Frequency domain performance analysis of nonlinearly controlled motion systems

NARCIS (Netherlands)

Pavlov, A.V.; Wouw, van de N.; Pogromski, A.Y.; Heertjes, M.F.; Nijmeijer, H.

2007-01-01

At the heart of the performance analysis of linear motion control systems lie essential frequency domain characteristics such as sensitivity and complementary sensitivity functions. For a class of nonlinear motion control systems called convergent systems, generalized versions of these sensitivity

A Fully Nonlinear, Dynamically Consistent Numerical Model for Solid-Body Ship Motion. I. Ship Motion with Fixed Heading

Science.gov (United States)

Lin, Ray-Quing; Kuang, Weijia

2011-01-01

In this paper, we describe the details of our numerical model for simulating ship solidbody motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...

African Journals Online (AJOL)

With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...

The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases

KAUST Repository

Gomes, Diogo A.; Mitake, Hiroyoshi; Tran, Hung V.

2018-01-01

Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.

The selection problem for discounted Hamilton–Jacobi equations: some non-convex cases

KAUST Repository

Gomes, Diogo A.

2018-01-26

Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton–Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex Hamiltonians has thus far not been studied. We begin our study by examining a generalized discounted Hamilton–Jacobi equation. Next, using an exponential transformation, we apply our methods to strictly quasi-convex and to some non-convex Hamilton–Jacobi equations. Finally, we examine a non-convex Hamiltonian with flat parts to which our results do not directly apply. In this case, we establish the convergence by a direct approach.

A parallel Discrete Element Method to model collisions between non-convex particles

Directory of Open Access Journals (Sweden)

Rakotonirina Andriarimina Daniel

2017-01-01

Full Text Available In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called “glued-convex method” (in the sense clumping convex bodies together, as an extension of the popular “glued-spheres” method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i the collapse of a granular column made of convex particles and (i the microstructure of a heap of non-convex particles in a cylindrical reactor.

Speckle Noise Reduction via Nonconvex High Total Variation Approach

Directory of Open Access Journals (Sweden)

Yulian Wu

2015-01-01

Full Text Available We address the problem of speckle noise removal. The classical total variation is extensively used in this field to solve such problem, but this method suffers from the staircase-like artifacts and the loss of image details. In order to resolve these problems, a nonconvex total generalized variation (TGV regularization is used to preserve both edges and details of the images. The TGV regularization which is able to remove the staircase effect has strong theoretical guarantee by means of its high order smooth feature. Our method combines the merits of both the TGV method and the nonconvex variational method and avoids their main drawbacks. Furthermore, we develop an efficient algorithm for solving the nonconvex TGV-based optimization problem. We experimentally demonstrate the excellent performance of the technique, both visually and quantitatively.

Nonconvex Model Predictive Control for Commercial Refrigeration

DEFF Research Database (Denmark)

Hovgaard, Tobias Gybel; Larsen, Lars F.S.; Jørgensen, John Bagterp

2013-01-01

function, however, is nonconvex due to the temperature dependence of thermodynamic efficiency. To handle this nonconvexity we propose a sequential convex optimization method, which typically converges in fewer than 5 or so iterations. We employ a fast convex quadratic programming solver to carry out...... the iterations, which is more than fast enough to run in real-time. We demonstrate our method on a realistic model, with a full year simulation and 15 minute time periods, using historical electricity prices and weather data, as well as random variations in thermal load. These simulations show substantial cost...... capacity associated with large penetration of intermittent renewable energy sources in a future smart grid....

Nonlinear model of a rotating hub-beams structure: Equations of motion

Science.gov (United States)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

Comparison of Nonlinear Model Results Using Modified Recorded and Synthetic Ground Motions

International Nuclear Information System (INIS)

Spears, Robert E.; Wilkins, J. Kevin

2011-01-01

A study has been performed that compares results of nonlinear model runs using two sets of earthquake ground motion time histories that have been modified to fit the same design response spectra. The time histories include applicable modified recorded earthquake ground motion time histories and synthetic ground motion time histories. The modified recorded earthquake ground motion time histories are modified from time history records that are selected based on consistent magnitude and distance. The synthetic ground motion time histories are generated using appropriate Fourier amplitude spectrums, Arias intensity, and drift correction. All of the time history modification is performed using the same algorithm to fit the design response spectra. The study provides data to demonstrate that properly managed synthetic ground motion time histories are reasonable for use in nonlinear seismic analysis.

