor. The phase variable model neglects core losses and this affects its accuracy when modelling fractional-slot machines. The inaccuracy of phase variable mod...... on the detailed analysis of the flux path and the variation of flux in different components of the machine. A prototype of fractional slot axial flux PMBLDC in-wheel motor is used to assess the proposed nonlinear dynamic model....... of fractional-slot machines can be attributed to considerable armature flux harmonics, which causes an increased core loss. This study proposes a nonlinear phase variable model of PMBLDC motor that considers the core losses induced in the stator and the rotor. The core loss model is developed based...

Power-level regulation and simulation of nonlinear pressurized water reactor core with xenon oscillation using H-infinity loop shaping control

Directory of Open Access Journals (Sweden)

Li Gang

2016-01-01

Full Text Available This investigation is to solve the power-level control issue of a nonlinear pressurized water reactor core with xenon oscillations. A nonlinear pressurized water reactor core is modeled using the lumped parameter method, and a linear model of the core is then obtained through the small perturbation linearization way. The H∞loop shapingcontrolis utilized to design a robust controller of the linearized core model.The calculated H∞loop shaping controller is applied to the nonlinear core model. The nonlinear core model and the H∞ loop shaping controller build the nonlinear core power-level H∞loop shaping control system.Finally, the nonlinear core power-level H∞loop shaping control system is simulatedconsidering two typical load processes that are a step load maneuver and a ramp load maneuver, and simulation results show that the nonlinear control system is effective.

A numerical study of linear and nonlinear kinematic models in fish swimming with the DSD/SST method

Science.gov (United States)

Tian, Fang-Bao

2015-03-01

Flow over two fish (modeled by two flexible plates) in tandem arrangement is investigated by solving the incompressible Navier-Stokes equations numerically with the DSD/SST method to understand the differences between the geometrically linear and nonlinear models. In the simulation, the motions of the plates are reconstructed from a vertically flowing soap film tunnel experiment with linear and nonlinear kinematic models. Based on the simulations, the drag, lift, power consumption, vorticity and pressure fields are discussed in detail. It is found that the linear and nonlinear models are able to reasonably predict the forces and power consumption of a single plate in flow. Moreover, if multiple plates are considered, these two models yield totally different results, which implies that the nonlinear model should be used. The results presented in this work provide a guideline for future studies in fish swimming.

A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes

Directory of Open Access Journals (Sweden)

Qi-Zhi Zhang

2005-01-01

Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.

Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models

DEFF Research Database (Denmark)

Kristensen, Dennis; Rahbæk, Anders

In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated...... symmetric non-linear error correction considered. A simulation study shows that the fi…nite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes....

Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models

DEFF Research Database (Denmark)

Kristensen, Dennis; Rahbek, Anders

In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated...... symmetric non-linear error correction are considered. A simulation study shows that the finite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes....

Study of dispersive and nonlinear effects of coastal wave dynamics with a fully nonlinear potential flow model

Science.gov (United States)

Benoit, Michel; Yates, Marissa L.; Raoult, Cécile

2017-04-01

Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the

Strategies for Enhancing Nonlinear Internal Model Control of pH Processes

Energy Technology Data Exchange (ETDEWEB)

Hu, Qiuping.; Rangaiah, G.P. [The National University of Singapore, Singapore (Singapore). Dept. of Chemical and Environmental Engineering

1999-02-01

Control of neutralization processes is very difficult due to nonlinear dynamics, different types of disturbances and modeling errors. The objective of the paper is to evaluate two strategies (augmented internal model control, AuIMC and adaptive internal model control, AdIMC) for enhancing pH control by nonlinear internal model control (NIMC). A NIMC controller is derived directly form input output linearization. The AuIMC is composed of NIMC and an additional loop through which the difference between the process and model outputs is fed back and added to the input of the controller. For the AdIMC, and adaptive law with two tuning parameters is proposed for estimating the unknown parameter. Both AuIMC and AdIMC are extensively tested via simulation for pH neutralization. The theoretical and simulation results show that both the proposed strategies can reduce the effect of modeling errors and disturbances, and thereby enhance the performance of NIMC for pH processes. (author)

New human-centered linear and nonlinear motion cueing algorithms for control of simulator motion systems

Science.gov (United States)

Telban, Robert J.

While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. To address this, new human-centered motion cueing algorithms were developed. A revised "optimal algorithm" uses time-invariant filters developed by optimal control, incorporating human vestibular system models. The "nonlinear algorithm" is a novel approach that is also formulated by optimal control, but can also be updated in real time. It incorporates a new integrated visual-vestibular perception model that includes both visual and vestibular sensation and the interaction between the stimuli. A time-varying control law requires the matrix Riccati equation to be solved in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. As a result of unsatisfactory sensation, an augmented turbulence cue was added to the vertical mode for both the optimal and nonlinear algorithms. The relative effectiveness of the algorithms, in simulating aircraft maneuvers, was assessed with an eleven-subject piloted performance test conducted on the NASA Langley Visual Motion Simulator (VMS). Two methods, the quasi-objective NASA Task Load Index (TLX), and power spectral density analysis of pilot control, were used to assess pilot workload. TLX analysis reveals, in most cases, less workload and variation among pilots with the nonlinear algorithm. Control input

Predominant nonlinear atmospheric response to meridional shift of the Gulf Stream path from the WRF atmospheric model simulations

Science.gov (United States)

Seo, H.; Kwon, Y. O.; Joyce, T. M.

2016-02-01

A remarkably strong nonlinear behavior of the atmospheric circulation response to North Atlantic SST anomalies (SSTA) is revealed from a set of large-ensemble, high-resolution, and hemispheric-scale Weather Research and Forecasting (WRF) model simulations. The model is forced with the SSTA associated with meridional shift of the Gulf Stream (GS) path, constructed from a lag regression of the winter SST on a GS Index from observation. Analysis of the systematic set of experiments with SSTAs of varied amplitudes and switched signs representing various GS-shift scenarios provides unique insights into mechanism for emergence and evolution of transient and equilibrium response of atmospheric circulation to extratropical SSTA. Results show that, independent of sign of the SSTA, the equilibrium response is characterized by an anomalous trough over the North Atlantic Ocean and the Western Europe concurrent with enhanced storm track, increased rainfall, and reduced blocking days. To the north of the anomalous low, an anomalous ridge emerges over the Greenland, Iceland, and Norwegian Seas accompanied by weakened storm track, reduced rainfall and increased blocking days. This nonlinear component of the total response dominates the weak and oppositely signed linear response that is directly forced by the SSTA, yielding an anomalous ridge (trough) downstream of the warm (cold) SSTA. The amplitude of the linear response is proportional to that of the SSTA, but this is masked by the overwhelmingly strong nonlinear behavior showing no clear correspondence to the SSTA amplitude. The nonlinear pattern emerges 3-4 weeks after the model initialization in November and reaches its first peak amplitude in December/January. It appears that altered baroclinic wave activity due to the GS SSTA in November lead to low-frequency height responses in December/January through transient eddy vorticity flux convergence.

NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES

Directory of Open Access Journals (Sweden)

SILVA R. G.

1999-01-01

Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.

Nonlinear Epigenetic Variance: Review and Simulations

Science.gov (United States)

Kan, Kees-Jan; Ploeger, Annemie; Raijmakers, Maartje E. J.; Dolan, Conor V.; van Der Maas, Han L. J.

2010-01-01

We present a review of empirical evidence that suggests that a substantial portion of phenotypic variance is due to nonlinear (epigenetic) processes during ontogenesis. The role of such processes as a source of phenotypic variance in human behaviour genetic studies is not fully appreciated. In addition to our review, we present simulation studies…

A Nonlinear Dynamic Inversion Predictor-Based Model Reference Adaptive Controller for a Generic Transport Model

Science.gov (United States)

Campbell, Stefan F.; Kaneshige, John T.

2010-01-01

Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

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YanBin Liu

2017-01-01

Full Text Available The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller.

Simulation-based optimal Bayesian experimental design for nonlinear systems

KAUST Repository

Huan, Xun

2013-01-01

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters.Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics. © 2012 Elsevier Inc.

Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction

International Nuclear Information System (INIS)

Upadrashta, Deepesh; Yang, Yaowen

2015-01-01

Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical–mechanical–magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction. (paper)

Nonlinear soil-structure interaction calculations simulating the SIMQUAKE experiment using STEALTH 2D

Science.gov (United States)

Tang, H. T.; Hofmann, R.; Yee, G.; Vaughan, D. K.

1980-01-01

Transient, nonlinear soil-structure interaction simulations of an Electric Power Research Institute, SIMQUAKE experiment were performed using the large strain, time domain STEALTH 2D code and a cyclic, kinematically hardening cap soil model. Results from the STEALTH simulations were compared to identical simulations performed with the TRANAL code and indicate relatively good agreement between all the STEALTH and TRANAL calculations. The differences that are seen can probably be attributed to: (1) large (STEALTH) vs. small (TRANAL) strain formulation and/or (2) grid discretization differences.

Nonlinear excitation of electron cyclotron waves by a monochromatic strong microwave: computer simulation analysis of the MINIX results

Energy Technology Data Exchange (ETDEWEB)

Matsumoto, H.; Kimura, T.

1986-01-01

Triggered by the experimental results of the MINIX, a computer simulation study was initiated on the nonlinear excitation of electrostatic electron cyclotron waves by a monochromatic electromagnetic wave such as the transmitted microwave in the MINIX. The model used assumes that both of the excited waves and exciting (pumping) electromagnetic wave as well as the idler electromagnetic wave propagate in the direction perpendicular to the external magnetic field. The simulation code used for this study was the one-and-two-half dimensional electromagnetic particle code named KEMPO. The simulation result shows the high power electromagnetic wave produces both the backscattered electromagnetic wave and electrostatic electron cyclotron waves as a result of nonlinear parametric instability. Detailed nonlinear microphysics related to the wave excitation is discussed in terms of the nonlinear wave-wave couplings and associated ponderomotive force produced by the high power electromagnetic waves. 2 references, 4 figures.

Nonlinear excitation of electron cyclotron waves by a monochromatic strong microwave: computer simulation analysis of the MINIX results

International Nuclear Information System (INIS)

Matsumoto, H.; Kimura, T.

1986-01-01

Triggered by the experimental results of the MINIX, a computer simulation study was initiated on the nonlinear excitation of electrostatic electron cyclotron waves by a monochromatic electromagnetic wave such as the transmitted microwave in the MINIX. The model used assumes that both of the excited waves and exciting (pumping) electromagnetic wave as well as the idler electromagnetic wave propagate in the direction perpendicular to the external magnetic field. The simulation code used for this study was the one-and-two-half dimensional electromagnetic particle code named KEMPO. The simulation result shows the high power electromagnetic wave produces both the backscattered electromagnetic wave and electrostatic electron cyclotron waves as a result of nonlinear parametric instability. Detailed nonlinear microphysics related to the wave excitation is discussed in terms of the nonlinear wave-wave couplings and associated ponderomotive force produced by the high power electromagnetic waves. 2 references, 4 figures

Angular spectrum approach for fast simulation of pulsed non-linear ultrasound fields

DEFF Research Database (Denmark)

Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt

2011-01-01

The paper presents an Angular Spectrum Approach (ASA) for simulating pulsed non-linear ultrasound fields. The source of the ASA is generated by Field II, which can simulate array transducers of any arbitrary geometry and focusing. The non-linear ultrasound simulation program - Abersim, is used...... as the reference. A linear array transducer with 64 active elements is simulated by both Field II and Abersim. The excitation is a 2-cycle sine wave with a frequency of 5 MHz. The second harmonic field in the time domain is simulated using ASA. Pulse inversion is used in the Abersim simulation to remove...... the fundamental and keep the second harmonic field, since Abersim simulates non-linear fields with all harmonic components. ASA and Abersim are compared for the pulsed fundamental and second harmonic fields in the time domain at depths of 30 mm, 40 mm (focal depth) and 60 mm. Full widths at -6 dB (FWHM) are f0...

Modeling and Analysis of a Nonlinear Age-Structured Model for Tumor Cell Populations with Quiescence

Science.gov (United States)

Liu, Zijian; Chen, Jing; Pang, Jianhua; Bi, Ping; Ruan, Shigui

2018-05-01

We present a nonlinear first-order hyperbolic partial differential equation model to describe age-structured tumor cell populations with proliferating and quiescent phases at the avascular stage in vitro. The division rate of the proliferating cells is assumed to be nonlinear due to the limitation of the nutrient and space. The model includes a proportion of newborn cells that enter directly the quiescent phase with age zero. This proportion can reflect the effect of treatment by drugs such as erlotinib. The existence and uniqueness of solutions are established. The local and global stabilities of the trivial steady state are investigated. The existence and local stability of the positive steady state are also analyzed. Numerical simulations are performed to verify the results and to examine the impacts of parameters on the nonlinear dynamics of the model.

Contribution to the Development of Simulation Model of Ship Turbine

Directory of Open Access Journals (Sweden)

Božić Ratko

2015-01-01

Full Text Available Simulation modelling, performed by System Dynamics Modelling Approach and intensive use of computers, is one of the most convenient and most successful scientific methods of analysis of performance dynamics of nonlinear and very complex natural technical and organizational systems [1]. The purpose of this work is to demonstrate the successful application of system dynamics simulation modelling at analyzing performance dynamics of a complex system of ship’s propulsion system. Gas turbine is a complex non-linear system, which needs to be systematically investigated as a unit consisting of a number of subsystems and elements, which are linked by cause-effect (UPV feedback loops (KPD, both within the propulsion system and with the relevant surrounding. In this paper the authors will present an efficient application of scientific methods for the study of complex dynamic systems called qualitative and quantitative simulation System Dynamics Methodology. Gas turbine will be presented by a set of non-linear differential equations, after which mental-verbal structural models and flowcharts in System dynamics symbols will be produced, and the performance dynamics in load condition will be simulated in POWERSIM simulation language.

Nonlinear Model of Tape Wound Core Transformers

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A. Vahedi

2015-03-01

Full Text Available Recently, tape wound cores due to their excellent magnetic properties, are widely used in different types of transformers. Performance prediction of these transformers needs an accurate model with ability to determine flux distribution within the core and magnetic loss. Spiral structure of tape wound cores affects the flux distribution and always cause complication of analysis. In this paper, a model based on reluctance networks method is presented for analysis of magnetic flux in wound cores. Using this model, distribution of longitudinal and transverse fluxes within the core can be determined. To consider the nonlinearity of the core, a dynamic hysteresis model is included in the presented model. Having flux density in different points of the core, magnetic losses can be calculated. To evaluate the validity of the model, results are compared with 2-D FEM simulations. In addition, a transformer designed for series-resonant converter and simulation results are compared with experimental measurements. Comparisons show accuracy of the model besides simplicity and fast convergence

Nonlinear magnetohydrodynamics simulation using high-order finite elements

International Nuclear Information System (INIS)

Plimpton, Steven James; Schnack, D.D.; Tarditi, A.; Chu, M.S.; Gianakon, T.A.; Kruger, S.E.; Nebel, R.A.; Barnes, D.C.; Sovinec, C.R.; Glasser, A.H.

2005-01-01

A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p (ge) 2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity (x(parallel)/x(perpendicular)) is computed accurately with p (ge) 3 without mesh alignment. A simulation of tearing-mode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

International Nuclear Information System (INIS)

Lin-Jie, Chen; Chang-Feng, Ma

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

Nonlinear Modeling by Assembling Piecewise Linear Models

Science.gov (United States)

Yao, Weigang; Liou, Meng-Sing

2013-01-01

To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

Non-linear time variant model intended for polypyrrole-based actuators

Science.gov (United States)

Farajollahi, Meisam; Madden, John D. W.; Sassani, Farrokh

2014-03-01

Polypyrrole-based actuators are of interest due to their biocompatibility, low operation voltage and relatively high strain and force. Modeling and simulation are very important to predict the behaviour of each actuator. To develop an accurate model, we need to know the electro-chemo-mechanical specifications of the Polypyrrole. In this paper, the non-linear time-variant model of Polypyrrole film is derived and proposed using a combination of an RC transmission line model and a state space representation. The model incorporates the potential dependent ionic conductivity. A function of ionic conductivity of Polypyrrole vs. local charge is proposed and implemented in the non-linear model. Matching of the measured and simulated electrical response suggests that ionic conductivity of Polypyrrole decreases significantly at negative potential vs. silver/silver chloride and leads to reduced current in the cyclic voltammetry (CV) tests. The next stage is to relate the distributed charging of the polymer to actuation via the strain to charge ratio. Further work is also needed to identify ionic and electronic conductivities as well as capacitance as a function of oxidation state so that a fully predictive model can be created.

Comparison of Simulated and Measured Non-linear Ultrasound Fields

DEFF Research Database (Denmark)

Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt

2011-01-01

In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...... fundamental and second harmonic elds. The focused piston transducer with a center frequency of 5 MHz is excited by a waveform generator emitting a 6-cycle sine wave. The hydrophone is mounted in the focal plane 118 mm from the transducer. The point spread functions at the focal depth from Field II...

An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

KAUST Repository

Xu, Tiantian

2014-08-17

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

A combined nonlinear and hysteresis model of shock absorber for quarter car simulation on the basis of experimental data

Directory of Open Access Journals (Sweden)

Vijay Barethiye

2017-12-01

Full Text Available Modeling dynamic characteristics of an automotive shock absorber is a challenging task due to its complex behavior. In the present paper, the nonparametric and hybrid approach is proposed to represent the nonlinear and hysteresis characteristics of the shock absorber. An experiment is carried out on a car damper utilizing INSTRON to obtain force-velocity characteristics of the shock absorber. The experimental data is used to devise two different models, namely, piecewise linear model and hysteresis model, to capture the damping properties of the absorber and for consequent use in simulations. The complexity involved due to certain physical phenomenon such as oil compressibility, gas entrapment etc. gives rise to hysteresis behavior and the present paper tries to model such behavior with the help of Neural Networks. Finally, a combined (hybrid shock absorber model (including the characteristics of both piecewise linear and hysteresis behavior is developed in Simulink and integrated into a quarter car simulation to verify its feasibility. The results generated by the combined (hybrid model are compared with linear as well as piecewise linear model and the comparison shows that the proposed model substantially a better option to study the vehicle characteristics more accurately and precisely.

Adaptive regression for modeling nonlinear relationships

CERN Document Server

Knafl, George J

2016-01-01

This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the s...

Controller Design of Complex System Based on Nonlinear Strength

Directory of Open Access Journals (Sweden)

Rongjun Mu

2015-01-01

Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

An adaptive nonlinear solution scheme for reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Lett, G.S. [Scientific Software - Intercomp, Inc., Denver, CO (United States)

1996-12-31

Numerical reservoir simulation involves solving large, nonlinear systems of PDE with strongly discontinuous coefficients. Because of the large demands on computer memory and CPU, most users must perform simulations on very coarse grids. The average properties of the fluids and rocks must be estimated on these grids. These coarse grid {open_quotes}effective{close_quotes} properties are costly to determine, and risky to use, since their optimal values depend on the fluid flow being simulated. Thus, they must be found by trial-and-error techniques, and the more coarse the grid, the poorer the results. This paper describes a numerical reservoir simulator which accepts fine scale properties and automatically generates multiple levels of coarse grid rock and fluid properties. The fine grid properties and the coarse grid simulation results are used to estimate discretization errors with multilevel error expansions. These expansions are local, and identify areas requiring local grid refinement. These refinements are added adoptively by the simulator, and the resulting composite grid equations are solved by a nonlinear Fast Adaptive Composite (FAC) Grid method, with a damped Newton algorithm being used on each local grid. The nonsymmetric linear system of equations resulting from Newton`s method are in turn solved by a preconditioned Conjugate Gradients-like algorithm. The scheme is demonstrated by performing fine and coarse grid simulations of several multiphase reservoirs from around the world.

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.

Science.gov (United States)

Shang, Xituan; Yen, Michael R T; Gaber, M Waleed

2010-06-01

The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.

A general U-block model-based design procedure for nonlinear polynomial control systems

Science.gov (United States)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Nonlinear finite element modeling of concrete deep beams with openings strengthened with externally-bonded composites

International Nuclear Information System (INIS)

Hawileh, Rami A.; El-Maaddawy, Tamer A.; Naser, Mohannad Z.

2012-01-01

Highlights: ► A 3D nonlinear FE model is developed of RC deep beams with web openings. ► We used cohesion elements to simulate bond. ► The developed FE model is suitable for analysis of such complex structures. -- Abstract: This paper aims to develop 3D nonlinear finite element (FE) models for reinforced concrete (RC) deep beams containing web openings and strengthened in shear with carbon fiber reinforced polymer (CFRP) composite sheets. The web openings interrupted the natural load path either fully or partially. The FE models adopted realistic materials constitutive laws that account for the nonlinear behavior of materials. In the FE models, solid elements for concrete, multi-layer shell elements for CFRP and link elements for steel reinforcement were used to simulate the physical models. Special interface elements were implemented in the FE models to simulate the interfacial bond behavior between the concrete and CFRP composites. A comparison between the FE results and experimental data published in the literature demonstrated the validity of the computational models in capturing the structural response for both unstrengthened and CFRP-strengthened deep beams with openings. The developed FE models can serve as a numerical platform for performance prediction of RC deep beams with openings strengthened in shear with CFRP composites.

Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

Science.gov (United States)

Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.

2011-01-01

We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

SEIR model simulation for Hepatitis B

Science.gov (United States)

Side, Syafruddin; Irwan, Mulbar, Usman; Sanusi, Wahidah

2017-09-01

Mathematical modelling and simulation for Hepatitis B discuss in this paper. Population devided by four variables, namely: Susceptible, Exposed, Infected and Recovered (SEIR). Several factors affect the population in this model is vaccination, immigration and emigration that occurred in the population. SEIR Model obtained Ordinary Differential Equation (ODE) non-linear System 4-D which then reduces to 3-D. SEIR model simulation undertaken to predict the number of Hepatitis B cases. The results of the simulation indicates the number of Hepatitis B cases will increase and then decrease for several months. The result of simulation using the number of case in Makassar also found the basic reproduction number less than one, that means, Makassar city is not an endemic area of Hepatitis B.

A New Nonlinear Model of Body Resistance in Nanometer PD SOI MOSFETs

Directory of Open Access Journals (Sweden)

Arash Daghighi

2011-01-01

Full Text Available In this paper, a nonlinear model for the body resistance of a 45nm PD SOI MOSFET is developed. This model verified on the base of the small signal three-dimensional simulation results. In this paper by using the three-dimensional simulation of ISE-TCAD software, the indicating factors of body resistance in nanometer transistors and then are shown, using the surface potential model. A mathematical relation to calculat the body resistance incorporating device width and body potential was derived. Excellent agreement was obtained by comparing the model outputs and three-dimensional simulation results.

Simulating nonlinear neutrino flavor evolution

Energy Technology Data Exchange (ETDEWEB)

Duan, H [Institute for Nuclear Theory, University of Washington, Seattle, WA 98195 (United States); Fuller, G M [Department of Physics, University of California, San Diego, La Jolla, CA 92093 (United States); Carlson, J [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)], E-mail: hduan@phys.washington.edu, E-mail: gfuller@ucsd.edu, E-mail: carlson@lanl.gov

2008-10-01

We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical coupling of intersecting neutrino trajectories and the associated nonlinearity which characterizes neutrino flavor conversion. We describe here the two codes developed to attack this problem. We also describe the surprising phenomena revealed by these numerical calculations. Chief among these is that the nonlinearities in the problem can engineer neutrino flavor transformation which is dramatically different to that in standard Mikheyev-Smirnov-Wolfenstein treatments. This happens even though the neutrino mass-squared differences are measured to be small, and even when neutrino self-coupling is sub-dominant. Our numerical work has revealed potential signatures which, if detected in the neutrino burst from a Galactic core collapse event, could reveal heretofore unmeasurable properties of the neutrinos, such as the mass hierarchy and vacuum mixing angle {theta}{sub 13}.

Simulating nonlinear neutrino flavor evolution

Science.gov (United States)

Duan, H.; Fuller, G. M.; Carlson, J.

2008-10-01

We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical coupling of intersecting neutrino trajectories and the associated nonlinearity which characterizes neutrino flavor conversion. We describe here the two codes developed to attack this problem. We also describe the surprising phenomena revealed by these numerical calculations. Chief among these is that the nonlinearities in the problem can engineer neutrino flavor transformation which is dramatically different to that in standard Mikheyev Smirnov Wolfenstein treatments. This happens even though the neutrino mass-squared differences are measured to be small, and even when neutrino self-coupling is sub-dominant. Our numerical work has revealed potential signatures which, if detected in the neutrino burst from a Galactic core collapse event, could reveal heretofore unmeasurable properties of the neutrinos, such as the mass hierarchy and vacuum mixing angle θ13.

Nonlinear time-dependent simulation of helix traveling wave tubes

International Nuclear Information System (INIS)

Peng Wei-Feng; Yang Zhong-Hai; Hu Yu-Lu; Li Jian-Qing; Lu Qi-Ru; Li Bin

2011-01-01

A one-dimensional nonlinear time-dependent theory for helix traveling wave tubes is studied. A generalized electromagnetic field is applied to the expression of the radio frequency field. To simulate the variations of the high frequency structure, such as the pitch taper and the effect of harmonics, the spatial average over a wavelength is substituted by a time average over a wave period in the equation of the radio frequency field. Under this assumption, the space charge field of the electron beam can be treated by a space charge wave model along with the space charge coefficient. The effects of the radio frequency and the space charge fields on the electrons are presented by the equations of the electron energy and the electron phase. The time-dependent simulation is compared with the frequency-domain simulation for a helix TWT, which validates the availability of this theory. (interdisciplinary physics and related areas of science and technology)

Comparisons of measurements and numerical simulations of a nonlinear beam subjected to a multi-harmonic non-ideal input signal

International Nuclear Information System (INIS)

Claeys, M.; Sinou, J.J.; Lambelin, J.P.; Alcoverro, B.

2014-01-01

This study presents a direct comparison of measured and predicted nonlinear vibrations of a clamped-clamped steel beam. A multi-harmonic comparison of simulations with measurements is performed at the vicinity of the primary resonance. First of all, a nonlinear analytical model of the beam is developed taking into account non-ideal boundary conditions. The Harmonic Balance Method is implemented to estimate the nonlinear behavior of the clamped-clamped beam. This nonlinear method enables to simulate the vibration stationary response of a nonlinear system projected on several harmonics. This study then proposes a method to compare numerical simulations with measurements on all these harmonics. A signal analysis tool is developed to extract the system harmonics' frequency responses from a temporal signal of a swept sine experiment. An evolutionary updating algorithm (Covariance Matrix Adaptation Evolution Strategy), coupled with highly selective filters is used to identify both fundamental frequency and harmonics' amplitude in the temporal signal, at every moment. This tool enables to extract the harmonic amplitudes of the output signal as well as the input signal. The input of the Harmonic Balance Method can then be either an ideal mono-harmonic signal or a multi-harmonic experimental input signal. Finally, the present work focuses on the comparison of experimental and simulated results. From experimental output harmonics and numerical simulations, it is shown that it is possible to distinguish the nonlinearities of the clamped-clamped beam and the effect of the non-ideal input signal. (authors)

Non-linear simulations of ELMs in ASDEX upgrade

Energy Technology Data Exchange (ETDEWEB)

Lessig, Alexander; Hoelzl, Matthias; Orain, Francois; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, Boltzmannstrasse 2, 85748 Garching (Germany); Becoulet, Marina; Huysmans, Guido [CEA-IRFM, Cadarache, 13108 Saint-Paul-Lez-Durance (France); Collaboration: the ASDEX Upgrade Team

2016-07-01

Large edge localized modes (ELMs) are a severe concern for the operation of future tokamak devices like ITER or DEMO due to the high transient heat loads induced on divertor targets and wall structures. It is therefore important to study ELMs both theoretically and experimentally in order to obtain a comprehensive understanding of the underlying mechanisms which is necessary for the prediction of ELM properties and the design of ELM mitigation systems. Using the non-linear MHD code JOREK, we have performed first simulations of full ELM crashes in ASDEX Upgrade, taking into account a large number of toroidal Fourier harmonics. The evolution of the toroidal mode spectrum has been investigated. In particular, we confirm the previously observed non-linear drive of linearly sub-dominant low-n components in the early non-linear phase of the ELM crash. Preliminary comparisons of the simulations with experimental observations regarding heat and particle losses, pedestal evolution and heat deposition patterns are shown. On the long run we aim at code validation as well as an improved understanding of the ELM dynamics and possibly a better characterization of different ELM types.

An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

KAUST Repository

Xu, Tiantian; Younis, Mohammad I.

2014-01-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction

Nonlinear delta f Simulations of Collective Effects in Intense Charged Particle Beams

CERN Document Server

Hong Qi

2003-01-01

A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, ...

Development of the Transport Class Model (TCM) Aircraft Simulation From a Sub-Scale Generic Transport Model (GTM) Simulation

Science.gov (United States)

Hueschen, Richard M.

2011-01-01

A six degree-of-freedom, flat-earth dynamics, non-linear, and non-proprietary aircraft simulation was developed that is representative of a generic mid-sized twin-jet transport aircraft. The simulation was developed from a non-proprietary, publicly available, subscale twin-jet transport aircraft simulation using scaling relationships and a modified aerodynamic database. The simulation has an extended aerodynamics database with aero data outside the normal transport-operating envelope (large angle-of-attack and sideslip values). The simulation has representative transport aircraft surface actuator models with variable rate-limits and generally fixed position limits. The simulation contains a generic 40,000 lb sea level thrust engine model. The engine model is a first order dynamic model with a variable time constant that changes according to simulation conditions. The simulation provides a means for interfacing a flight control system to use the simulation sensor variables and to command the surface actuators and throttle position of the engine model.

Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

Science.gov (United States)

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.

A nonlinear q-voter model with deadlocks on the Watts-Strogatz graph

Science.gov (United States)

Sznajd-Weron, Katarzyna; Michal Suszczynski, Karol

2014-07-01

We study the nonlinear $q$-voter model with deadlocks on a Watts-Strogats graph. Using Monte Carlo simulations, we obtain so called exit probability and exit time. We determine how network properties, such as randomness or density of links influence exit properties of a model.

Complex fluid network optimization and control integrative design based on nonlinear dynamic model

International Nuclear Information System (INIS)

Sui, Jinxue; Yang, Li; Hu, Yunan

2016-01-01

In view of distribution according to complex fluid network’s needs, this paper proposed one optimization computation method of the nonlinear programming mathematical model based on genetic algorithm. The simulation result shows that the overall energy consumption of the optimized fluid network has a decrease obviously. The control model of the fluid network is established based on nonlinear dynamics. We design the control law based on feedback linearization, take the optimal value by genetic algorithm as the simulation data, can also solve the branch resistance under the optimal value. These resistances can provide technical support and reference for fluid network design and construction, so can realize complex fluid network optimization and control integration design.

Observing and modeling nonlinear dynamics in an internal combustion engine

International Nuclear Information System (INIS)

Daw, C.S.; Kennel, M.B.; Finney, C.E.; Connolly, F.T.

1998-01-01

We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model close-quote s simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements. copyright 1998 The American Physical Society

Nonlinear signal processing using neural networks: Prediction and system modelling

Energy Technology Data Exchange (ETDEWEB)

Lapedes, A.; Farber, R.

1987-06-01

The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.

Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity

Directory of Open Access Journals (Sweden)

Dae Woo Park

2016-01-01

Full Text Available Shear wave elasticity imaging (SWEI can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE- based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard tumor and surrounding tissue (soft. The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.

Ultrasound Shear Wave Simulation of Breast Tumor Using Nonlinear Tissue Elasticity.

Science.gov (United States)

Park, Dae Woo

2015-01-01

Shear wave elasticity imaging (SWEI) can assess the elasticity of tissues, but the shear modulus estimated in SWEI is often less sensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues. Because most soft tissues exhibit mechanical nonlinearity that differs in tissue types, mechanical contrast can be enhanced if the tissues are compressed. In this study, a finite element- (FE-) based simulation was performed for a breast tissue model, which consists of a circular (D: 10 mm, hard) tumor and surrounding tissue (soft). The SWEI was performed with 0% to 30% compression of the breast tissue model. The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above 10% overall applied compression. As a result, the elastic modulus contrast of the tumor to the surrounding tissue was increased from 0.46 at 0% compression to 1.45 at 30% compression.

A penalized framework for distributed lag non-linear models.

Science.gov (United States)

Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G

2017-09-01

Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.

Recent progress of nonlinear simulation on the toroidal Alfven eigenmode

International Nuclear Information System (INIS)

Todo, Yasushi; Sato, Tetsuya

1998-01-01

Linear and nonlinear particle-magnetohydrodynamic (MHD) simulation codes are developed to study interactions between energetic ions and MHD modes. Energetic alpha particles with a slowing-down distribution are considered and the behavior of n=2 toroidal Alfven eigenmodes (TAE modes) is investigated with the parameters pertinent to the present large tokamaks. The linear simulation reveals the resonance condition between alpha particles and TAE mode. In the nonlinear simulation two n=2 TAE modes are destabilized and alpha particle losses induced by these TAE modes take place. Counter-passing particles are lost when they cross the passing-trapped boundary as a result of the interaction with the TAE modes. They are the major part of lost particles, but trapped particles are also lost appreciably. (author)

Modeling of memristor-based chaotic systems using nonlinear Wiener adaptive filters based on backslash operator

International Nuclear Information System (INIS)

Zhao, Yibo; Jiang, Yi; Feng, Jiuchao; Wu, Lifu

2016-01-01

Highlights: • A novel nonlinear Wiener adaptive filters based on the backslash operator are proposed. • The identification approach to the memristor-based chaotic systems using the proposed adaptive filters. • The weight update algorithm and convergence characteristics for the proposed adaptive filters are derived. - Abstract: Memristor-based chaotic systems have complex dynamical behaviors, which are characterized as nonlinear and hysteresis characteristics. Modeling and identification of their nonlinear model is an important premise for analyzing the dynamical behavior of the memristor-based chaotic systems. This paper presents a novel nonlinear Wiener adaptive filtering identification approach to the memristor-based chaotic systems. The linear part of Wiener model consists of the linear transversal adaptive filters, the nonlinear part consists of nonlinear adaptive filters based on the backslash operator for the hysteresis characteristics of the memristor. The weight update algorithms for the linear and nonlinear adaptive filters are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics. Comparing with the adaptive nonlinear polynomial filters, the proposed nonlinear adaptive filters have less identification error.

Modeling exposure–lag–response associations with distributed lag non-linear models

Science.gov (United States)

Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

Nonlinear hybrid simulation of toroidicity-induced alfven eigenmode

International Nuclear Information System (INIS)

Fu, G.Y.; Park, W.

1994-11-01

Gyrokinetic/Magnetohydrodynamics hybrid simulations have been carried out using MH3D-K code to study the nonlinear saturation of the toroidicity-induced Alfven eigenmode driven by energetic particles in a tokamak plasma. It is shown that the wave particle trapping is the nonlinear saturation mechanism for the parameters considered. The corresponding density profile flattening of hot particles is observed. The saturation amplitude is proportional to the square of linear growth rate. In addition to TAE modes, a new n = 1, m = 0 global Alfven eigenmode is shown to be excited by the energetic particles

Generalized Nonlinear Yule Models

Science.gov (United States)

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-11-01

With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction

Energy Technology Data Exchange (ETDEWEB)

Carlberg, Kevin Thomas [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling and Analysis; Drohmann, Martin [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling and Analysis; Tuminaro, Raymond S. [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Computational Mathematics; Boggs, Paul T. [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling and Analysis; Ray, Jaideep [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling and Analysis; van Bloemen Waanders, Bart Gustaaf [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Optimization and Uncertainty Estimation

2014-10-01

Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximated Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model

Convergence Guaranteed Nonlinear Constraint Model Predictive Control via I/O Linearization

Directory of Open Access Journals (Sweden)

Xiaobing Kong

2013-01-01

Full Text Available Constituting reliable optimal solution is a key issue for the nonlinear constrained model predictive control. Input-output feedback linearization is a popular method in nonlinear control. By using an input-output feedback linearizing controller, the original linear input constraints will change to nonlinear constraints and sometimes the constraints are state dependent. This paper presents an iterative quadratic program (IQP routine on the continuous-time system. To guarantee its convergence, another iterative approach is incorporated. The proposed algorithm can reach a feasible solution over the entire prediction horizon. Simulation results on both a numerical example and the continuous stirred tank reactors (CSTR demonstrate the effectiveness of the proposed method.

Extended MHD modeling of nonlinear instabilities in fusion and space plasmas

Energy Technology Data Exchange (ETDEWEB)

Germaschewski, Kai [Univ. of New Hampshire, Durham, NH (United States)

2017-11-15

A number of different sub-projects where pursued within this DOE early career project. The primary focus was on using fully nonlinear, curvilinear, extended MHD simulations of instabilities with applications to fusion and space plasmas. In particular, we performed comprehensive studies of the dynamics of the double tearing mode in different regimes and confi gurations, using Cartesian and cyclindrical geometry and investigating both linear and non-linear dynamics. In addition to traditional extended MHD involving Hall term and electron pressure gradient, we also employed a new multi-fluid moment model, which shows great promise to incorporate kinetic effects, in particular off-diagonal elements of the pressure tensor, in a fluid model, which is naturally computationally much cheaper than fully kinetic particle or Vlasov simulations. We used our Vlasov code for detailed studies of how weak collisions effect plasma echos. In addition, we have played an important supporting role working with the PPPL theory group around Will Fox and Amitava Bhattacharjee on providing simulation support for HED plasma experiments performed at high-powered laser facilities like OMEGA-EP in Rochester, NY. This project has support a great number of computational advances in our fluid and kinetic plasma models, and has been crucial to winning multiple INCITE computer time awards that supported our computational modeling.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Nonlinear aeroacoustic characterization of Helmholtz resonators with a local-linear neuro-fuzzy network model

Science.gov (United States)

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.