Utility Maximization in Nonconvex Wireless Systems

CERN Document Server

Brehmer, Johannes

2012-01-01

This monograph formulates a framework for modeling and solving utility maximization problems in nonconvex wireless systems. First, a model for utility optimization in wireless systems is defined. The model is general enough to encompass a wide array of system configurations and performance objectives. Based on the general model, a set of methods for solving utility maximization problems is developed. The development is based on a careful examination of the properties that are required for the application of each method. The focus is on problems whose initial formulation does not allow for a solution by standard convex methods. Solution approaches that take into account the nonconvexities inherent to wireless systems are discussed in detail. The monograph concludes with two case studies that demonstrate the application of the proposed framework to utility maximization in multi-antenna broadcast channels.

Heart Motion Prediction in Robotic-Assisted Beating Heart Surgery: A Nonlinear Fast Adaptive Approach

Directory of Open Access Journals (Sweden)

Fan Liang

2013-01-01

Full Text Available Off-pump Coronary Artery Bypass Graft (CABG surgery outperforms traditional on-pump surgery because the assisted robotic tools can alleviate the relative motion between the beating heart and robotic tools. Therefore, it is possible for the surgeon to operate on the beating heart and thus lessens post surgery complications for the patients. Due to the highly irregular and non-stationary nature of heart motion, it is critical that the beating heart motion is predicted in the model-based track control procedures. It is technically preferable to model heart motion in a nonlinear way because the characteristic analysis of 3D heart motion data through Bi-spectral analysis and Fourier methods demonstrates the involved nonlinearity of heart motion. We propose an adaptive nonlinear heart motion model based on the Volterra Series in this paper. We also design a fast lattice structure to achieve computational-efficiency for real-time online predictions. We argue that the quadratic term of the Volterra Series can improve the prediction accuracy by covering sharp change points and including the motion with sufficient detail. The experiment results indicate that the adaptive nonlinear heart motion prediction algorithm outperforms the autoregressive (AR and the time-varying Fourier-series models in terms of the root mean square of the prediction error and the prediction error in extreme cases.

Nonlinear motion of cantilevered SWNT and Its Meaning to Phonon Dynamics

Science.gov (United States)

Koh, Heeyuen; Cannon, James; Chiashi, Shohei; Shiomi, Junichiro; Maruyama, Shigeo

2013-03-01

Based on the finding that the lowest frequency mode of cantilevered SWNT is described by the continuum beam theory in frequency domain, we considered its effect of the symmetric structure for the coupling of orthogonal transverse modes to explain the nonlinear motion of free thermal vibration. This nonlinear motion calculated by our molecular dynamics simulation, once regarded as noise, is observed to have the periodic order with duffing and beating, which is dependent on aspect ratio and temperature. It could be dictated by the governing equation from the Green Lagrangian strain tensor. The nonlinear beam equation from strain tensor described the motion well for various models which has different aspect ratio in molecular dynamics simulation. Since this motion is nothing but the interaction between 2nd mode of radial, tangential mode and 1st longitudinal mode, it was found that Green Lagrangian strain tensor is capable to deal such coupling. The free thermal motion of suspended SWNT is also considered without temperature gradient. The Q factor measured by this theoretical analysis will be discussed. Part of this work was financially supported by Grant-in-Aid for Scientific Research (19054003 and 22226006), and Global COE Program 'Global Center for Excellence for Mechanical Systems Innovation'

Nonlinear-drifted Brownian motion with multiple hidden states for remaining useful life prediction of rechargeable batteries

Science.gov (United States)

Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung

2017-09-01

Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.

Respiratory lung motion analysis using a nonlinear motion correction technique for respiratory-gated lung perfusion SPECT images

International Nuclear Information System (INIS)