Neoclassical viscous stress tensor for non-linear MHD simulations with XTOR-2F

International Nuclear Information System (INIS)

Mellet, N.; Maget, P.; Meshcheriakov, D.; Lütjens, H.

2013-01-01

The neoclassical viscous stress tensor is implemented in the non-linear MHD code XTOR-2F (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), allowing consistent bi-fluid simulations of MHD modes, including the metastable branch of neoclassical tearing modes (NTMs) (Carrera et al 1986 Phys. Fluids 29 899–902). Equilibrium flows and bootstrap current from the neoclassical theory are formally recovered in this Chew–Goldberger–Low formulation. The non-linear behaviour of the new model is verified on a test case coming from a Tore Supra non-inductive discharge. A NTM threshold that is larger than with the previous model is obtained. This is due to the fact that the velocity is now part of the bootstrap current and that it differs from the theoretical neoclassical value. (paper)

Self-consistent nonlinear simulations of high-power free-electron lasers

International Nuclear Information System (INIS)

Freund, H.P.; Jackson, R.H.

1993-01-01

Two 3-D nonlinear formulations of FEL amplifiers are described which treat both planar and helical wiggler geometries. For convenience, the authors refer to the planar (helical) formulation and simulation code as WIGGLIN (ARACHNE). These formulations are slow-time-scale models for FEL amplifiers in which the electron dynamics are treated using the complete 3-D Lorentz force equations without recourse to a wiggler period average. The application of these codes to the description of a collective reversed-field FEL experiment and to random wiggler field errors is described

Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

International Nuclear Information System (INIS)

Chen, Jin

2009-01-01

Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

Performance of nonlinear mixed effects models in the presence of informative dropout.

Science.gov (United States)

Björnsson, Marcus A; Friberg, Lena E; Simonsson, Ulrika S H

2015-01-01

Informative dropout can lead to bias in statistical analyses if not handled appropriately. The objective of this simulation study was to investigate the performance of nonlinear mixed effects models with regard to bias and precision, with and without handling informative dropout. An efficacy variable and dropout depending on that efficacy variable were simulated and model parameters were reestimated, with or without including a dropout model. The Laplace and FOCE-I estimation methods in NONMEM 7, and the stochastic simulations and estimations (SSE) functionality in PsN, were used in the analysis. For the base scenario, bias was low, less than 5% for all fixed effects parameters, when a dropout model was used in the estimations. When a dropout model was not included, bias increased up to 8% for the Laplace method and up to 21% if the FOCE-I estimation method was applied. The bias increased with decreasing number of observations per subject, increasing placebo effect and increasing dropout rate, but was relatively unaffected by the number of subjects in the study. This study illustrates that ignoring informative dropout can lead to biased parameters in nonlinear mixed effects modeling, but even in cases with few observations or high dropout rate, the bias is relatively low and only translates into small effects on predictions of the underlying effect variable. A dropout model is, however, crucial in the presence of informative dropout in order to make realistic simulations of trial outcomes.

Nonlinear detection of disordered voice productions from short time series based on a Volterra-Wiener-Korenberg model

Energy Technology Data Exchange (ETDEWEB)

Zhang Yu, E-mail: yuzhang@xmu.edu.cn [Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen Fujian 361005 (China); Sprecher, Alicia J. [Department of Surgery, Division of Otolaryngology - Head and Neck Surgery, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792-7375 (United States); Zhao Zongxi [Key Laboratory of Underwater Acoustic Communication and Marine Information Technology of the Ministry of Education, Xiamen University, Xiamen Fujian 361005 (China); Jiang, Jack J. [Department of Surgery, Division of Otolaryngology - Head and Neck Surgery, University of Wisconsin School of Medicine and Public Health, Madison, WI 53792-7375 (United States)

2011-09-15

Highlights: > The VWK method effectively detects the nonlinearity of a discrete map. > The method describes the chaotic time series of a biomechanical vocal fold model. > Nonlinearity in laryngeal pathology is detected from short and noisy time series. - Abstract: In this paper, we apply the Volterra-Wiener-Korenberg (VWK) model method to detect nonlinearity in disordered voice productions. The VWK method effectively describes the nonlinearity of a third-order nonlinear map. It allows for the analysis of short and noisy data sets. The extracted VWK model parameters show an agreement with the original nonlinear map parameters. Furthermore, the VWK mode method is applied to successfully assess the nonlinearity of a biomechanical voice production model simulating irregular vibratory dynamics of vocal folds with a unilateral vocal polyp. Finally, we show the clinical applicability of this nonlinear detection method to analyze the electroglottographic data generated by 14 patients with vocal nodules or polyps. The VWK model method shows potential in describing the nonlinearity inherent in disordered voice productions from short and noisy time series that are common in the clinical setting.

Nonlinear detection of disordered voice productions from short time series based on a Volterra-Wiener-Korenberg model

International Nuclear Information System (INIS)

Zhang Yu; Sprecher, Alicia J.; Zhao Zongxi; Jiang, Jack J.

2011-01-01

Highlights: → The VWK method effectively detects the nonlinearity of a discrete map. → The method describes the chaotic time series of a biomechanical vocal fold model. → Nonlinearity in laryngeal pathology is detected from short and noisy time series. - Abstract: In this paper, we apply the Volterra-Wiener-Korenberg (VWK) model method to detect nonlinearity in disordered voice productions. The VWK method effectively describes the nonlinearity of a third-order nonlinear map. It allows for the analysis of short and noisy data sets. The extracted VWK model parameters show an agreement with the original nonlinear map parameters. Furthermore, the VWK mode method is applied to successfully assess the nonlinearity of a biomechanical voice production model simulating irregular vibratory dynamics of vocal folds with a unilateral vocal polyp. Finally, we show the clinical applicability of this nonlinear detection method to analyze the electroglottographic data generated by 14 patients with vocal nodules or polyps. The VWK model method shows potential in describing the nonlinearity inherent in disordered voice productions from short and noisy time series that are common in the clinical setting.

Enzymatic Synthesis of Ampicillin: Nonlinear Modeling, Kinetics Estimation, and Adaptive Control

Directory of Open Access Journals (Sweden)

Monica Roman

2012-01-01

Full Text Available Nowadays, the use of advanced control strategies in biotechnology is quite low. A main reason is the lack of quality of the data, and the fact that more sophisticated control strategies must be based on a model of the dynamics of bioprocesses. The nonlinearity of the bioprocesses and the absence of cheap and reliable instrumentation require an enhanced modeling effort and identification strategies for the kinetics. The present work approaches modeling and control strategies for the enzymatic synthesis of ampicillin that is carried out inside a fed-batch bioreactor. First, a nonlinear dynamical model of this bioprocess is obtained by using a novel modeling procedure for biotechnology: the bond graph methodology. Second, a high gain observer is designed for the estimation of the imprecisely known kinetics of the synthesis process. Third, by combining an exact linearizing control law with the on-line estimation kinetics algorithm, a nonlinear adaptive control law is designed. The case study discussed shows that a nonlinear feedback control strategy applied to the ampicillin synthesis bioprocess can cope with disturbances, noisy measurements, and parametric uncertainties. Numerical simulations performed with MATLAB environment are included in order to test the behavior and the performances of the proposed estimation and control strategies.

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

Science.gov (United States)

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.

Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schr(o)dinger Equation

Institute of Scientific and Technical Information of China (English)

ZHANG Yun-qiu; ZHANG Ning-chuan; PEI Yu-guo

2007-01-01

A numerical wave model based on the modified four-order nonlinear Schrodinger (NLS) equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is performed by changing sideband conditions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.

Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

Science.gov (United States)

Xiang, Hong-Jun; Zhang, Zhi-Wei; Shi, Zhi-Fei; Li, Hong

2018-04-01

A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

Nonlinear models for autoregressive conditional heteroskedasticity

DEFF Research Database (Denmark)

Teräsvirta, Timo

This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation are discu...

Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.

Science.gov (United States)

Idkaidek, Ashraf; Jasiuk, Iwona

2015-12-01

We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents.

Evaluation of bias associated with capture maps derived from nonlinear groundwater flow models

Science.gov (United States)

Nadler, Cara; Allander, Kip K.; Pohll, Greg; Morway, Eric D.; Naranjo, Ramon C.; Huntington, Justin

2018-01-01

The impact of groundwater withdrawal on surface water is a concern of water users and water managers, particularly in the arid western United States. Capture maps are useful tools to spatially assess the impact of groundwater pumping on water sources (e.g., streamflow depletion) and are being used more frequently for conjunctive management of surface water and groundwater. Capture maps have been derived using linear groundwater flow models and rely on the principle of superposition to demonstrate the effects of pumping in various locations on resources of interest. However, nonlinear models are often necessary to simulate head-dependent boundary conditions and unconfined aquifers. Capture maps developed using nonlinear models with the principle of superposition may over- or underestimate capture magnitude and spatial extent. This paper presents new methods for generating capture difference maps, which assess spatial effects of model nonlinearity on capture fraction sensitivity to pumping rate, and for calculating the bias associated with capture maps. The sensitivity of capture map bias to selected parameters related to model design and conceptualization for the arid western United States is explored. This study finds that the simulation of stream continuity, pumping rates, stream incision, well proximity to capture sources, aquifer hydraulic conductivity, and groundwater evapotranspiration extinction depth substantially affect capture map bias. Capture difference maps demonstrate that regions with large capture fraction differences are indicative of greater potential capture map bias. Understanding both spatial and temporal bias in capture maps derived from nonlinear groundwater flow models improves their utility and defensibility as conjunctive-use management tools.

Nonlinear Modeling and Identification of an Aluminum Honeycomb Panel with Multiple Bolts

Directory of Open Access Journals (Sweden)

Yongpeng Chu

2016-01-01

Full Text Available This paper focuses on the nonlinear dynamics modeling and parameter identification of an Aluminum Honeycomb Panel (AHP with multiple bolted joints. Finite element method using eight-node solid elements is exploited to model the panel and the bolted connection interface as a homogeneous, isotropic plate and as a thin layer of nonlinear elastic-plastic material, respectively. The material properties of a thin layer are defined by a bilinear elastic plastic model, which can describe the energy dissipation and softening phenomena in the bolted joints under nonlinear states. Experimental tests at low and high excitation levels are performed to reveal the dynamic characteristics of the bolted structure. In particular, the linear material parameters of the panel are identified via experimental tests at low excitation levels, whereas the nonlinear material parameters of the thin layer are updated by using the genetic algorithm to minimize the residual error between the measured and the simulation data at a high excitation level. It is demonstrated by comparing the frequency responses of the updated FEM and the experimental system that the thin layer of bilinear elastic-plastic material is very effective for modeling the nonlinear joint interface of the assembled structure with multiple bolts.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

Science.gov (United States)

Lan, C. Edward; Ge, Fuying

1989-01-01

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Non-linear Characteristic Modeling of Frictional Suspension Using Measured Data

Energy Technology Data Exchange (ETDEWEB)

Yoon, Chang Gyu; Jang, Jin Seok; Jin, Jae Hoon; Yoo, Wan Suk [Pusan National University, Busan (Korea, Republic of)

2015-01-15

Large-capacity of household washing machine can become unbalanced during the dehydration process. To solve this problem, several types of suspensions have been installed in a washing machine. In this study, physical tests were carried out on a frictional suspension, and the nonlinear characteristics were modeled by combining several simple physical models. The parameters were estimated based on the least squares solution. The simulation and test results were compared to verify the validity of the friction damper model.

Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.

Science.gov (United States)

Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J

2016-10-03

Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

Nonlinear spectral mixing theory to model multispectral signatures

Energy Technology Data Exchange (ETDEWEB)

Borel, C.C. [Los Alamos National Lab., NM (United States). Astrophysics and Radiation Measurements Group

1996-02-01

Nonlinear spectral mixing occurs due to multiple reflections and transmissions between discrete surfaces, e.g. leaves or facets of a rough surface. The radiosity method is an energy conserving computational method used in thermal engineering and it models nonlinear spectral mixing realistically and accurately. In contrast to the radiative transfer method the radiosity method takes into account the discreteness of the scattering surfaces (e.g. exact location, orientation and shape) such as leaves and includes mutual shading between them. An analytic radiosity-based scattering model for vegetation was developed and used to compute vegetation indices for various configurations. The leaf reflectance and transmittance was modeled using the PROSPECT model for various amounts of water, chlorophyll and variable leaf structure. The soil background was modeled using SOILSPEC with a linear mixture of reflectances of sand, clay and peat. A neural network and a geometry based retrieval scheme were used to retrieve leaf area index and chlorophyll concentration for dense canopies. Only simulated canopy reflectances in the 6 visible through short wave IR Landsat TM channels were used. The authors used an empirical function to compute the signal-to-noise ratio of a retrieved quantity.

Advanced Emergency Braking Control Based on a Nonlinear Model Predictive Algorithm for Intelligent Vehicles

Directory of Open Access Journals (Sweden)

Ronghui Zhang

2017-05-01

Full Text Available Focusing on safety, comfort and with an overall aim of the comprehensive improvement of a vision-based intelligent vehicle, a novel Advanced Emergency Braking System (AEBS is proposed based on Nonlinear Model Predictive Algorithm. Considering the nonlinearities of vehicle dynamics, a vision-based longitudinal vehicle dynamics model is established. On account of the nonlinear coupling characteristics of the driver, surroundings, and vehicle itself, a hierarchical control structure is proposed to decouple and coordinate the system. To avoid or reduce the collision risk between the intelligent vehicle and collision objects, a coordinated cost function of tracking safety, comfort, and fuel economy is formulated. Based on the terminal constraints of stable tracking, a multi-objective optimization controller is proposed using the theory of non-linear model predictive control. To quickly and precisely track control target in a finite time, an electronic brake controller for AEBS is designed based on the Nonsingular Fast Terminal Sliding Mode (NFTSM control theory. To validate the performance and advantages of the proposed algorithm, simulations are implemented. According to the simulation results, the proposed algorithm has better integrated performance in reducing the collision risk and improving the driving comfort and fuel economy of the smart car compared with the existing single AEBS.

Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model

Directory of Open Access Journals (Sweden)

Yue-bao Deng

2016-01-01

Full Text Available A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.

On concurvity in nonlinear and nonparametric regression models

Directory of Open Access Journals (Sweden)

Sonia Amodio

2014-12-01

Full Text Available When data are affected by multicollinearity in the linear regression framework, then concurvity will be present in fitting a generalized additive model (GAM. The term concurvity describes nonlinear dependencies among the predictor variables. As collinearity results in inflated variance of the estimated regression coefficients in the linear regression model, the result of the presence of concurvity leads to instability of the estimated coefficients in GAMs. Even if the backfitting algorithm will always converge to a solution, in case of concurvity the final solution of the backfitting procedure in fitting a GAM is influenced by the starting functions. While exact concurvity is highly unlikely, approximate concurvity, the analogue of multicollinearity, is of practical concern as it can lead to upwardly biased estimates of the parameters and to underestimation of their standard errors, increasing the risk of committing type I error. We compare the existing approaches to detect concurvity, pointing out their advantages and drawbacks, using simulated and real data sets. As a result, this paper will provide a general criterion to detect concurvity in nonlinear and non parametric regression models.

Proceedings of the workshop on nonlinear MHD and extended MHD

International Nuclear Information System (INIS)

1998-01-01

Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database

Proceedings of the workshop on nonlinear MHD and extended MHD

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-12-01

Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

Pseudo-transient Continuation Based Variable Relaxation Solve in Nonlinear Magnetohydrodynamic Simulations

Energy Technology Data Exchange (ETDEWEB)

Jin Chen

2009-12-07

Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.

Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

DEFF Research Database (Denmark)

Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

2013-01-01

We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

Directory of Open Access Journals (Sweden)

Hamed Kharrati

2012-01-01

Full Text Available This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.

Modelling the influence of sensory dynamics on linear and nonlinear driver steering control

Science.gov (United States)

Nash, C. J.; Cole, D. J.

2018-05-01

A recent review of the literature has indicated that sensory dynamics play an important role in the driver-vehicle steering task, motivating the design of a new driver model incorporating human sensory systems. This paper presents a full derivation of the linear driver model developed in previous work, and extends the model to control a vehicle with nonlinear tyres. Various nonlinear controllers and state estimators are compared with different approximations of the true system dynamics. The model simulation time is found to increase significantly with the complexity of the controller and state estimator. In general the more complex controllers perform best, although with certain vehicle and tyre models linearised controllers perform as well as a full nonlinear optimisation. Various extended Kalman filters give similar results, although the driver's sensory dynamics reduce control performance compared with full state feedback. The new model could be used to design vehicle systems which interact more naturally and safely with a human driver.

Pressure fluctuation prediction of a model pump turbine at no load opening by a nonlinear k-ε turbulence model

International Nuclear Information System (INIS)

Liu, J T; Zuo, Z G; Liu, S H; Wu, Y L

2014-01-01

In this paper, a new nonlinear k-ε turbulence model based on RNG k-ε turbulence model and Wilcox's k-ω turbulence model was proposed to simulate the unsteady flow and to predict the pressure fluctuation through a model pump turbine for engineering application. Calculations on a curved rectangular duct proved that the nonlinear k-ε turbulence model is applicable for high pressure gradient flows and large curvature flows. The numerically predicted relative pressure amplitude (peak to peak) in time domain to the pump turbine head at no load condition is very close to the experimental data. It is indicated that the prediction of the pressure fluctuation is valid by the present nonlinear k-ε method. The high pressure fluctuation in this area is the main issue for pump turbine design, especially at high head condition

Development an efficient calibrated nonlocal plate model for nonlinear axial instability of zirconia nanosheets using molecular dynamics simulation.

Science.gov (United States)

Sahmani, S; Fattahi, A M

2017-08-01

New ceramic materials containing nanoscaled crystalline phases create a main object of scientific interest due to their attractive advantages such as biocompatibility. Zirconia as a transparent glass ceramic is one of the most useful binary oxides in a wide range of applications. In the present study, a new size-dependent plate model is constructed to predict the nonlinear axial instability characteristics of zirconia nanosheets under axial compressive load. To accomplish this end, the nonlocal continuum elasticity of Eringen is incorporated to a refined exponential shear deformation plate theory. A perturbation-based solving process is put to use to derive explicit expressions for nonlocal equilibrium paths of axial-loaded nanosheets. After that, some molecular dynamics (MD) simulations are performed for axial instability response of square zirconia nanosheets with different side lengths, the results of which are matched with those of the developed nonlocal plate model to capture the proper value of nonlocal parameter. It is demonstrated that the calibrated nonlocal plate model with nonlocal parameter equal to 0.37nm has a very good capability to predict the axial instability characteristics of zirconia nanosheets, the accuracy of which is comparable with that of MD simulation. Copyright © 2017 Elsevier Inc. All rights reserved.

Finite element model for nonlinear shells of revolution

International Nuclear Information System (INIS)

Cook, W.A.

1979-01-01

Nuclear material shipping containers have shells of revolution as basic structural components. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Existing models are limited to large displacements, small rotations, and nonlinear materials. The paper presents a finite element model for a nonlinear shell of revolution that will account for large displacements, large strains, large rotations, and nonlinear materials

Halo Mitigation Using Nonlinear Lattices

CERN Document Server

Sonnad, Kiran G

2005-01-01

This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It is well established that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC is analysed using the Lie Transform perturbation theory showing that by averaging over a lattice period, one can reuduce the focusing force to a form that is identical to that used in the PIC simula...

Simulation of 3D parachute fluid–structure interaction based on nonlinear finite element method and preconditioning finite volume method

Directory of Open Access Journals (Sweden)

Fan Yuxin

2014-12-01

Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.

Nonlinear simulations with and computational issues for NIMROD

International Nuclear Information System (INIS)

Sovinec, C.R.

1998-01-01

The NIMROD (Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion) code development project was commissioned by the US Department of Energy in February, 1996 to provide the fusion research community with a computational tool for studying low-frequency behavior in experiments. Specific problems of interest include the neoclassical evolution of magnetic islands and the nonlinear behavior of tearing modes in the presence of rotation and nonideal walls in tokamaks; they also include topics relevant to innovative confinement concepts such as magnetic turbulence. Besides having physics models appropriate for these phenomena, an additional requirement is the ability to perform the computations in realistic geometries. The NIMROD Team is using contemporary management and computational methods to develop a computational tool for investigating low-frequency behavior in plasma fusion experiments. The authors intend to make the code freely available, and are taking steps to make it as easy to learn and use as possible. An example application for NIMROD is the nonlinear toroidal RFP simulation--the first in a series to investigate how toroidal geometry affects MHD activity in RFPs. Finally, the most important issue facing the project is execution time, and they are exploring better matrix solvers and a better parallel decomposition to address this

Nonlinear simulations with and computational issues for NIMROD

Energy Technology Data Exchange (ETDEWEB)

Sovinec, C.R. [Los Alamos National Lab., NM (United States)

1998-12-31

The NIMROD (Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion) code development project was commissioned by the US Department of Energy in February, 1996 to provide the fusion research community with a computational tool for studying low-frequency behavior in experiments. Specific problems of interest include the neoclassical evolution of magnetic islands and the nonlinear behavior of tearing modes in the presence of rotation and nonideal walls in tokamaks; they also include topics relevant to innovative confinement concepts such as magnetic turbulence. Besides having physics models appropriate for these phenomena, an additional requirement is the ability to perform the computations in realistic geometries. The NIMROD Team is using contemporary management and computational methods to develop a computational tool for investigating low-frequency behavior in plasma fusion experiments. The authors intend to make the code freely available, and are taking steps to make it as easy to learn and use as possible. An example application for NIMROD is the nonlinear toroidal RFP simulation--the first in a series to investigate how toroidal geometry affects MHD activity in RFPs. Finally, the most important issue facing the project is execution time, and they are exploring better matrix solvers and a better parallel decomposition to address this.

Numerical Material Model for Composite Laminates in High-Velocity Impact Simulation

Directory of Open Access Journals (Sweden)

Tao Liu

Full Text Available Abstract A numerical material model for composite laminate, was developed and integrated into the nonlinear dynamic explicit finite element programs as a material user subroutine. This model coupling nonlinear state of equation (EOS, was a macro-mechanics model, which was used to simulate the major mechanical behaviors of composite laminate under high-velocity impact conditions. The basic theoretical framework of the developed material model was introduced. An inverse flyer plate simulation was conducted, which demonstrated the advantage of the developed model in characterizing the nonlinear shock response. The developed model and its implementation were validated through a classic ballistic impact issue, i.e. projectile impacting on Kevlar29/Phenolic laminate. The failure modes and ballistic limit velocity were analyzed, and a good agreement was achieved when comparing with the analytical and experimental results. The computational capacity of this model, for Kevlar/Epoxy laminates with different architectures, i.e. plain-woven and cross-plied laminates, was further evaluated and the residual velocity curves and damage cone were accurately predicted.

Robust large-scale parallel nonlinear solvers for simulations.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)

2005-11-01

This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their use in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

Science.gov (United States)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Nonlinear Delta-f Particle Simulations of Collective Effects in High-Intensity Bunched Beams

CERN Document Server

Qin, Hong; Hudson, Stuart R; Startsev, Edward

2005-01-01

The collective effects in high-intensity 3D bunched beams are described self-consistently by the nonlinear Vlasov-Maxwell equations.* The nonlinear delta-f method,** a particle simulation method for solving the nonlinear Vlasov-Maxwell equations, is being used to study the collective effects in high-intensity 3D bunched beams. The delta-f method, as a nonlinear perturbative scheme, splits the distribution function into equilibrium and perturbed parts. The perturbed distribution function is represented as a weighted summation over discrete particles, where the particle orbits are advanced by equations of motion in the focusing field and self-consistent fields, and the particle weights are advanced by the coupling between the perturbed fields and the zero-order distribution function. The nonlinear delta-f method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. A self-consistent 3D kinetic equilibrium is first established for high intensity bunched beams. The...

Superspace formulation of new nonlinear sigma models

International Nuclear Information System (INIS)

Gates, S.J. Jr.

1983-07-01

The superspace formulation of two classes of supersymmetric nonlinear σ-models are presented. Two alternative N=1 superspace formulations are given for the d=2 supersymmetric nonlinear σ-models with Killing vector potentials: (a) formulation uses an active central charge and, (b) formulation uses a spurion superfield without inducing a classical breakdown of supersymmetry. The N=2 vector multiplet is used to construct a new class of d=4 nonlinear σ-models which when reduced to d=2 possess N=4 supersymmetry. Implications of these two classes of nonlinear σ-models for N>=4 superfield supergravity are discussed. (author)

Support-Vector-Machine-Based Reduced-Order Model for Limit Cycle Oscillation Prediction of Nonlinear Aeroelastic System

Directory of Open Access Journals (Sweden)

Gang Chen

2012-01-01

Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.

Dynamic modelling and simulation for control of a cylindrical robotic manipulator

International Nuclear Information System (INIS)

Iqbal, A.; Athar, S.M.

1995-03-01

In this report a dynamic model for the three degrees-of-freedom cylindrical manipulator, INFOMATE has been developed. Although the robot dynamics are highly coupled and non-linear, the developed model is relatively straight forward and compact for control engineering and simulation applications. The model has been simulated using the graphical simulation package SIMULINK. Different aspects of INFOMATE associated with forward dynamics, inverse dynamics and control have been investigated by performing various simulation experiments. These simulation experiments confirm the accuracy and applicability of the dynamic robot model. (author) 18 figs

Nonlinear filtering for LIDAR signal processing

Directory of Open Access Journals (Sweden)

D. G. Lainiotis

1996-01-01

Full Text Available LIDAR (Laser Integrated Radar is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF, which has been the standard nonlinear filter in past engineering applications.

Unified Nonlinear Flight Dynamics and Aeroelastic Simulator Tool, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — ZONA Technology, Inc. (ZONA) proposes a R&D effort to develop a Unified Nonlinear Flight Dynamics and Aeroelastic Simulator (UNFDAS) Tool that will combine...

Nonlinear Model Predictive Control of a Cable-Robot-Based Motion Simulator

DEFF Research Database (Denmark)

Katliar, Mikhail; Fischer, Joerg; Frison, Gianluca

2017-01-01

In this paper we present the implementation of a model-predictive controller (MPC) for real-time control of a cable-robot-based motion simulator. The controller computes control inputs such that a desired acceleration and angular velocity at a defined point in simulator's cabin are tracked while...... satisfying constraints imposed by working space and allowed cable forces of the robot. In order to fully use the simulator capabilities, we propose an approach that includes the motion platform actuation in the MPC model. The tracking performance and computation time of the algorithm are investigated...

Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing

Science.gov (United States)

Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng

2017-05-01

Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.

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

Science.gov (United States)

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.

The nonlinear Maxwell-type model for viscoelastoplastic materials: simulation of temperature influence on creep, relaxation and strain-stress curves

Directory of Open Access Journals (Sweden)

Andrew V. Khokhlov

2017-04-01

Full Text Available The nonlinear Maxwell-type constitutive relation with two arbitrary material functions for viscoelastoplastic multi-modulus materials is studied analytically in uniaxial isothermic case to reveal the model abilities and applicability scope and to develop techniques of its identification, tuning and fitting. The constitutive equation is aimed at adequate modeling of the rheological phenomena set which is typical for reonomic materials exhibiting non-linear hereditary properties, strong strain rate sensitivity, secondary creep, yielding at constant stress, tension compression asymmetry and such temperature effects as increase of material compliance, strain rate sensitivity and rates of dissipation, relaxation, creep and plastic strain accumulation with temperature growth. The model is applicable for simulation of mechanical behaviour of various polymers, their solutions and melts, solid propellants, sand-asphalt concretes, composite materials, titanium and aluminum alloys, ceramics at high temperature and so on. To describe the influence of temperature on material mechanical behavior (under isothermic conditions, two scalar material parameters of the model (viscosity coefficient and “modulus of elasticity” are considered as a functions of temperature level. The general restrictions on their properties which are necessary and sufficient for adequate qualitative description of the basic thermomechanical phenomena related to typical temperature influence on creep and relaxation curves, creep recovery curves, creep curves under step-wise loading and quasi-static stress-strain curves of viscoelastoplastic materials are obtained. The restrictions are derived using systematic analytical study of general qualitative features of the theoretic creep and relaxation curves, creep curves under step-wise loading, long-term strength curves and stress-strain curves at constant strain or stress rates generated by the constitutive equation (under minimal

Calibration of Mine Ventilation Network Models Using the Non-Linear Optimization Algorithm

Directory of Open Access Journals (Sweden)

Guang Xu

2017-12-01

Full Text Available Effective ventilation planning is vital to underground mining. To ensure stable operation of the ventilation system and to avoid airflow disorder, mine ventilation network (MVN models have been widely used in simulating and optimizing the mine ventilation system. However, one of the challenges for MVN model simulation is that the simulated airflow distribution results do not match the measured data. To solve this problem, a simple and effective calibration method is proposed based on the non-linear optimization algorithm. The calibrated model not only makes simulated airflow distribution results in accordance with the on-site measured data, but also controls the errors of other parameters within a minimum range. The proposed method was then applied to calibrate an MVN model in a real case, which is built based on ventilation survey results and Ventsim software. Finally, airflow simulation experiments are carried out respectively using data before and after calibration, whose results were compared and analyzed. This showed that the simulated airflows in the calibrated model agreed much better to the ventilation survey data, which verifies the effectiveness of calibrating method.

Application of H∞ control theory to power control of a nonlinear reactor model

International Nuclear Information System (INIS)

Suzuki, Katsuo; Shimazaki, Junya; Shinohara, Yoshikuni

1993-01-01

The H∞ control theory is applied to the compensator design of a nonlinear nuclear reactor model, and the results are compared with standard linear quadratic Gaussian (LQG) control. The reactor model is assumed to be provided with a control rod drive system having the compensation of rod position feedback. The nonlinearity of the reactor model exerts a great influence on the stability of the control system, and hence, it is desirable for a power control system of a nuclear reactor to achieve robust stability and to improve the sensitivity of the feedback control system. A computer simulation based on a power control system synthesized by LQG control was performed revealing that the control system has some stationary offset and less stability. Therefore, here, attention is given to the development of a methodology for robust control that can withstand exogenous disturbances and nonlinearity in view of system parameter changes. The developed methodology adopts H∞ control theory in the feedback system and shows interesting features of robustness. The results of the computer simulation indicate that the feedback control system constructed by the developed H∞ compensator possesses sufficient robustness of control on the stability and disturbance attenuation, which are essential for the safe operation of a nuclear reactor

Single-step emulation of nonlinear fiber-optic link with gaussian mixture model

DEFF Research Database (Denmark)

Borkowski, Robert; Doberstein, Andy; Haisch, Hansjörg

2015-01-01

We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission.......We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission....

Identification of nonlinear anelastic models

International Nuclear Information System (INIS)

Draganescu, G E; Bereteu, L; Ercuta, A

2008-01-01

A useful nonlinear identification technique applied to the anelastic and rheologic models is presented in this paper. First introduced by Feldman, the method is based on the Hilbert transform, and is currently used for identification of the nonlinear vibrations

Relation between nonlinear models and gauge ambiguities

International Nuclear Information System (INIS)

Balachandran, A.P.; Ramachandran, R.; Rupertsberger, H.; Skagerstam, B.S.

1980-01-01

We show that the solutions of a class of nonlinear models also generate gauge ambiguities in the vacuum sector of Yang-Mills theories. Our results extend known connections between gauge ambiguities and certain nonlinear sigma-models, and clarify the underlying group theory. For many nonlinear models, we also give a simple, intrinsic parametrization of physical fields (which have values in a homogeneous space of a group). (orig.)

Development and validation of a viscoelastic and nonlinear liver model for needle insertion

Energy Technology Data Exchange (ETDEWEB)

Kobayashi, Yo [Waseda University, Consolidated Research Institute for Advanced Science and Medical Care, Shinjuku, Tokyo (Japan); Onishi, Akinori; Hoshi, Takeharu; Kawamura, Kazuya [Waseda University, Graduate School of Science and Engineering, Shinjuku (Japan); Hashizume, Makoto [Kyushu University Hospital, Center for the Integration of Advanced Medicine and Innovative Technology, Fukuoka (Japan); Fujie, Masakatsu G. [Waseda University, Graduate School of Science and Engineering, Faculty of Science and Engineering, Shinjuku (Japan)

2009-01-15

The objective of our work is to develop and validate a viscoelastic and nonlinear physical liver model for organ model-based needle insertion, in which the deformation of an organ is estimated and predicted, and the needle path is determined with organ deformation taken into consideration. First, an overview is given of the development of the physical liver model. The material properties of the liver considering viscoelasticity and nonlinearity are modeled based on the measured data collected from a pig's liver. The method to develop the liver model using FEM is also shown. Second, the experimental method to validate the model is explained. Both in vitro and in vivo experiments that made use of a pig's liver were conducted for comparison with the simulation using the model. Results of the in vitro experiment showed that the model reproduces nonlinear and viscoelastic response of displacement at an internally located point with high accuracy. For a force up to 0.45 N, the maximum error is below 1 mm. Results of the in vivo experiment showed that the model reproduces the nonlinear increase of load upon the needle during insertion. Based on these results, the liver model developed and validated in this work reproduces the physical response of a liver in both in vitro and in vivo situations. (orig.)

Nonlinear Dynamic Modeling of a Fixed-Wing Unmanned Aerial Vehicle: a Case Study of Wulung

Directory of Open Access Journals (Sweden)

Fadjar Rahino Triputra

2015-07-01

Full Text Available Developing a nonlinear adaptive control system for a fixed-wing unmanned aerial vehicle (UAV requires a mathematical representation of the system dynamics analytically as a set of differential equations in the form of a strict-feedback systems. This paper presents a method for modeling a nonlinear flight dynamics of the fixed-wing UAV of BPPT Wulung in any conditions of the flight altitude and airspeed for the first step into designing a nonlinear adaptive controller. The model was formed into 10-DOF differential equations in the form of strict-feedback systems which separates the terms of elevator, aileron, rudder and throttle from the model. The model simulation results show the behavior of the flight dynamics of the Wulung UAV and also prove the compliance with the actual flight test results.

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

The cultural implications of growth: Modeling nonlinear interaction of trait selection and population dynamics.

Science.gov (United States)

Antoci, Angelo; Galeotti, Marcello; Russu, Paolo; Luigi Sacco, Pier

2018-05-01

In this paper, we study a nonlinear model of the interaction between trait selection and population dynamics, building on previous work of Ghirlanda et al. [Theor. Popul. Biol. 77, 181-188 (2010)] and Antoci et al. [Commun. Nonlinear Sci. Numer. Simul. 58, 92-106 (2018)]. We establish some basic properties of the model dynamics and present some simulations of the fine-grained structure of alternative dynamic regimes for chosen combinations of parameters. The role of the parameters that govern the reinforcement/corruption of maladaptive vs. adaptive traits is of special importance in determining the model's dynamic evolution. The main implication of this result is the need to pay special attention to the structural forces that may favor the emergence and consolidation of maladaptive traits in contemporary socio-economies, as it is the case, for example, for the stimulation of dysfunctional consumption habits and lifestyles in the pursuit of short-term profits.

The cultural implications of growth: Modeling nonlinear interaction of trait selection and population dynamics

Science.gov (United States)

Antoci, Angelo; Galeotti, Marcello; Russu, Paolo; Luigi Sacco, Pier

2018-05-01

In this paper, we study a nonlinear model of the interaction between trait selection and population dynamics, building on previous work of Ghirlanda et al. [Theor. Popul. Biol. 77, 181-188 (2010)] and Antoci et al. [Commun. Nonlinear Sci. Numer. Simul. 58, 92-106 (2018)]. We establish some basic properties of the model dynamics and present some simulations of the fine-grained structure of alternative dynamic regimes for chosen combinations of parameters. The role of the parameters that govern the reinforcement/corruption of maladaptive vs. adaptive traits is of special importance in determining the model's dynamic evolution. The main implication of this result is the need to pay special attention to the structural forces that may favor the emergence and consolidation of maladaptive traits in contemporary socio-economies, as it is the case, for example, for the stimulation of dysfunctional consumption habits and lifestyles in the pursuit of short-term profits.

Simulating nonlinear steady-state traveling waves on the falling liquid film entrained by a gas flow

Science.gov (United States)

Tsvelodub, O. Yu; Bocharov, A. A.

2017-09-01

The article is devoted to the simulation of nonlinear waves on a liquid film flowing under gravity in the known stress field at the interface. The paper studies nonlinear waves on a liquid film, flowing under the action of gravity in a known stress field at the interface. In the case of small Reynolds numbers the problem is reduced to the consideration of solutions of the nonlinear integral-differential equation for film thickness deviation from the undisturbed level. The periodic and soliton steady-state traveling solutions of this equation have been numerically found. The analysis of branching of new families of steady-state traveling solutions has been performed. In particular, it is shown that this model equation has solutions in the form of solitons-humps.