Ue, Hidenori; Haneishi, Hideaki; Iwanaga, Hideyuki; Suga, Kazuyoshi

2007-01-01

This study evaluated the respiratory motion of lungs using a nonlinear motion correction technique for respiratory-gated single photon emission computed tomography (SPECT) images. The motion correction technique corrects the respiratory motion of the lungs nonlinearly between two-phase images obtained by respiratory-gated SPECT. The displacement vectors resulting from respiration can be computed at every location of the lungs. Respiratory lung motion analysis is carried out by calculating the mean value of the body axis component of the displacement vector in each of the 12 small regions into which the lungs were divided. In order to enable inter-patient comparison, the 12 mean values were normalized by the length of the lung region along the direction of the body axis. This method was applied to 25 Technetium (Tc)-99m-macroaggregated albumin (MAA) perfusion SPECT images, and motion analysis results were compared with the diagnostic results. It was confirmed that the respiratory lung motion reflects the ventilation function. A statistically significant difference in the amount of the respiratory lung motion was observed between the obstructive pulmonary diseases and other conditions, based on an unpaired Student's t test (P<0.0001). A difference in the motion between normal lungs and lungs with a ventilation obstruction was detected by the proposed method. This method is effective for evaluating obstructive pulmonary diseases such as pulmonary emphysema and diffuse panbronchiolitis. (author)

Nonlinear Site Response Validation Studies Using KIK-net Strong Motion Data

Science.gov (United States)

Asimaki, D.; Shi, J.

2014-12-01

Earthquake simulations are nowadays producing realistic ground motion time-series in the range of engineering design applications. Of particular significance to engineers are simulations of near-field motions and large magnitude events, for which observations are scarce. With the engineering community slowly adopting the use of simulated ground motions, site response models need to be re-evaluated in terms of their capabilities and limitations to 'translate' the simulated time-series from rock surface output to structural analyses input. In this talk, we evaluate three one-dimensional site response models: linear viscoelastic, equivalent linear and nonlinear. We evaluate the performance of the models by comparing predictions to observations at 30 downhole stations of the Japanese network KIK-Net that have recorded several strong events, including the 2011 Tohoku earthquake. Velocity profiles are used as the only input to all models, while additional parameters such as quality factor, density and nonlinear dynamic soil properties are estimated from empirical correlations. We quantify the differences of ground surface predictions and observations in terms of both seismological and engineering intensity measures, including bias ratios of peak ground response and visual comparisons of elastic spectra, and inelastic to elastic deformation ratio for multiple ductility ratios. We observe that PGV/Vs,30 — as measure of strain— is a better predictor of site nonlinearity than PGA, and that incremental nonlinear analyses are necessary to produce reliable estimates of high-frequency ground motion components at soft sites. We finally discuss the implications of our findings on the parameterization of nonlinear amplification factors in GMPEs, and on the extensive use of equivalent linear analyses in probabilistic seismic hazard procedures.

Non-linear time series analysis on flow instability of natural circulation under rolling motion condition

International Nuclear Information System (INIS)

Zhang, Wenchao; Tan, Sichao; Gao, Puzhen; Wang, Zhanwei; Zhang, Liansheng; Zhang, Hong

2014-01-01

Highlights: • Natural circulation flow instabilities in rolling motion are studied. • The method of non-linear time series analysis is used. • Non-linear evolution characteristic of flow instability is analyzed. • Irregular complex flow oscillations are chaotic oscillations. • The effect of rolling parameter on the threshold of chaotic oscillation is studied. - Abstract: Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions were studied by the method of non-linear time series analysis. Experimental flow time series of different dimensionless power and rolling parameters were analyzed based on phase space reconstruction theory. Attractors which were reconstructed in phase space and the geometric invariants, including correlation dimension, Kolmogorov entropy and largest Lyapunov exponent, were determined. Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions was studied based on the results of the geometric invariant analysis. The results indicated that the values of the geometric invariants first increase and then decrease as dimensionless power increases which indicated the non-linear characteristics of the system first enhance and then weaken. The irregular complex flow oscillation is typical chaotic oscillation because the value of geometric invariants is at maximum. The threshold of chaotic oscillation becomes larger as the rolling frequency or rolling amplitude becomes big. The main influencing factors that influence the non-linear characteristics of the natural circulation system under rolling motion are thermal driving force, flow resistance and the additional forces caused by rolling motion. The non-linear characteristics of the natural circulation system under rolling motion changes caused by the change of the feedback and coupling degree among these influencing factors when the dimensionless power or rolling parameters changes

Complex motion in nonlinear-map model of elevators in energy-saving traffic

International Nuclear Information System (INIS)

Nagatani, Takashi

2011-01-01

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M. The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M-1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips. - Highlights: → We propose the nonlinear-map model in energy-saving traffic of elevators. → We study the dynamical behavior and dynamical transitions in the system of elevators. → We derive the fixed point of the nonlinear map analytically. → We clarify the dependence of the motion on the loading parameter and the number.