Nonlinear analysis and simulation of soliton in the traffic flow; Kotsu jutai soliton no hassei kiko nikansuru kenkyu

Energy Technology Data Exchange (ETDEWEB)

Matsumura, M. [Shizuoka University, Shizuoka (Japan); Nagatani, T. [Shizuoka University, Shizuoka (Japan). Faculty of Engineering

1999-07-25

Traffic jams are investigated numerically and analystically in the optimal velocity model on a single-line highway. The condition is found whether or not traffic jams occur when a car stops instantly. It is shown that traffic soliton appears at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability point. The soliton obtained from the nonlinear analysis is consistent with that of the numerical simulation. (author)

3D nonlinear numerical simulation of the current-convective instability in detached diverter plasma

Science.gov (United States)

Stepanenko, Alexander; Krasheninnikov, Sergei

2017-10-01

One of the possible mechanisms responsible for strong radiation fluctuations observed in the recent experiments with detached plasmas at ASDEX Upgrade [Potzel et al., Nuclear Fusion, 2014] can be related to the onset of the current-convective instability (CCI) driven by strong asymmetry of detachment in the inner and outer tokamak divertors [Krasheninnikov and Smolyakov, PoP, 2016]. In this study we present the first results of 3D nonlinear numerical simulations of the CCI in divertor plasma for the conditions relevant to the AUG experiment. The general physical model used to simulate the CCI, qualitative estimates for the instability characteristic growth rate and transverse wavelengths derived for plasma, which is spatially inhomogeneous both across and along the magnetic field lines, are presented. The simulation results, demonstrating nonlinear dynamics of the CCI, provide the frequency spectra of turbulent divertor plasma fluctuations showing good agreement with the available experimental data. This material is based upon the work supported by the U.S. Department of Energy under Award No. DE-FG02-04ER54739 at UCSD and by the Russian Ministry of Education and Science Grant No. 14.Y26.31.0008 at MEPhI.

An expert system for national economy model simulations

Directory of Open Access Journals (Sweden)

Roljić Lazo

2002-01-01

Full Text Available There are some fundamental economic uncertainties. We cannot forecast economic events with a very high scientific precision. It is very clear that there does not exist a unique 'general' model, which can yield all answers to a wide range of macroeconomic issues. Therefore, we use several different kinds of models on segments of the macroeconomic problem. Different models can distinguish/solve economy desegregation, time series analysis and other subfactors involved in macroeconomic problem solving. A major issue becomes finding a meaningful method to link these econometric models. Macroeconomic models were linked through development of an Expert System for National Economy Model Simulations (ESNEMS. ESNEMS consists of five parts: (1 small-scale short-term national econometric model, (2 Methodology of Interactive Nonlinear Goal Programming (MINGP, (3 data-base of historical macro-economic aggregates, (4 software interface for interactive communications between a model and a decision maker, and (5 software for solving problems. ESNEMS was developed to model the optimum macro-economic policy of a developing country (SFRY-formerly Yugoslavia. Most econometric models are very complex. Optimizing of the economic policy is typically defined as a nonlinear goal programming problem. To solve/optimize these models, a new methodology, MINGP, was developed as a part of ESNEMS. MINGP is methodologically based on linear goal programming and feasible directions method. Using Euler's Homogeneous Function Theorem, MINGP linearizes nonlinear homogeneous functions. The highest priorities in minimizing the objective function are the growth of gross domestic product and the decrease of inflation. In the core of the optimization model, MINGP, there is a small-scale econometric model. This model was designed through analysis of the causal relations in the SFRY's social reproduction process of the past 20 years. The objective of the econometric model is to simulate

Fast simulation of non-linear pulsed ultrasound fields using an angular spectrum approach

DEFF Research Database (Denmark)

Du, Yigang; Jensen, Jørgen Arendt

2013-01-01

A fast non-linear pulsed ultrasound field simulation is presented. It is implemented based on an angular spectrum approach (ASA), which analytically solves the non-linear wave equation. The ASA solution to the Westervelt equation is derived in detail. The calculation speed is significantly...... increased compared to a numerical solution using an operator splitting method (OSM). The ASA has been modified and extended to pulsed non-linear ultrasound fields in combination with Field II, where any array transducer with arbitrary geometry, excitation, focusing and apodization can be simulated...... with a center frequency of 5 MHz. The speed is increased approximately by a factor of 140 and the calculation time is 12 min with a standard PC, when simulating the second harmonic pulse at the focal point. For the second harmonic point spread function the full width error is 1.5% at 6 dB and 6.4% at 12 d...

Physics constrained nonlinear regression models for time series

International Nuclear Information System (INIS)

Majda, Andrew J; Harlim, John

2013-01-01

A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)

Non-linear finite element modeling

DEFF Research Database (Denmark)

Mikkelsen, Lars Pilgaard

The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...

Correlations and Non-Linear Probability Models

DEFF Research Database (Denmark)

Breen, Richard; Holm, Anders; Karlson, Kristian Bernt

2014-01-01

the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....

Modeling of Nonlinear Propagation in Multi-layer Biological Tissues for Strong Focused Ultrasound

International Nuclear Information System (INIS)

Ting-Bo, Fan; Zhen-Bo, Liu; Zhe, Zhang; Dong, Zhang; Xiu-Fen, Gong

2009-01-01

A theoretical model of the nonlinear propagation in multi-layered tissues for strong focused ultrasound is proposed. In this model, the spheroidal beam equation (SBE) is utilized to describe the nonlinear sound propagation in each layer tissue, and generalized oblique incidence theory is used to deal with the sound transmission between two layer tissues. Computer simulation is performed on a fat-muscle-liver tissue model under the irradiation of a 1 MHz focused transducer with a large aperture angle of 35°. The results demonstrate that the tissue layer would change the amplitude of sound pressure at the focal region and cause the increase of side petals. (fundamental areas of phenomenology (including applications))

A nonlinear finite element model of a piezoelectric tube actuator with hysteresis and creep

International Nuclear Information System (INIS)

Chung, S H; Fung, Eric H K

2010-01-01

Piezoelectric tube actuators are commonly used for nanopositioning in atomic force microscopes (AFMs). However, piezoelectric tube actuators exhibit hysteresis and creep which significantly limit the accuracy of nanopositioning. A finite element model of a piezoelectric tube actuator with hysteresis and creep is important for control purposes, but so far one has not been developed. The purpose of this paper is to present a nonlinear finite element (FE) model with hysteresis and creep for design purposes. Prandtl–Ishlinskii (PI) hysteresis operators and creep operators are adopted into constitutive equations. The nonlinear FE model is formulated using energy approach and Hamilton's principle. The parameters of the PI hysteresis operators and the creep operators are identified by comparing the simulation results and experimental results of other researchers. The working operation of the piezoelectric tube actuator is simulated by the reduced order FE model, and the displacement error due to hysteresis, creep and coupling effect is investigated. An output feedback controller is implemented into the reduced order FE model to show that this model is controllable

Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents

International Nuclear Information System (INIS)

Hoelzl, M; Merkel, P; Lackner, K; Strumberger, E; Huijsmans, G T A; Aleynikova, K; Liu, F; Atanasiu, C; Nardon, E; Fil, A; McAdams, R; Chapman, I

2014-01-01

The dynamics of large scale plasma instabilities can be strongly influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK [1, 2] has been coupled [3] with the resistive wall code STARWALL [4], which allows us to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described

Modelling long term rockslide displacements with non-linear time-dependent relationships

Science.gov (United States)

De Caro, Mattia; Volpi, Giorgio; Castellanza, Riccardo; Crosta, Giovanni; Agliardi, Federico

2015-04-01

Rockslides undergoing rapid changes in behaviour pose major risks in alpine areas, and require careful characterization and monitoring both for civil protection and mitigation activities. In particular, these instabilities can undergo very slow movement with occasional and intermittent acceleration/deceleration stages of motion potentially leading to collapse. Therefore, the analysis of such instabilities remains a challenging issue. Rockslide displacements are strongly conditioned by hydrologic factors as suggested by correlations with groundwater fluctuations, snowmelt, with a frequently observed delay between perturbation and system reaction. The aim of this work is the simulation of the complex time-dependent behaviour of two case studies for which also a 2D transient hydrogeological simulation has been performed: Vajont rockslide (1960 to 1963) and the recent Mt. de La Saxe rockslide (2009 to 2012). Non-linear time-dependent constitutive relationships have been used to describe long-term creep deformation. Analyses have been performed using a "rheological-mechanical" approach that fits idealized models (e.g. viscoelastic, viscoplastic, elasto-viscoplastic, Burgers, nonlinear visco-plastic) to the experimental behaviour of specific materials by means of numerical constants. Bidimensional simulations were carried out using the finite difference code FLAC. Displacements time-series, available for the two landslides, show two superimposed deformation mechanisms: a creep process, leading to movements under "steady state" conditions (e.g. constant groundwater level), and a "dynamic" process, leading to an increase in displacement rate due to changes of external loads (e.g. groundwater level). For both cases sliding mass is considered as an elasto-plastic body subject to its self-weight, inertial and seepage forces varying with time according to water table fluctuation (due to snowmelt or changing in reservoir level) and derived from the previous hydrogeological

Decoupled ARX and RBF Neural Network Modeling Using PCA and GA Optimization for Nonlinear Distributed Parameter Systems.

Science.gov (United States)

Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing

2018-02-01

Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.

Stationary nonlinear Airy beams

International Nuclear Information System (INIS)

Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.

2011-01-01

We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.

Systematic simulations of modified gravity: symmetron and dilaton models

International Nuclear Information System (INIS)

Brax, Philippe; Davis, Anne-Christine; Li, Baojiu; Winther, Hans A.; Zhao, Gong-Bo

2012-01-01

We study the linear and nonlinear structure formation in the dilaton and symmetron models of modified gravity using a generic parameterisation which describes a large class of scenarios using only a few parameters, such as the coupling between the scalar field and the matter, and the range of the scalar force on very large scales. For this we have modified the N-body simulation code ECOSMOG, which is a variant of RAMSES working in modified gravity scenarios, to perform a set of 110 simulations for different models and parameter values, including the default ΛCDM. These simulations enable us to explore a large portion of the parameter space. We have studied the effects of modified gravity on the matter power spectrum and mass function, and found a rich and interesting phenomenology where the difference with the ΛCDM template cannot be reproduced by a linear analysis even on scales as large as k ∼ 0.05 hMpc −1 . Our results show the full effect of screening on nonlinear structure formation and the associated deviation from ΛCDM. We also investigate how differences in the force mediated by the scalar field in modified gravity models lead to qualitatively different features for the nonlinear power spectrum and the halo mass function, and how varying the individual model parameters changes these observables. The differences are particularly large in the nonlinear power spectra whose shapes for f(R), dilaton and symmetron models vary greatly, and where the characteristic bump around 1 hMpc −1 of f(R) models is preserved for symmetrons, whereas an increase on much smaller scales is particular to symmetrons. No bump is present for dilatons where a flattening of the power spectrum takes place on small scales. These deviations from ΛCDM and the differences between modified gravity models, such as dilatons and symmetrons, could be tested with future surveys

Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints

Directory of Open Access Journals (Sweden)

Shaochong Yang

2017-01-01

Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.

A non-linear and stochastic response surface method for Bayesian estimation of uncertainty in soil moisture simulation from a land surface model

Directory of Open Access Journals (Sweden)

F. Hossain

2004-01-01

Full Text Available This study presents a simple and efficient scheme for Bayesian estimation of uncertainty in soil moisture simulation by a Land Surface Model (LSM. The scheme is assessed within a Monte Carlo (MC simulation framework based on the Generalized Likelihood Uncertainty Estimation (GLUE methodology. A primary limitation of using the GLUE method is the prohibitive computational burden imposed by uniform random sampling of the model's parameter distributions. Sampling is improved in the proposed scheme by stochastic modeling of the parameters' response surface that recognizes the non-linear deterministic behavior between soil moisture and land surface parameters. Uncertainty in soil moisture simulation (model output is approximated through a Hermite polynomial chaos expansion of normal random variables that represent the model's parameter (model input uncertainty. The unknown coefficients of the polynomial are calculated using limited number of model simulation runs. The calibrated polynomial is then used as a fast-running proxy to the slower-running LSM to predict the degree of representativeness of a randomly sampled model parameter set. An evaluation of the scheme's efficiency in sampling is made through comparison with the fully random MC sampling (the norm for GLUE and the nearest-neighborhood sampling technique. The scheme was able to reduce computational burden of random MC sampling for GLUE in the ranges of 10%-70%. The scheme was also found to be about 10% more efficient than the nearest-neighborhood sampling method in predicting a sampled parameter set's degree of representativeness. The GLUE based on the proposed sampling scheme did not alter the essential features of the uncertainty structure in soil moisture simulation. The scheme can potentially make GLUE uncertainty estimation for any LSM more efficient as it does not impose any additional structural or distributional assumptions.

An evaluation of bias in propensity score-adjusted non-linear regression models.

Science.gov (United States)

Wan, Fei; Mitra, Nandita

2018-03-01

Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

Aerodynamic Modeling of NREL 5-MW Wind Turbine for Nonlinear Control System Design: A Case Study Based on Real-Time Nonlinear Receding Horizon Control

Directory of Open Access Journals (Sweden)

Pedro A. Galvani

2016-08-01

Full Text Available The work presented in this paper has two major aspects: (i investigation of a simple, yet efficient model of the NREL (National Renewable Energy Laboratory 5-MW reference wind turbine; (ii nonlinear control system development through a real-time nonlinear receding horizon control methodology with application to wind turbine control dynamics. In this paper, the results of our simple wind turbine model and a real-time nonlinear control system implementation are shown in comparison with conventional control methods. For this purpose, the wind turbine control problem is converted into an optimization problem and is directly solved by the nonlinear backwards sweep Riccati method to generate the control protocol, which results in a non-iterative algorithm. One main contribution of this paper is that we provide evidence through simulations, that such an advanced control strategy can be used for real-time control of wind turbine dynamics. Examples are provided to validate and demonstrate the effectiveness of the presented scheme.

Global attractivity of an almost periodic N-species nonlinear ecological competitive model

Science.gov (United States)

Xia, Yonghui; Han, Maoan; Huang, Zhenkun

2008-01-01

By using comparison theorem and constructing suitable Lyapunov functional, we study the following almost periodic nonlinear N-species competitive Lotka-Volterra model: A set of sufficient conditions is obtained for the existence and global attractivity of a unique positive almost periodic solution of the above model. As applications, some special competition models are studied again, our new results improve and generalize former results. Examples and their simulations show the feasibility of our main results.

Neurobiologically Inspired Approaches to Nonlinear Process Control and Modeling

Science.gov (United States)

1999-12-31

incorporates second messenger reaction kinetics and calcium dynamics to represent the nonlinear dynamics and the crucial role of neuromodulation in local...reflex). The dynamic neuromodulation as a mechanism for the nonlinear attenuation is the novel result of this study. Ear- lier simulations have shown

International Benchmark on Numerical Simulations for 1D, Nonlinear Site Response (PRENOLIN) : Verification Phase Based on Canonical Cases

NARCIS (Netherlands)

Régnier, Julie; Bonilla, Luis-Fabian; Bard, Pierre-Yves; Bertrand, Etienne; Hollender, Fabrice; Kawase, Hiroshi; Sicilia, Deborah; Arduino, Pedro; Amorosi, Angelo; Asimaki, Dominiki; Pisano, F.

2016-01-01

PREdiction of NOn‐LINear soil behavior (PRENOLIN) is an international benchmark aiming to test multiple numerical simulation codes that are capable of predicting nonlinear seismic site response with various constitutive models. One of the objectives of this project is the assessment of the

Nonlinear electromechanical modelling and dynamical behavior analysis of a satellite reaction wheel

Science.gov (United States)

Aghalari, Alireza; Shahravi, Morteza

2017-12-01

The present research addresses the satellite reaction wheel (RW) nonlinear electromechanical coupling dynamics including dynamic eccentricity of brushless dc (BLDC) motor and gyroscopic effects, as well as dry friction of shaft-bearing joints (relative small slip) and bearing friction. In contrast to other studies, the rotational velocity of the flywheel is considered to be controllable, so it is possible to study the reaction wheel dynamical behavior in acceleration stages. The RW is modeled as a three-phases BLDC motor as well as flywheel with unbalances on a rigid shaft and flexible bearings. Improved Lagrangian dynamics for electromechanical systems is used to obtain the mathematical model of the system. The developed model can properly describe electromechanical nonlinear coupled dynamical behavior of the satellite RW. Numerical simulations show the effectiveness of the presented approach.

Nonlinear Simulations of Trapped Electron Mode Turbulence in Low Magnetic Shear Stellarators

Science.gov (United States)

Faber, B. J.; Pueschel, M. J.; Terry, P. W.; Hegna, C. C.

2017-10-01

Optimized stellarators, like the Helically Symmetric eXperiment (HSX), often operate with small global magnetic shear to avoid low-order rational surfaces and magnetic islands. Nonlinear, flux-tube gyrokinetic simulations of density-gradient-driven Trapped Electron Mode (TEM) turbulence in HSX shows two distinct spectral fluctuation regions: long-wavelength slab-like TEMs localized by global magnetic shear that extend along field lines and short-wavelength TEMs localized by local magnetic shear to a single helical bad curvature region. The slab-like TEMs require computational domains significantly larger than one poloidal turn and are computationally expensive, making turbulent optimization studies challenging. A computationally more efficient, zero-average-magnetic-shear approximation is shown to sufficiently describe the relevant nonlinear physics and replicate finite-shear computations, and can be exploited in quasilinear models based on linear gyrokinetics as a feasible optimization tool. TEM quasilinear heat fluxes are computed with the zero-shear approximation and compared to experimentally-relevant nonlinear gyrokinetic TEM heat fluxes for HSX. Research supported by U.S. DoE Grants DE-FG02-99ER54546, DE-FG02-93ER54222 and DE-FG02-89ER53291.

Explicit Nonlinear Model Predictive Control for a Saucer-Shaped Unmanned Aerial Vehicle

Directory of Open Access Journals (Sweden)

Zhihui Xing

2013-01-01

Full Text Available A lifting body unmanned aerial vehicle (UAV generates lift by its body and shows many significant advantages due to the particular shape, such as huge loading space, small wetted area, high-strength fuselage structure, and large lifting area. However, designing the control law for a lifting body UAV is quite challenging because it has strong nonlinearity and coupling, and usually lacks it rudders. In this paper, an explicit nonlinear model predictive control (ENMPC strategy is employed to design a control law for a saucer-shaped UAV which can be adequately modeled with a rigid 6-degrees-of-freedom (DOF representation. In the ENMPC, control signal is calculated by approximation of the tracking error in the receding horizon by its Taylor-series expansion to any specified order. It enhances the advantages of the nonlinear model predictive control and eliminates the time-consuming online optimization. The simulation results show that ENMPC is a propriety strategy for controlling lifting body UAVs and can compensate the insufficient control surface area.

Models of the delayed nonlinear Raman response in diatomic gases

International Nuclear Information System (INIS)

Palastro, J. P.; Antonsen, T. M. Jr.; Pearson, A.

2011-01-01

We examine the delayed response of a diatomic gas to a polarizing laser field with the goal of obtaining computationally efficient methods for use with laser pulse propagation simulations. We demonstrate that for broadband pulses, heavy molecules such as O 2 and N 2 , and typical atmospheric temperatures, the initial delayed response requires only classical physics. The linear kinetic Green's function is derived from the Boltzmann equation and shown to be in excellent agreement with full density-matrix calculations. A straightforward perturbation approach for the fully nonlinear, kinetic impulse response is also presented. With the kinetic theory a reduced fluid model of the diatomic gas' orientation is derived. Transport coefficients are introduced to model the kinetic phase mixing of the delayed response. In addition to computational rapidity, the fluid model provides intuition through the use of familiar macroscopic quantities. Both the kinetic and the fluid descriptions predict a nonlinear steady-state alignment after passage of the laser pulse, which in the fluid model is interpreted as an anisotropic temperature of the diatomic fluid with respect to motion about the polarization axis.

Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics

DEFF Research Database (Denmark)

Iwankiewicz, R.; Nielsen, Søren R. K.

Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...

Nonlinearities in modified gravity cosmology: Signatures of modified gravity in the nonlinear matter power spectrum

International Nuclear Information System (INIS)

Cui Weiguang; Zhang Pengjie; Yang Xiaohu

2010-01-01

A large fraction of cosmological information on dark energy and gravity is encoded in the nonlinear regime. Precision cosmology thus requires precision modeling of nonlinearities in general dark energy and modified gravity models. We modify the Gadget-2 code and run a series of N-body simulations on modified gravity cosmology to study the nonlinearities. The modified gravity model that we investigate in the present paper is characterized by a single parameter ζ, which determines the enhancement of particle acceleration with respect to general relativity (GR), given the identical mass distribution (ζ=1 in GR). The first nonlinear statistics we investigate is the nonlinear matter power spectrum at k < or approx. 3h/Mpc, which is the relevant range for robust weak lensing power spectrum modeling at l < or approx. 2000. In this study, we focus on the relative difference in the nonlinear power spectra at corresponding redshifts where different gravity models have the same linear power spectra. This particular statistics highlights the imprint of modified gravity in the nonlinear regime and the importance of including the nonlinear regime in testing GR. By design, it is less susceptible to the sample variance and numerical artifacts. We adopt a mass assignment method based on wavelet to improve the power spectrum measurement. We run a series of tests to determine the suitable simulation specifications (particle number, box size, and initial redshift). We find that, the nonlinear power spectra can differ by ∼30% for 10% deviation from GR (|ζ-1|=0.1) where the rms density fluctuations reach 10. This large difference, on one hand, shows the richness of information on gravity in the corresponding scales, and on the other hand, invalidates simple extrapolations of some existing fitting formulae to modified gravity cosmology.

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

Science.gov (United States)

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

A model reference and sensitivity model-based self-learning fuzzy logic controller as a solution for control of nonlinear servo systems

NARCIS (Netherlands)

Kovacic, Z.; Bogdan, S.; Balenovic, M.

1999-01-01

In this paper, the design, simulation and experimental verification of a self-learning fuzzy logic controller (SLFLC) suitable for the control of nonlinear servo systems are described. The SLFLC contains a learning algorithm that utilizes a second-order reference model and a sensitivity model

A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials

International Nuclear Information System (INIS)

Zhou Haomiao; Zhou Youhe; Zheng Xiaojing; Ye Qiang; Wei Jing

2009-01-01

In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material

Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

Science.gov (United States)

Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

2017-12-01

An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

Response to a pure tone in a nonlinear mechanical-electrical-acoustical model of the cochlea.

Science.gov (United States)

Meaud, Julien; Grosh, Karl

2012-03-21

In this article, a nonlinear mathematical model is developed based on the physiology of the cochlea of the guinea pig. The three-dimensional intracochlear fluid dynamics are coupled to a micromechanical model of the organ of Corti and to electrical potentials in the cochlear ducts and outer hair cells (OHC). OHC somatic electromotility is modeled by linearized piezoelectric relations whereas the OHC hair-bundle mechanoelectrical transduction current is modeled as a nonlinear function of the hair-bundle deflection. The steady-state response of the cochlea to a single tone is simulated in the frequency domain using an alternating frequency time scheme. Compressive nonlinearity, harmonic distortion, and DC shift on the basilar membrane (BM), tectorial membrane (TM), and OHC potentials are predicted using a single set of parameters. The predictions of the model are verified by comparing simulations to available in vivo experimental data for basal cochlear mechanics. In particular, the model predicts more amplification on the reticular lamina (RL) side of the cochlear partition than on the BM, which replicates recent measurements. Moreover, small harmonic distortion and DC shifts are predicted on the BM, whereas more significant harmonic distortion and DC shifts are predicted in the RL and TM displacements and in the OHC potentials. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Modeling of Volatility with Non-linear Time Series Model

OpenAIRE

Kim Song Yon; Kim Mun Chol

2013-01-01

In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.

Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment

Directory of Open Access Journals (Sweden)

Junhong Li

2013-01-01

Full Text Available This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.

Nonlinear dynamic modeling of a V-shaped metal based thermally driven MEMS actuator for RF switches

Science.gov (United States)

Bakri-Kassem, Maher; Dhaouadi, Rached; Arabi, Mohamed; Estahbanati, Shahabeddin V.; Abdel-Rahman, Eihab

2018-05-01

In this paper, we propose a new dynamic model to describe the nonlinear characteristics of a V-shaped (chevron) metallic-based thermally driven MEMS actuator. We developed two models for the thermal actuator with two configurations. The first MEMS configuration has a small tip connected to the shuttle, while the second configuration has a folded spring and a wide beam attached to the shuttle. A detailed finite element model (FEM) and a lumped element model (LEM) are proposed for each configuration to completely characterize the electro-thermal and thermo-mechanical behaviors. The nonlinear resistivity of the polysilicon layer is extracted from the measured current-voltage (I-V) characteristics of the actuator and the simulated corresponding temperatures in the FEM model, knowing the resistivity of the polysilicon at room temperature from the manufacture’s handbook. Both developed models include the nonlinear temperature-dependent material properties. Numerical simulations in comparison with experimental data using a dedicated MEMS test apparatus verify the accuracy of the proposed LEM model to represent the complex dynamics of the thermal MEMS actuator. The LEM and FEM simulation results show an accuracy ranging from a maximum of 13% error down to a minimum of 1.4% error. The actuator with the lower thermal load to air that includes a folded spring (FS), also known as high surface area actuator is compared to the actuator without FS, also known as low surface area actuator, in terms of the I-V characteristics, power consumption, and experimental static and dynamic responses of the tip displacement.

Comparison of linear and nonlinear implementation of the compartmental tissue uptake model for dynamic contrast-enhanced MRI.

Science.gov (United States)

Kallehauge, Jesper F; Sourbron, Steven; Irving, Benjamin; Tanderup, Kari; Schnabel, Julia A; Chappell, Michael A

2017-06-01

Fitting tracer kinetic models using linear methods is much faster than using their nonlinear counterparts, although this comes often at the expense of reduced accuracy and precision. The aim of this study was to derive and compare the performance of the linear compartmental tissue uptake (CTU) model with its nonlinear version with respect to their percentage error and precision. The linear and nonlinear CTU models were initially compared using simulations with varying noise and temporal sampling. Subsequently, the clinical applicability of the linear model was demonstrated on 14 patients with locally advanced cervical cancer examined with dynamic contrast-enhanced magnetic resonance imaging. Simulations revealed equal percentage error and precision when noise was within clinical achievable ranges (contrast-to-noise ratio >10). The linear method was significantly faster than the nonlinear method, with a minimum speedup of around 230 across all tested sampling rates. Clinical analysis revealed that parameters estimated using the linear and nonlinear CTU model were highly correlated (ρ ≥ 0.95). The linear CTU model is computationally more efficient and more stable against temporal downsampling, whereas the nonlinear method is more robust to variations in noise. The two methods may be used interchangeably within clinical achievable ranges of temporal sampling and noise. Magn Reson Med 77:2414-2423, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Modeling, Simulation, and Experiment of Switched Reluctance Ocean Current Generator System

Directory of Open Access Journals (Sweden)

Hao Chen

2013-01-01

Full Text Available This paper presents nonlinear simulation model of switched reluctance (SR ocean current generator system on MATLAB/SIMULINK with describing the structure of generator system. The developed model is made up of main model, rotor position calculation module, controller module, gate module, power converter module, phase windings module, flux-linkage module, torque module, and power calculation module. The magnetization curves obtained by two-dimensional finite-element electromagnetic field calculation and the conjugated magnetic energy graphics obtained from the three-dimensional graphics of flux linkage are stored in the “Lookup Table” modules on MATLAB/SIMULINK. The hardware of the developed three-phase 12/8 structure SR ocean current generator system prototype with the experimental platform is presented. The simulation of the prototype is performed by the developed models, and the experiments have been carried out under the same condition with different output power, turn-off angle, and rotor speed. The simulated phase current waveforms agree well with the tested phase current waveforms experimentally. The simulated output voltage curves agree well with the tested output voltage curves experimentally. It is shown that the developed nonlinear simulation model of the three-phase 12/8 structure SR ocean current generator system is valid.

Recursive prediction error methods for online estimation in nonlinear state-space models

Directory of Open Access Journals (Sweden)

Dag Ljungquist

1994-04-01

Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.

A discrete element model for the investigation of the geometrically nonlinear behaviour of solids

Science.gov (United States)

Ockelmann, Felix; Dinkler, Dieter

2018-07-01

A three-dimensional discrete element model for elastic solids with large deformations is presented. Therefore, an discontinuum approach is made for solids. The properties of elastic material are transferred analytically into the parameters of a discrete element model. A new and improved octahedron gap-filled face-centred cubic close packing of spheres is split into unit cells, to determine the parameters of the discrete element model. The symmetrical unit cells allow a model with equal shear components in each contact plane and fully isotropic behaviour for Poisson's ratio above 0. To validate and show the broad field of applications of the new model, the pin-pin Euler elastica is presented and investigated. The thin and sensitive structure tends to undergo large deformations and rotations with a highly geometrically nonlinear behaviour. This behaviour of the elastica can be modelled and is compared to reference solutions. Afterwards, an improved more realistic simulation of the elastica is presented which softens secondary buckling phenomena. The model is capable of simulating solids with small strains but large deformations and a strongly geometrically nonlinear behaviour, taking the shear stiffness of the material into account correctly.

Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations

Science.gov (United States)

Liang, Fayun; Chen, Haibing; Huang, Maosong

2017-07-01

To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

The inherent complexity in nonlinear business cycle model in resonance

International Nuclear Information System (INIS)

Ma Junhai; Sun Tao; Liu Lixia

2008-01-01

Based on Abraham C.-L. Chian's research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions to one category of the nonlinear business cycle model in resonance condition. We have also analyzed the relation between amplitude and phase of second-order approximate solutions as well as the relation between outer excitements' amplitude, frequency approximate solutions, and system bifurcation parameters. Then we studied the system quasi-periodical solutions, annulus periodical solutions and the path leading to system bifurcation and chaotic state with different parameter combinations. Finally, we conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation for detecting the complexity of business cycles and systems in the future

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

Science.gov (United States)

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.

Linear and non-linear simulation of joints contact surface using ...

African Journals Online (AJOL)

The joint modelling including non-linear effects needs accurate and precise study of their behaviors. When joints are under the dynamic loading, micro, macro- slip happens in contact surface which is non-linear reason of the joint contact surface. The non-linear effects of joint contact surface on total behavior of structure are ...

Simulations of fluid flow through porous media based on cellular automata and non-linear dynamics

Energy Technology Data Exchange (ETDEWEB)

Paulson, K V

1992-05-15

A study is being carried out to apply cellular automata and non-linear dynamics in the construction of efficient and accurate computer simulations of multiphase fluid flow through porous media, with the objective of application to reservoir modelling for hydrocarbon recovery. An algorithm based on Boolean operations has been developed which transforms a PC clone into a highly efficient vector processor capable of cellular automata simulation of single fluid flow through two-dimensional rock matrix models of varying porosities. Macroscopic flow patterns have been established through spatial and temporal averaging with no floating point operations. Permeabilities of the different models have been calculated. Hardware allows the algorithm to function on dual processors on a PC platform using a video recording and editing facility. Very encouraging results have been obtained. 4 figs.

A coupling method for a cardiovascular simulation model which includes the Kalman filter.

Science.gov (United States)

Hasegawa, Yuki; Shimayoshi, Takao; Amano, Akira; Matsuda, Tetsuya

2012-01-01

Multi-scale models of the cardiovascular system provide new insight that was unavailable with in vivo and in vitro experiments. For the cardiovascular system, multi-scale simulations provide a valuable perspective in analyzing the interaction of three phenomenons occurring at different spatial scales: circulatory hemodynamics, ventricular structural dynamics, and myocardial excitation-contraction. In order to simulate these interactions, multiscale cardiovascular simulation systems couple models that simulate different phenomena. However, coupling methods require a significant amount of calculation, since a system of non-linear equations must be solved for each timestep. Therefore, we proposed a coupling method which decreases the amount of calculation by using the Kalman filter. In our method, the Kalman filter calculates approximations for the solution to the system of non-linear equations at each timestep. The approximations are then used as initial values for solving the system of non-linear equations. The proposed method decreases the number of iterations required by 94.0% compared to the conventional strong coupling method. When compared with a smoothing spline predictor, the proposed method required 49.4% fewer iterations.

Comparing coefficients of nested nonlinear probability models

DEFF Research Database (Denmark)

Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders

2011-01-01

In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...

Semi-physical Simulation Platform of a Parafoil Nonlinear Dynamic System

International Nuclear Information System (INIS)

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

2013-01-01

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

Lower extremity finite element model for crash simulation

Energy Technology Data Exchange (ETDEWEB)

Schauer, D.A.; Perfect, S.A.

1996-03-01

A lower extremity model has been developed to study occupant injury mechanisms of the major bones and ligamentous soft tissues resulting from vehicle collisions. The model is based on anatomically correct digitized bone surfaces of the pelvis, femur, patella and the tibia. Many muscles, tendons and ligaments were incrementally added to the basic bone model. We have simulated two types of occupant loading that occur in a crash environment using a non-linear large deformation finite element code. The modeling approach assumed that the leg was passive during its response to the excitation, that is, no active muscular contraction and therefore no active change in limb stiffness. The approach recognized that the most important contributions of the muscles to the lower extremity response are their ability to define and modify the impedance of the limb. When nonlinear material behavior in a component of the leg model was deemed important to response, a nonlinear constitutive model was incorporated. The accuracy of these assumptions can be verified only through a review of analysis results and careful comparison with test data. As currently defined, the model meets the objective for which it was created. Much work remains to be done, both from modeling and analysis perspectives, before the model can be considered complete. The model implements a modeling philosophy that can accurately capture both kinematic and kinetic response of the lower limb. We have demonstrated that the lower extremity model is a valuable tool for understanding the injury processes and mechanisms. We are now in a position to extend the computer simulation to investigate the clinical fracture patterns observed in actual crashes. Additional experience with this model will enable us to make a statement on what measures are needed to significantly reduce lower extremity injuries in vehicle crashes. 6 refs.

Non-linear friction in reciprocating hydraulic rod seals: Simulation and measurement

International Nuclear Information System (INIS)

Bullock, A K; Tilley, D G; Johnston, D N; Bowen, C R; Keogh, P S

2009-01-01

Non-linear seal friction can impede the performance of hydraulic actuation systems designed for high precision positioning with favourable dynamic response. Methods for predicting seal friction are required to help develop sealing systems for this type of application. Recent simulation techniques have claimed progress, although have yet to be validated experimentally. A conventional reciprocating rod seal is analysed using established elastohydrodynamic theory and the mixed lubrication Greenwood-Williamson-average Reynolds model. A test rig was used to assess the accuracy of the simulation results for both instroke and outstroke. Inverse hydrodynamic theory is shown to predict a U 0.5 power law between rod speed and friction. Comparison with experimental data shows the theory to be qualitatively inaccurate and to predict friction levels an order of magnitude lower than those measured. It was not possible to model the regions very close to the inlet and outlet due to the high pressure gradients at the edges of the contact. The mixed lubrication model produces friction levels within the correct order of magnitude, although incorrectly predicts higher friction during instroke than outstroke. Previous experiments have reported higher friction during instroke than outstroke for rectangular seals, suggesting that the mixed lubrication model used could possibly be suitable for symmetric seals, although not for seal tribology in general.

Modeling and simulation of different and representative engineering problems using Network Simulation Method.

Science.gov (United States)

Sánchez-Pérez, J F; Marín, F; Morales, J L; Cánovas, M; Alhama, F

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model.

Modeling, Simulation and Position Control of 3DOF Articulated Manipulator

Directory of Open Access Journals (Sweden)

Hossein Sadegh Lafmejani

2014-08-01

Full Text Available In this paper, the modeling, simulation and control of 3 degrees of freedom articulated robotic manipulator have been studied. First, we extracted kinematics and dynamics equations of the mentioned manipulator by using the Lagrange method. In order to validate the analytical model of the manipulator we compared the model simulated in the simulation environment of Matlab with the model was simulated with the SimMechanics toolbox. A sample path has been designed for analyzing the tracking subject. The system has been linearized with feedback linearization and then a PID controller was applied to track a reference trajectory. Finally, the control results have been compared with a nonlinear PID controller.

Nonlinear Control of Heartbeat Models

Directory of Open Access Journals (Sweden)

Witt Thanom

2011-02-01

Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.

Atomistic simulation and continuum modeling of graphene nanoribbons under uniaxial tension

International Nuclear Information System (INIS)

Lu, Qiang; Gao, Wei; Huang, Rui

2011-01-01

Atomistic simulations are performed to study the nonlinear mechanical behavior of graphene nanoribbons under quasistatic uniaxial tension, emphasizing the effects of edge structures (armchair and zigzag, without and with hydrogen passivation) on elastic modulus and fracture strength. The numerical results are analyzed within a theoretical model of thermodynamics, which enables determination of the bulk strain energy density, the edge energy density and the hydrogen adsorption energy density as nonlinear functions of the applied strain based on static molecular mechanics simulations. These functions can be used to describe mechanical behavior of graphene nanoribbons from the initial linear elasticity to fracture. It is found that the initial Young's modulus of a graphene nanoribbon depends on the ribbon width and the edge chirality. Furthermore, it is found that the nominal strain to fracture is considerably lower for graphene nanoribbons with armchair edges than for ribbons with zigzag edges. Molecular dynamics simulations reveal two distinct fracture nucleation mechanisms: homogeneous nucleation for the zigzag-edged graphene nanoribbons and edge-controlled heterogeneous nucleation for the armchair-edged ribbons. The modeling and simulations in this study highlight the atomistic mechanisms for the nonlinear mechanical behavior of graphene nanoribbons with the edge effects, which is potentially important for developing integrated graphene-based devices

A mathematical model for the simulation of thermal transients in the water loop of IPEN

International Nuclear Information System (INIS)

Pontedeiro, A.C.