Complex motion in nonlinear-map model of elevators in energy-saving traffic

Energy Technology Data Exchange (ETDEWEB)

Nagatani, Takashi, E-mail: tmtnaga@ipc.shizuoka.ac.j [Department of Mechanical Engineering, Division of Thermal Science, Shizuoka University, Hamamatsu 432-8561 (Japan)

2011-05-16

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M. The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M-1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips. - Highlights: We propose the nonlinear-map model in energy-saving traffic of elevators. We study the dynamical behavior and dynamical transitions in the system of elevators. We derive the fixed point of the nonlinear map analytically. We clarify the dependence of the motion on the loading parameter and the number.

Exploring Nonconvex, Crossed and Degenerate Polygons

Science.gov (United States)

Contreras, Jose N.

2004-01-01

An exploration of nonconvex, crossed, and degenerate polygons (NCCDPs) are described with the help of examples with pedagogical tips and recommendations that are found useful when teaching the mathematical process of extending geometric patterns to NCCDPs. The study concludes that investigating such extensions with interactive geometry software…

Canonical Primal-Dual Method for Solving Non-convex Minimization Problems

OpenAIRE

Wu, Changzhi; Li, Chaojie; Gao, David Yang

2012-01-01

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a convex-concave saddle point optimization problem, which is then solved by a quadratically perturbed primal-dual method. %It is proved that the popular SDP method is indeed a special case of the canonical duality theory. Numerical examples are illustrated. Comparing...

Recent advances in multiparametric nonlinear programming

KAUST Repository

Domí nguez, Luis F.; Narciso, Diogo A.; Pistikopoulos, Efstratios N.

2010-01-01

In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

Recent advances in multiparametric nonlinear programming

KAUST Repository

Domínguez, Luis F.

2010-05-01

In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

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.

Molecular dynamics simulation of nonlinear spectroscopies of intermolecular motions in liquid water.

Science.gov (United States)

Yagasaki, Takuma; Saito, Shinji

2009-09-15

Water is the most extensively studied of liquids because of both its ubiquity and its anomalous thermodynamic and dynamic properties. The properties of water are dominated by hydrogen bonds and hydrogen bond network rearrangements. Fundamental information on the dynamics of liquid water has been provided by linear infrared (IR), Raman, and neutron-scattering experiments; molecular dynamics simulations have also provided insights. Recently developed higher-order nonlinear spectroscopies open new windows into the study of the hydrogen bond dynamics of liquid water. For example, the vibrational lifetimes of stretches and a bend, intramolecular features of water dynamics, can be accurately measured and are found to be on the femtosecond time scale at room temperature. Higher-order nonlinear spectroscopy is expressed by a multitime correlation function, whereas traditional linear spectroscopy is given by a one-time correlation function. Thus, nonlinear spectroscopy yields more detailed information on the dynamics of condensed media than linear spectroscopy. In this Account, we describe the theoretical background and methods for calculating higher order nonlinear spectroscopy; equilibrium and nonequilibrium molecular dynamics simulations, and a combination of both, are used. We also present the intermolecular dynamics of liquid water revealed by fifth-order two-dimensional (2D) Raman spectroscopy and third-order IR spectroscopy. 2D Raman spectroscopy is sensitive to couplings between modes; the calculated 2D Raman signal of liquid water shows large anharmonicity in the translational motion and strong coupling between the translational and librational motions. Third-order IR spectroscopy makes it possible to examine the time-dependent couplings. The 2D IR spectra and three-pulse photon echo peak shift show the fast frequency modulation of the librational motion. A significant effect of the translational motion on the fast frequency modulation of the librational motion is

Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays

International Nuclear Information System (INIS)

Hagenaars, T.J.; Tiesinga, P.H.E.; van Himbergen, J.E.; Jose, J.V.

1994-01-01

When a vortex in a two-dimensional Josephson-junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a nonlinear viscous force of the form F D =η(y)y=[A/(1+By]y, where y is the vortex velocity, η(y) is the velocity-dependent viscosity, and A and B are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies

The bounds of feasible space on constrained nonconvex quadratic programming

Science.gov (United States)

Zhu, Jinghao

2008-03-01

This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.

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

Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty.