1980-01-01

A mathematical model for simulation of thermal transients in the water loop at the Instituto de Pesquisas Energeticas e Nucleares, Sao Paulo, Brasil, is developed. The model is based on energy equations applied to the components of the experimental water loop. The non-linear system of first order diferencial equations and of non-linear algebraic equations obtained through the utilization of the IBM 'System/360-Continous System Modeling Program' (CSMP) is resolved. An optimization of the running time of the computer is made and a typical simulation of the water loop is executed. (Author) [pt

Impact of loudspeaker nonlinear distortion on personal sound zones

DEFF Research Database (Denmark)

Ma, Xiaohui; J. Hegarty, Patrick; Abildgaard Pedersen, Jan

2018-01-01

Personal sound zone systems aim at creating multiple listening zones within a shared space with minimum interference between zones, but the performance is often poorer than simulations predict and effects of nonlinear distortion are sometimes audible. This paper assesses the impact of nonlinear...... distortion on sound zones through simulations and measurements performed under anechoic conditions. Two sound zones, one bright and one dark, are created with acoustic contrast control using two loudspeaker arrays driven at 250 Hz. Nonlinear distortion is modelled using second or third order nonlinearities....... Simulations show that nonlinear distortion degrades the acoustic contrast, which is confirmed by experimental measurements. The harmonic distortion is audible in the dark zone. Frequency resolved measurements reveal that harmonic distortion contributes to contrast loss, but nonlinear effects...

Global-local nonlinear model reduction for flows in heterogeneous porous media

KAUST Repository

AlOtaibi, Manal; Calo, Victor M.; Efendiev, Yalchin R.; Galvis, Juan; Ghommem, Mehdi

2015-01-01

In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.

Global-local nonlinear model reduction for flows in heterogeneous porous media

KAUST Repository

AlOtaibi, Manal

2015-08-01

In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.

Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channel's Nonlinear Controllers Design

Directory of Open Access Journals (Sweden)

Juing-Shian Chiou

2013-01-01

Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.

Finite element simulation of nanoindentation tests using a macroscopic computational model

International Nuclear Information System (INIS)

Khelifa, Mourad; Fierro, Vanessa; Celzard, Alain

2014-01-01

The aim of this work was to develop a numerical procedure to simulate nanoindentation tests using a macroscopic computational model. Both theoretical and numerical aspects of the proposed methodology, based on the coupling of isotropic elasticity and anisotropic plasticity described with the quadratic criterion of Hill are presented to model this behaviour. The anisotropic plastic behaviour accounts for the mixed nonlinear hardening (isotropic and kinematic) under large plastic deformation. Nanoindentation tests were simulated to analyse the nonlinear mechanical behaviour of aluminium alloy. The predicted results of the finite element (FE) modelling are in good agreement with the experimental data, thereby confirming the accuracy level of the suggested FE method of analysis. The effects of some technological and mechanical parameters known to have an influence during the nanoindentation tests were also investigated.

Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps

Science.gov (United States)

Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin

2016-11-01

In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.

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

Science.gov (United States)

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.

Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials

Science.gov (United States)

Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)

1996-01-01

There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.

An axisymmetrical non-linear finite element model for induction heating in injection molding tools

DEFF Research Database (Denmark)

Guerrier, Patrick; Nielsen, Kaspar Kirstein; Menotti, Stefano

2016-01-01

To analyze the heating and cooling phase of an induction heated injection molding tool accurately, the temperature dependent magnetic properties, namely the non-linear B-H curves, need to be accounted for in an induction heating simulation. Hence, a finite element model has been developed......, including the non-linear temperature dependent magnetic data described by a three-parameter modified Frohlich equation fitted to the magnetic saturation curve, and solved with an iterative procedure. The numerical calculations are compared with experiments conducted with two types of induction coils, built...... in to the injection molding tool. The model shows very good agreement with the experimental temperature measurements. It is also shown that the non-linearity can be used without the temperature dependency in some cases, and a proposed method is presented of how to estimate an effective linear permeability to use...

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

Explicit Nonlinear Model Predictive Control Theory and Applications

CERN Document Server

Grancharova, Alexandra

2012-01-01

Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

Analysis of nonlinear systems using ARMA [autoregressive moving average] models

International Nuclear Information System (INIS)

Hunter, N.F. Jr.

1990-01-01

While many vibration systems exhibit primarily linear behavior, a significant percentage of the systems encountered in vibration and model testing are mildly to severely nonlinear. Analysis methods for such nonlinear systems are not yet well developed and the response of such systems is not accurately predicted by linear models. Nonlinear ARMA (autoregressive moving average) models are one method for the analysis and response prediction of nonlinear vibratory systems. In this paper we review the background of linear and nonlinear ARMA models, and illustrate the application of these models to nonlinear vibration systems. We conclude by summarizing the advantages and disadvantages of ARMA models and emphasizing prospects for future development. 14 refs., 11 figs

Nonlinear gyrokinetic simulations of the I-mode high confinement regime and comparisons with experiment

Energy Technology Data Exchange (ETDEWEB)

White, A. E., E-mail: whitea@mit.edu; Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G. [MIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139 (United States); Mikkelsen, D. R.; Edlund, E. M.; Kung, C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540 (United States); Holland, C. [University of California, San Diego (UCSD) San Diego, California 92093 (United States); Candy, J.; Petty, C. C. [General Atomics, P.O. Box 85608, San Diego, California 92186 (United States); Reinke, M. L. [York University, Heslington, York YO10 5DD (United Kingdom); and others

2015-05-15

For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.

Nonlinear system identification based on Takagi-Sugeno fuzzy modeling and unscented Kalman filter.

Science.gov (United States)

Vafamand, Navid; Arefi, Mohammad Mehdi; Khayatian, Alireza

2018-03-01

This paper proposes two novel Kalman-based learning algorithms for an online Takagi-Sugeno (TS) fuzzy model identification. The proposed approaches are designed based on the unscented Kalman filter (UKF) and the concept of dual estimation. Contrary to the extended Kalman filter (EKF) which utilizes derivatives of nonlinear functions, the UKF employs the unscented transformation. Consequently, non-differentiable membership functions can be considered in the structure of the TS models. This makes the proposed algorithms to be applicable for the online parameter calculation of wider classes of TS models compared to the recently published papers concerning the same issue. Furthermore, because of the great capability of the UKF in handling severe nonlinear dynamics, the proposed approaches can effectively approximate the nonlinear systems. Finally, numerical and practical examples are provided to show the advantages of the proposed approaches. Simulation results reveal the effectiveness of the proposed methods and performance improvement based on the root mean square (RMS) of the estimation error compared to the existing results. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear State Space Modeling and System Identification for Electrohydraulic Control

Directory of Open Access Journals (Sweden)

Jun Yan

2013-01-01

Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.

Modeling and analysis of Galfenol cantilever vibration energy harvester with nonlinear magnetic force

Science.gov (United States)

Cao, Shuying; Sun, Shuaishuai; Zheng, Jiaju; Wang, Bowen; Wan, Lili; Pan, Ruzheng; Zhao, Ran; Zhang, Changgeng

2018-05-01

Galfenol traditional cantilever energy harvesters (TCEHs) have bigger electrical output only at resonance and exhibit nonlinear mechanical-magnetic-electric coupled (NMMEC) behaviors. To increase low-frequency broadband performances of a TCEH, an improved CEH (ICEH) with magnetic repulsive force is studied. Based on the magnetic dipole model, the nonlinear model of material, the Faraday law and the dynamic principle, a lumped parameter NMMEC model of the devices is established. Comparisons between the calculated and measured results show that the proposed model can provide reasonable data trends of TCEH under acceleration, bias field and different loads. Simulated results show that ICEH exhibits low-frequency resonant, hard spring and bistable behaviors, thus can harvest more low-frequency broadband vibration energy than TCEH, and can elicit snap-through and generate higher voltage even under weak noise. The proposed structure and model are useful for improving performances of the devices.

Statistical identifiability and convergence evaluation for nonlinear pharmacokinetic models with particle swarm optimization.

Science.gov (United States)

Kim, Seongho; Li, Lang

2014-02-01

The statistical identifiability of nonlinear pharmacokinetic (PK) models with the Michaelis-Menten (MM) kinetic equation is considered using a global optimization approach, which is particle swarm optimization (PSO). If a model is statistically non-identifiable, the conventional derivative-based estimation approach is often terminated earlier without converging, due to the singularity. To circumvent this difficulty, we develop a derivative-free global optimization algorithm by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. We further propose an efficient approach to not only checking the convergence of estimation but also detecting the identifiability of nonlinear PK models. PK simulation studies demonstrate that the convergence and identifiability of the PK model can be detected efficiently through the proposed approach. The proposed approach is then applied to clinical PK data along with a two-compartmental model. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Accurate lithography simulation model based on convolutional neural networks

Science.gov (United States)

Watanabe, Yuki; Kimura, Taiki; Matsunawa, Tetsuaki; Nojima, Shigeki

2017-07-01

Lithography simulation is an essential technique for today's semiconductor manufacturing process. In order to calculate an entire chip in realistic time, compact resist model is commonly used. The model is established for faster calculation. To have accurate compact resist model, it is necessary to fix a complicated non-linear model function. However, it is difficult to decide an appropriate function manually because there are many options. This paper proposes a new compact resist model using CNN (Convolutional Neural Networks) which is one of deep learning techniques. CNN model makes it possible to determine an appropriate model function and achieve accurate simulation. Experimental results show CNN model can reduce CD prediction errors by 70% compared with the conventional model.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

Science.gov (United States)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Density-based Monte Carlo filter and its applications in nonlinear stochastic differential equation models.

Science.gov (United States)

Huang, Guanghui; Wan, Jianping; Chen, Hui

2013-02-01

Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error. Copyright © 2012 Elsevier Ltd. All rights reserved.

Performance of Linear and Nonlinear Two-Leaf Light Use Efficiency Models at Different Temporal Scales

DEFF Research Database (Denmark)

Wu, Xiaocui; Ju, Weimin; Zhou, Yanlian

2015-01-01

The reliable simulation of gross primary productivity (GPP) at various spatial and temporal scales is of significance to quantifying the net exchange of carbon between terrestrial ecosystems and the atmosphere. This study aimed to verify the ability of a nonlinear two-leaf model (TL-LUEn), a linear...... two-leaf model (TL-LUE), and a big-leaf light use efficiency model (MOD17) to simulate GPP at half-hourly, daily and 8-day scales using GPP derived from 58 eddy-covariance flux sites in Asia, Europe and North America as benchmarks. Model evaluation showed that the overall performance of TL...

Model-on-Demand Predictive Control for Nonlinear Hybrid Systems With Application to Adaptive Behavioral Interventions

Science.gov (United States)

Nandola, Naresh N.; Rivera, Daniel E.

2011-01-01

This paper presents a data-centric modeling and predictive control approach for nonlinear hybrid systems. System identification of hybrid systems represents a challenging problem because model parameters depend on the mode or operating point of the system. The proposed algorithm applies Model-on-Demand (MoD) estimation to generate a local linear approximation of the nonlinear hybrid system at each time step, using a small subset of data selected by an adaptive bandwidth selector. The appeal of the MoD approach lies in the fact that model parameters are estimated based on a current operating point; hence estimation of locations or modes governed by autonomous discrete events is achieved automatically. The local MoD model is then converted into a mixed logical dynamical (MLD) system representation which can be used directly in a model predictive control (MPC) law for hybrid systems using multiple-degree-of-freedom tuning. The effectiveness of the proposed MoD predictive control algorithm for nonlinear hybrid systems is demonstrated on a hypothetical adaptive behavioral intervention problem inspired by Fast Track, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children. Simulation results demonstrate that the proposed algorithm can be useful for adaptive intervention problems exhibiting both nonlinear and hybrid character. PMID:21874087

Modeling and simulation of different and representative engineering problems using Network Simulation Method

Science.gov (United States)

2018-01-01

Mathematical models simulating different and representative engineering problem, atomic dry friction, the moving front problems and elastic and solid mechanics are presented in the form of a set of non-linear, coupled or not coupled differential equations. For different parameters values that influence the solution, the problem is numerically solved by the network method, which provides all the variables of the problems. Although the model is extremely sensitive to the above parameters, no assumptions are considered as regards the linearization of the variables. The design of the models, which are run on standard electrical circuit simulation software, is explained in detail. The network model results are compared with common numerical methods or experimental data, published in the scientific literature, to show the reliability of the model. PMID:29518121

Finite-time adaptive sliding mode force control for electro-hydraulic load simulator based on improved GMS friction model

Science.gov (United States)

Kang, Shuo; Yan, Hao; Dong, Lijing; Li, Changchun

2018-03-01

This paper addresses the force tracking problem of electro-hydraulic load simulator under the influence of nonlinear friction and uncertain disturbance. A nonlinear system model combined with the improved generalized Maxwell-slip (GMS) friction model is firstly derived to describe the characteristics of load simulator system more accurately. Then, by using particle swarm optimization (PSO) algorithm ​combined with the system hysteresis characteristic analysis, the GMS friction parameters are identified. To compensate for nonlinear friction and uncertain disturbance, a finite-time adaptive sliding mode control method is proposed based on the accurate system model. This controller has the ability to ensure that the system state moves along the nonlinear sliding surface to steady state in a short time as well as good dynamic properties under the influence of parametric uncertainties and disturbance, which further improves the force loading accuracy and rapidity. At the end of this work, simulation and experimental results are employed to demonstrate the effectiveness of the proposed sliding mode control strategy.

NONLINEAR PLANT PIECEWISE-CONTINUOUS MODEL MATRIX PARAMETERS ESTIMATION

Directory of Open Access Journals (Sweden)

Roman L. Leibov

2017-09-01

Full Text Available This paper presents a nonlinear plant piecewise-continuous model matrix parameters estimation technique using nonlinear model time responses and random search method. One of piecewise-continuous model application areas is defined. The results of proposed approach application for aircraft turbofan engine piecewisecontinuous model formation are presented

A Nonlinear Model of Mix Coil Spring – Rubber for Vertical Suspension of Railway Vehicle

Directory of Open Access Journals (Sweden)

Dumitriu Mădălina

2016-03-01

Full Text Available The paper focuses on a nonlinear model to represent the mechanical behaviour of a mix coil spring - rubber used in the secondary suspension of passenger rail vehicles. The principle of the model relies on overlapping of the forces corresponding to three components - the elastic component, the viscous component and the dry friction component. The model has two sources on non-linearity, in the elastic force and the friction force, respectively. The main attributes of the model are made visible by its response to an imposed displacement-type harmonic excitation. The results thus obtained from the applications of numerical simulation show a series of basic properties of the model, namely the dependence on amplitude and the excitation frequency of the model response, as well as of its stiffness and damping.

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

Science.gov (United States)

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.

Estimation methods for nonlinear state-space models in ecology

DEFF Research Database (Denmark)

Pedersen, Martin Wæver; Berg, Casper Willestofte; Thygesen, Uffe Høgsbro

2011-01-01

The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta...... logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden...... Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance...

Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow

Science.gov (United States)

Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.

2018-01-01

The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.

Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations

Science.gov (United States)

Krebs, I.; Jardin, S. C.; Günter, S.; Lackner, K.; Hoelzl, M.; Strumberger, E.; Ferraro, N.

2017-10-01

A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at q ≈1 , thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C1 code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated (m =1 ,n =1 ) quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if β is sufficiently high to provide the necessary drive for the (m =1 ,n =1 ) instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile.

Study of the nonlinear imperfect software debugging model

International Nuclear Information System (INIS)

Wang, Jinyong; Wu, Zhibo

2016-01-01

In recent years there has been a dramatic proliferation of research on imperfect software debugging phenomena. Software debugging is a complex process and is affected by a variety of factors, including the environment, resources, personnel skills, and personnel psychologies. Therefore, the simple assumption that debugging is perfect is inconsistent with the actual software debugging process, wherein a new fault can be introduced when removing a fault. Furthermore, the fault introduction process is nonlinear, and the cumulative number of nonlinearly introduced faults increases over time. Thus, this paper proposes a nonlinear, NHPP imperfect software debugging model in consideration of the fact that fault introduction is a nonlinear process. The fitting and predictive power of the NHPP-based proposed model are validated through related experiments. Experimental results show that this model displays better fitting and predicting performance than the traditional NHPP-based perfect and imperfect software debugging models. S-confidence bounds are set to analyze the performance of the proposed model. This study also examines and discusses optimal software release-time policy comprehensively. In addition, this research on the nonlinear process of fault introduction is significant given the recent surge of studies on software-intensive products, such as cloud computing and big data. - Highlights: • Fault introduction is a nonlinear changing process during the debugging phase. • The assumption that the process of fault introduction is nonlinear is credible. • Our proposed model can better fit and accurately predict software failure behavior. • Research on fault introduction case is significant to software-intensive products.

Three dimensional nonlinear simulations of edge localized modes on the EAST tokamak using BOUT++ code

Energy Technology Data Exchange (ETDEWEB)

Liu, Z. X., E-mail: zxliu316@ipp.ac.cn; Xia, T. Y.; Liu, S. C.; Ding, S. Y. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Xu, X. Q.; Joseph, I.; Meyer, W. H. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Gao, X.; Xu, G. S.; Shao, L. M.; Li, G. Q.; Li, J. G. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)

2014-09-15

Experimental measurements of edge localized modes (ELMs) observed on the EAST experiment are compared to linear and nonlinear theoretical simulations of peeling-ballooning modes using the BOUT++ code. Simulations predict that the dominant toroidal mode number of the ELM instability becomes larger for lower current, which is consistent with the mode structure captured with visible light using an optical CCD camera. The poloidal mode number of the simulated pressure perturbation shows good agreement with the filamentary structure observed by the camera. The nonlinear simulation is also consistent with the experimentally measured energy loss during an ELM crash and with the radial speed of ELM effluxes measured using a gas puffing imaging diagnostic.

Oscillating nonlinear acoustic shock waves

DEFF Research Database (Denmark)

Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth

2016-01-01

We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show that at resona......We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....

Heterotic sigma models and non-linear strings

International Nuclear Information System (INIS)

Hull, C.M.

1986-01-01

The two-dimensional supersymmetric non-linear sigma models are examined with respect to the heterotic string. The paper was presented at the workshop on :Supersymmetry and its applications', Cambridge, United Kingdom, 1985. The non-linear sigma model with Wess-Zumino-type term, the coupling of the fermionic superfields to the sigma model, super-conformal invariance, and the supersymmetric string, are all discussed. (U.K.)

Nonlinear saturation controller for vibration supersession of a nonlinear composite beam

Energy Technology Data Exchange (ETDEWEB)

Hamed, Y. S. [Menofia University, Menouf (Egypt); Amer, Y. A. [Zagazig University, Zagazig (Egypt)

2014-08-15

In this paper, a study for nonlinear saturation controller (NSC) is presented that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities of the feedback gain and a two-to-one internal resonance. The analytical solution for the system and the nonlinear saturation controller are obtained using method of multiple time scales perturbation up to the second order approximation. All possible resonance cases were extracted at this approximation order and studied numerically. The stability of the system at the worst resonance case (Ω = 2ω{sub s} and ω{sub s} =2ω{sub C}) is investigated using both frequency response equations and phase-plane trajectories. The effects of different parameters on the system and the controller are studied numerically. The effect of some types of controller on the system is investigated numerically. The simulation results are achieved using Matlab and Maple programs.