Science.gov (United States)

Du, Lei; Liu, Kefei; Yao, Xiaohui; Yan, Jingwen; Risacher, Shannon L; Han, Junwei; Guo, Lei; Saykin, Andrew J; Shen, Li

2017-10-25

Brain imaging genetics intends to uncover associations between genetic markers and neuroimaging quantitative traits. Sparse canonical correlation analysis (SCCA) can discover bi-multivariate associations and select relevant features, and is becoming popular in imaging genetic studies. The L1-norm function is not only convex, but also singular at the origin, which is a necessary condition for sparsity. Thus most SCCA methods impose [Formula: see text]-norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the [Formula: see text]-norm penalty over-penalizes large coefficients and may incurs estimation bias. A number of non-convex penalties are proposed to reduce the estimation bias in regression tasks. But using them in SCCA remains largely unexplored. In this paper, we design a unified non-convex SCCA model, based on seven non-convex functions, for unbiased estimation and stable feature selection simultaneously. We also propose an efficient optimization algorithm. The proposed method obtains both higher correlation coefficients and better canonical loading patterns. Specifically, these SCCA methods with non-convex penalties discover a strong association between the APOE e4 rs429358 SNP and the hippocampus region of the brain. They both are Alzheimer's disease related biomarkers, indicating the potential and power of the non-convex methods in brain imaging genetics.

Approximate message passing for nonconvex sparse regularization with stability and asymptotic analysis

Science.gov (United States)

Sakata, Ayaka; Xu, Yingying

2018-03-01

We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm considering nonconvex regularization, namely SCAD-AMP, and analytically show that the stability condition corresponds to the de Almeida-Thouless condition in spin glass literature. Through asymptotic analysis, we show the correspondence between the density evolution of SCAD-AMP and the replica symmetric (RS) solution. Numerical experiments confirm that for a sufficiently large system size, SCAD-AMP achieves the optimal performance predicted by the replica method. Through replica analysis, a phase transition between replica symmetric and replica symmetry breaking (RSB) region is found in the parameter space of SCAD. The appearance of the RS region for a nonconvex penalty is a significant advantage that indicates the region of smooth landscape of the optimization problem. Furthermore, we analytically show that the statistical representation performance of the SCAD penalty is better than that of \

Generalized Bregman distances and convergence rates for non-convex regularization methods

International Nuclear Information System (INIS)

Grasmair, Markus

2010-01-01

We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order δ 1/p holds, if the regularization term has a slightly faster growth at zero than |t| p

Efficiency measurement with a non-convex free disposal hull technology

DEFF Research Database (Denmark)

Fukuyama, Hirofumi; Hougaard, Jens Leth; Sekitani, Kazuyuki

2016-01-01

We investigate the basic monotonicity properties of least-distance (in)efficiency measures on the class of non-convex FDH (free disposable hull) technologies. We show that any known FDH least-distance measure violates strong monotonicity over the strongly (Pareto-Koopmans) efficient frontier. Tak....... Taking this result into account, we develop a new class of FDH least-distance measures that satisfy strong monotonicity and show that the developed (in)efficiency measurement framework has a natural profit interpretation.......We investigate the basic monotonicity properties of least-distance (in)efficiency measures on the class of non-convex FDH (free disposable hull) technologies. We show that any known FDH least-distance measure violates strong monotonicity over the strongly (Pareto-Koopmans) efficient frontier...

Anomalous dynamics triggered by a non-convex equation of state in relativistic flows

Science.gov (United States)

Ibáñez, J. M.; Marquina, A.; Serna, S.; Aloy, M. A.

2018-05-01

The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density (n0 ≈ 0.16 fm-3) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, the parameters of which can be restricted owing to causality and thermodynamic stability constraints. This EoS can be regarded as a toy model with which we may mimic realistic (and far more complex) EoSs of practical use in the realm of relativistic hydrodynamics.

Towards reproducible experimental studies for non-convex polyhedral shaped particles

Directory of Open Access Journals (Sweden)

Wilke Daniel N.

2017-01-01

Full Text Available The packing density and flat bottomed hopper discharge of non-convex polyhedral particles are investigated in a systematic experimental study. The motivation for this study is two-fold. Firstly, to establish an approach to deliver quality experimental particle packing data for non-convex polyhedral particles that can be used for characterization and validation purposes of discrete element codes. Secondly, to make the reproducibility of experimental setups as convenient and readily available as possible using affordable and accessible technology. The primary technology for this study is fused deposition modeling used to 3D print polylactic acid (PLA particles using readily available 3D printer technology. A total of 8000 biodegradable particles were printed, 1000 white particles and 1000 black particles for each of the four particle types considered in this study. Reproducibility is one benefit of using fused deposition modeling to print particles, but an extremely important additional benefit is that specific particle properties can be explicitly controlled. As an example in this study the volume fraction of each particle can be controlled i.e. the effective particle density can be adjusted. In this study the particle volumes reduces drastically as the non-convexity is increased, however all printed white particles in this study have the same mass within 2% of each other.