Simulation of non-linear ultrasound fields

DEFF Research Database (Denmark)

Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.

2002-01-01

-linear propagation. The speed of sound is calculated from the instantaneous pressure of the pulse and the nonlinearity B/A parameter of the medium. The harmonic field is found by introducing a number of virtual planes in front of the aperture and then propagating the pulse using Burgers' solution between the planes....... Simulations on the acoustical axis of an array transducer were performed and compared to measurements made in a water tank. A 3 MHz convex array transducer with a pitch of 0.53 mm and a height of 13 mm was used. The electronic focus was at 45 mm and 16 elements were used for emission. The emitted pressure...... was 1.4 MPa measured 6 mm from the aperture by a Force Institute MH25-5 needle hydrophone in a water bath. The build-up of higher harmonics can here be predicted accurately up to the 5th harmonic. The second harmonic is simulated with an accuracy of ±2.6 dB and the third harmonic with ±2 dB compared...

Modeling and simulation of thermally actuated bilayer plates

Science.gov (United States)

Bartels, Sören; Bonito, Andrea; Muliana, Anastasia H.; Nochetto, Ricardo H.

2018-02-01

We present a mathematical model of polymer bilayers that undergo large bending deformations when actuated by non-mechanical stimuli such as thermal effects. The simple model captures a large class of nonlinear bending effects and can be discretized with standard plate elements. We devise a fully practical iterative scheme and apply it to the simulation of folding of several practically useful compliant structures comprising of thin elastic layers.

Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

Directory of Open Access Journals (Sweden)

Qixing Han

2013-01-01

Full Text Available We investigate a stochastic SIS model with nonlinear incidence rate. We show that there exists a unique nonnegative solution to the system, and condition for the infectious individuals I(t to be extinct is given. Moreover, we prove that the system has ergodic property. Finally, computer simulations are carried out to verify our results.

Nonlinear polarization of ionic liquids: theory, simulations, experiments

Science.gov (United States)

Kornyshev, Alexei

2010-03-01

Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.

Rail vehicle dynamic response to a nonlinear physical 'in-service' model of its secondary suspension hydraulic dampers

Science.gov (United States)

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.

Nonlinear Physics of Plasmas

CERN Document Server

Kono, Mitsuo

2010-01-01

A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.

MEMS linear and nonlinear statics and dynamics

CERN Document Server

Younis, Mohammad I

2011-01-01

MEMS Linear and Nonlinear Statics and Dynamics presents the necessary analytical and computational tools for MEMS designers to model and simulate most known MEMS devices, structures, and phenomena. This book also provides an in-depth analysis and treatment of the most common static and dynamic phenomena in MEMS that are encountered by engineers. Coverage also includes nonlinear modeling approaches to modeling various MEMS phenomena of a nonlinear nature, such as those due to electrostatic forces, squeeze-film damping, and large deflection of structures. The book also: Includes examples of nume

Mathematical modeling of zika virus disease with nonlinear incidence and optimal control

Science.gov (United States)

Goswami, Naba Kumar; Srivastav, Akhil Kumar; Ghosh, Mini; Shanmukha, B.

2018-04-01

The Zika virus was first discovered in a rhesus monkey in the Zika Forest of Uganda in 1947, and it was isolated from humans in Nigeria in 1952. Zika virus disease is primarily a mosquito-borne disease, which is transmitted to human primarily through the bite of an infected Aedes species mosquito. However, there is documented evidence of sexual transmission of this disease too. In this paper, a nonlinear mathematical model for Zika virus by considering nonlinear incidence is formulated and analyzed. The equilibria and the basic reproduction number (R0) of the model are found. The stability of the different equilibria of the model is discussed in detail. When the basic reproduction number R0 1, we have endemic equilibrium which is locally stable under some restriction on parameters. Further this model is extended to optimal control model and is analyzed by using Pontryagin’s Maximum Principle. It has been observed that optimal control plays a significant role in reducing the number of zika infectives. Finally, numerical simulation is performed to illustrate the analytical findings.

Practitioner's guide to laser pulse propagation models and simulation

Energy Technology Data Exchange (ETDEWEB)

Couairon, A. [Centre de Physique Theorique, CNRS, Ecole Polytechnique, 91128 Palaiseau (France); Brambilla, E.; Corti, T. [Department of Physics and Mathematics, University of Insubria, via Vallegio 11, 22100 Como (Italy); Majus, D. [Department of Quantum Electronics, Vilnius University, Sauletekio Avenue 9, Bldg. 3, 10222 Vilnius (Lithuania); Ramirez-Congora, O. de [Departamento de Ciencias Naturales y Matematicas, Pontificia Universidad Javeriana-Cali, Avenida Canas Gordas no 118-250 Cali (Colombia); Kolesik, M. [College of Optical Sciences, Tucson 85721 AZ (United States); Department of Physics, Constantine the Philosopher Uninversity, Nitra (Slovakia)

2011-11-15

The purpose of this article is to provide practical introduction into numerical modeling of ultrashort optical pulses in extreme nonlinear regimes. The theoretic background section covers derivation of modern pulse propagation models starting from Maxwell's equations, and includes both envelope-based models and carrier-resolving propagation equations. We then continue with a detailed description of implementation in software of Nonlinear Envelope Equations as an example of a mixed approach which combines finite-difference and spectral techniques. Fully spectral numerical solution methods for the Unidirectional Pulse Propagation Equation are discussed next. The modeling part of this guide concludes with a brief introduction into efficient implementations of nonlinear medium responses. Finally, we include several worked-out simulation examples. These are mini-projects designed to highlight numerical and modeling issues, and to teach numerical-experiment practices. They are also meant to illustrate, first and foremost for a non-specialist, how tools discussed in this guide can be applied in practical numerical modeling. (authors)

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

Science.gov (United States)

Bache, Morten; Lavrinenko, Andrei V.

2017-09-01

Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures

Science.gov (United States)

Maillou, Balbine; Lotton, Pierrick; Novak, Antonin; Simon, Laurent

2018-03-01

Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.

Estimating intratidal nonlinearity of respiratory system mechanics: a model study using the enhanced gliding-SLICE method

International Nuclear Information System (INIS)

Schumann, Stefan; Burcza, Boris; Guttmann, Josef; Haberthür, Christoph; Lichtwarck-Aschoff, Michael

2009-01-01

In the clinical situation and in most research work, the analysis of respiratory system mechanics is limited to the estimation of single-value compliances during static or quasi-static conditions. In contrast, our SLICE method analyses intratidal nonlinearity under the dynamic conditions of mechanical ventilation by calculating compliance and resistance for six conjoined volume portions (slices) of the pressure–volume loop by multiple linear regression analysis. With the gliding-SLICE method we present a new approach to determine continuous intratidal nonlinear compliance. The performance of the gliding-SLICE method was tested both in computer simulations and in a physical model of the lung, both simulating different intratidal compliance profiles. Compared to the original SLICE method, the gliding-SLICE method resulted in smaller errors when calculating the compliance or pressure course (all p 2 O s L −1 to 0.8 ± 0.3 cmH 2 O s L −1 (mathematical model) and from 7.2 ± 3.9 cmH 2 O s L −1 to 0.4 ± 0.2 cmH 2 O s L −1 (physical model) (all p < 0.001). We conclude that the new gliding-SLICE method allows detailed assessment of intratidal nonlinear respiratory system mechanics without discontinuity error

Nonlinear free vibration control of beams using acceleration delayed-feedback control

International Nuclear Information System (INIS)

Alhazza, Khaled A; Alajmi, Mohammed; Masoud, Ziyad N

2008-01-01

A single-mode delayed-feedback control strategy is developed to reduce the free vibrations of a flexible beam using a piezoelectric actuator. A nonlinear variational model of the beam based on the von Kàrmàn nonlinear type deformations is considered. Using Galerkin's method, the resulting governing partial differential equations of motion are reduced to a system of nonlinear ordinary differential equations. A linear model using the first mode is derived and is used to characterize the damping produced by the controller as a function of the controller's gain and delay. Three-dimensional figures showing the damping magnitude as a function of the controller gain and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controller gain and delay using both methods are obtained, simulated and compared. To validate the single-mode approximation, numerical simulations are performed using a three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the first-mode vibration

Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model

Energy Technology Data Exchange (ETDEWEB)

Yamagishi, Osamu, E-mail: yamagisi@nifs.ac.jp; Sugama, Hideo [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan)

2016-03-15

Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.

Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model

Science.gov (United States)

Yamagishi, Osamu; Sugama, Hideo

2016-03-01

Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.

A non-Linear transport model for determining shale rock characteristics

Science.gov (United States)

Ali, Iftikhar; Malik, Nadeem

2016-04-01

Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007

Math modeling and computer mechanization for real time simulation of rotary-wing aircraft

Science.gov (United States)

Howe, R. M.

1979-01-01

Mathematical modeling and computer mechanization for real time simulation of rotary wing aircraft is discussed. Error analysis in the digital simulation of dynamic systems, such as rotary wing aircraft is described. The method for digital simulation of nonlinearities with discontinuities, such as exist in typical flight control systems and rotor blade hinges, is discussed.

Design of a Discrete Tracking Controller for a Magnetic Levitation System: A Nonlinear Rational Model Approach

Directory of Open Access Journals (Sweden)

Fernando Gómez-Salas

2015-01-01

Full Text Available This work proposes a discrete-time nonlinear rational approximate model for the unstable magnetic levitation system. Based on this model and as an application of the input-output linearization technique, a discrete-time tracking control design will be derived using the corresponding classical state space representation of the model. A simulation example illustrates the efficiency of the proposed methodology.

Non-linear Model Predictive Control for cooling strings of superconducting magnets using superfluid helium

CERN Document Server

AUTHOR|(SzGeCERN)673023; Blanco Viñuela, Enrique

In each of eight arcs of the 27 km circumference Large Hadron Collider (LHC), 2.5 km long strings of super-conducting magnets are cooled with superfluid Helium II at 1.9 K. The temperature stabilisation is a challenging control problem due to complex non-linear dynamics of the magnets temperature and presence of multiple operational constraints. Strong nonlinearities and variable dead-times of the dynamics originate at strongly heat-flux dependent effective heat conductivity of superfluid that varies three orders of magnitude over the range of possible operational conditions. In order to improve the temperature stabilisation, a proof of concept on-line economic output-feedback Non-linear Model Predictive Controller (NMPC) is presented in this thesis. The controller is based on a novel complex first-principles distributed parameters numerical model of the temperature dynamics over a 214 m long sub-sector of the LHC that is characterized by very low computational cost of simulation needed in real-time optimizat...

Model reduction of nonlinear systems subject to input disturbances

KAUST Repository

Ndoye, Ibrahima

2017-07-10

The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.

Modeling and Simulation of DC Power Electronics Systems Using Harmonic State Space (HSS) Method

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

2015-01-01

based on the state-space averaging and generalized averaging, these also have limitations to show the same results as with the non-linear time domain simulations. This paper presents a modeling and simulation method for a large dc power electronic system by using Harmonic State Space (HSS) modeling......For the efficiency and simplicity of electric systems, the dc based power electronics systems are widely used in variety applications such as electric vehicles, ships, aircrafts and also in homes. In these systems, there could be a number of dynamic interactions between loads and other dc-dc....... Through this method, the required computation time and CPU memory for large dc power electronics systems can be reduced. Besides, the achieved results show the same results as with the non-linear time domain simulation, but with the faster simulation time which is beneficial in a large network....

Non-linear Growth Models in Mplus and SAS

Science.gov (United States)

Grimm, Kevin J.; Ram, Nilam

2013-01-01

Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134

Nonlinearity in structural and electronic materials

International Nuclear Information System (INIS)

Bishop, A.R.; Beardmore, K.M.; Ben-Naim, E.

1997-01-01

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project strengthens a nonlinear technology base relevant to a variety of problems arising in condensed matter and materials science, and applies this technology to those problems. In this way the controlled synthesis of, and experiments on, novel electronic and structural materials provide an important focus for nonlinear science, while nonlinear techniques help advance the understanding of the scientific principles underlying the control of microstructure and dynamics in complex materials. This research is primarily focused on four topics: (1) materials microstructure: growth and evolution, and porous media; (2) textures in elastic/martensitic materials; (3) electro- and photo-active polymers; and (4) ultrafast photophysics in complex electronic materials. Accomplishments included the following: organization of a ''Nonlinear Materials'' seminar series and international conferences including ''Fracture, Friction and Deformation,'' ''Nonequilibrium Phase Transitions,'' and ''Landscape Paradigms in Physics and Biology''; invited talks at international conference on ''Synthetic Metals,'' ''Quantum Phase Transitions,'' ''1996 CECAM Euroconference,'' and the 1995 Fall Meeting of the Materials Research Society; large-scale simulations and microscopic modeling of nonlinear coherent energy storage at crack tips and sliding interfaces; large-scale simulation and microscopic elasticity theory for precursor microstructure and dynamics at solid-solid diffusionless phase transformations; large-scale simulation of self-assembling organic thin films on inorganic substrates; analysis and simulation of smoothing of rough atomic surfaces; and modeling and analysis of flux pattern formation in equilibrium and nonequilibrium Josephson junction arrays and layered superconductors

Robust variable selection method for nonparametric differential equation models with application to nonlinear dynamic gene regulatory network analysis.

Science.gov (United States)

Lu, Tao

2016-01-01

The gene regulation network (GRN) evaluates the interactions between genes and look for models to describe the gene expression behavior. These models have many applications; for instance, by characterizing the gene expression mechanisms that cause certain disorders, it would be possible to target those genes to block the progress of the disease. Many biological processes are driven by nonlinear dynamic GRN. In this article, we propose a nonparametric differential equation (ODE) to model the nonlinear dynamic GRN. Specially, we address following questions simultaneously: (i) extract information from noisy time course gene expression data; (ii) model the nonlinear ODE through a nonparametric smoothing function; (iii) identify the important regulatory gene(s) through a group smoothly clipped absolute deviation (SCAD) approach; (iv) test the robustness of the model against possible shortening of experimental duration. We illustrate the usefulness of the model and associated statistical methods through a simulation and a real application examples.

Economic Optimization of Spray Dryer Operation using Nonlinear Model Predictive Control

DEFF Research Database (Denmark)

Petersen, Lars Norbert; Poulsen, Niels Kjølstad; Niemann, Hans Henrik

2014-01-01

In this paper we investigate an economically optimizing Nonlinear Model Predictive Control (E-NMPC) for a spray drying process. By simulation we evaluate the economic potential of this E-NMPC compared to a conventional PID based control strategy. Spray drying is the preferred process to reduce...... the water content for many liquid foodstuffs and produces a free flowing powder. The main challenge in controlling the spray drying process is to meet the residual moisture specifications and avoid that the powder sticks to the chamber walls of the spray dryer. We present a model for a spray dryer that has...... been validated on experimental data from a pilot plant. We use this model for simulation as well as for prediction in the E-NMPC. The E-NMPC is designed with hard input constraints and soft output constraints. The open-loop optimal control problem in the E-NMPC is solved using the single...

Nonlinear analysis of an extended traffic flow model in ITS environment

Energy Technology Data Exchange (ETDEWEB)

Yu Lei [College of Automation, Northwestern Polytechnical University, Xi' an, Shaanxi 710072 (China)], E-mail: yuleijk@126.com; Shi Zhongke [College of Automation, Northwestern Polytechnical University, Xi' an, Shaanxi 710072 (China)

2008-05-15

An extended traffic flow model is proposed by introducing the relative velocity of arbitrary number of cars that precede and that follow into the Newell-Whitham-type car-following model. The stability condition of this model is obtained by using the linear stability theory. The results show that the stability of traffic flow is improved by taking into account the relative velocity of cars ahead and backward. By applying the nonlinear analysis the modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point. The kink-antikink soliton, the solution of the mKdV equation, is obtained to describe the traffic jams. From the numerical simulation, it is shown that the traffic jams are suppressed efficiently by taking into account the relative velocity of cars ahead and backward. The analytical results are consistent with the simulation one.

Nonlinear analysis of an extended traffic flow model in ITS environment

International Nuclear Information System (INIS)

Yu Lei; Shi Zhongke

2008-01-01

An extended traffic flow model is proposed by introducing the relative velocity of arbitrary number of cars that precede and that follow into the Newell-Whitham-type car-following model. The stability condition of this model is obtained by using the linear stability theory. The results show that the stability of traffic flow is improved by taking into account the relative velocity of cars ahead and backward. By applying the nonlinear analysis the modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point. The kink-antikink soliton, the solution of the mKdV equation, is obtained to describe the traffic jams. From the numerical simulation, it is shown that the traffic jams are suppressed efficiently by taking into account the relative velocity of cars ahead and backward. The analytical results are consistent with the simulation one

The development and validation of a numerical integration method for non-linear viscoelastic modeling

Science.gov (United States)

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Speeding up N-body simulations of modified gravity: chameleon screening models

Science.gov (United States)

Bose, Sownak; Li, Baojiu; Barreira, Alexandre; He, Jian-hua; Hellwing, Wojciech A.; Koyama, Kazuya; Llinares, Claudio; Zhao, Gong-Bo

2017-02-01

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f(R) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f(R) simulations. For example, a test simulation with 5123 particles in a box of size 512 Mpc/h is now 5 times faster than before, while a Millennium-resolution simulation for f(R) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.

Speeding up N -body simulations of modified gravity: chameleon screening models

International Nuclear Information System (INIS)

Bose, Sownak; Li, Baojiu; He, Jian-hua; Llinares, Claudio; Barreira, Alexandre; Hellwing, Wojciech A.; Koyama, Kazuya; Zhao, Gong-Bo

2017-01-01

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512 3 particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millennium-resolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.

Speeding up N -body simulations of modified gravity: chameleon screening models

Energy Technology Data Exchange (ETDEWEB)

Bose, Sownak; Li, Baojiu; He, Jian-hua; Llinares, Claudio [Institute for Computational Cosmology, Department of Physics, Durham University, Durham DH1 3LE (United Kingdom); Barreira, Alexandre [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany); Hellwing, Wojciech A.; Koyama, Kazuya [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom); Zhao, Gong-Bo, E-mail: sownak.bose@durham.ac.uk, E-mail: baojiu.li@durham.ac.uk, E-mail: barreira@mpa-garching.mpg.de, E-mail: jianhua.he@durham.ac.uk, E-mail: wojciech.hellwing@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: claudio.llinares@durham.ac.uk, E-mail: gbzhao@nao.cas.cn [National Astronomy Observatories, Chinese Academy of Science, Beijing, 100012 (China)

2017-02-01

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512{sup 3} particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millennium-resolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.

Model of anisotropic nonlinearity in self-defocusing photorefractive media.

Science.gov (United States)

Barsi, C; Fleischer, J W