Towards reproducible experimental studies for non-convex polyhedral shaped particles

Science.gov (United States)

Wilke, Daniel N.; Pizette, Patrick; Govender, Nicolin; Abriak, Nor-Edine

2017-06-01

The packing density and flat bottomed hopper discharge of non-convex polyhedral particles are investigated in a systematic experimental study. The motivation for this study is two-fold. Firstly, to establish an approach to deliver quality experimental particle packing data for non-convex polyhedral particles that can be used for characterization and validation purposes of discrete element codes. Secondly, to make the reproducibility of experimental setups as convenient and readily available as possible using affordable and accessible technology. The primary technology for this study is fused deposition modeling used to 3D print polylactic acid (PLA) particles using readily available 3D printer technology. A total of 8000 biodegradable particles were printed, 1000 white particles and 1000 black particles for each of the four particle types considered in this study. Reproducibility is one benefit of using fused deposition modeling to print particles, but an extremely important additional benefit is that specific particle properties can be explicitly controlled. As an example in this study the volume fraction of each particle can be controlled i.e. the effective particle density can be adjusted. In this study the particle volumes reduces drastically as the non-convexity is increased, however all printed white particles in this study have the same mass within 2% of each other.

A duality recipe for non-convex variational problems

Science.gov (United States)

Bouchitté, Guy; Phan, Minh

2018-03-01

The aim of this paper is to present a general convexification recipe that can be useful for studying non-convex variational problems. In particular, this allows us to treat such problems by using a powerful primal-dual scheme. Possible further developments and open issues are given. xml:lang="fr"

Efficient Estimation of Extreme Non-linear Roll Motions using the First-order Reliability Method (FORM)

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2007-01-01

In on-board decision support systems efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given on-line information on the sea state and user defined ranges of possible headings and speeds. For linear responses standard...... frequency domain methods can be applied. To non-linear responses like the roll motion, standard methods like direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using...... the first-order reliability method (FORM), well-known from structural reliability problems. To illustrate the proposed procedure, the roll motion is modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments...

Nonlinear surge motions of a ship in bi-chromatic following waves

Science.gov (United States)

Spyrou, Kostas J.; Themelis, Nikos; Kontolefas, Ioannis

2018-03-01

Unintended motions of a ship operating in steep and long following waves are investigated. A well-known such case is ;surf-riding; where a ship is carried forward by a single wave, an event invoking sometimes lateral instability and even capsize. The dynamics underlying this behavior has been clarified earlier for monochromatic waves. However, the unsteadiness of the phase space associated with ship behavior in a multichromatic sea, combined with the intrinsically strong system nonlinearity, pose new challenges. Here, current theory is extended to cover surging and surf-riding behavior in unidirectional bi-chromatic waves encountering a ship from the stern. Excitation is provided by two unidirectional harmonic wave components having their lengths comparable to the ship length and their frequencies in rational ratio. The techniques applied include (a) continuation analysis; (b) tracking of Lagrangian coherent structures in phase space, approximated through a finite-time Lyapunov exponents' calculation; and (c) large scale simulation. A profound feature of surf-riding in bi-chromatic waves is that it is turned oscillatory. Initially it appears as a frequency-locked motion, ruled by the harmonic wave component dominating the excitation. Transformations of oscillatory surf-riding are realized as the waves become steeper. In particular, heteroclinic tanglings are identified, governing abrupt transitions between qualitatively different motions. Chaotic transients, as well as long-term chaotic motions, exist near to these events. Some extraordinary patterns of ship motion are discovered. These include a counterintuitive low speed motion at very high wave excitation level; and a hybrid motion characterized by a wildly fluctuating velocity. Due to the quite generic nature of the core mathematical model of our investigation, the current results are believed to offer clues about the behavior of a class of nonlinear dynamical systems having in their modeling some analogy with

Interior-Point Method for Non-Linear Non-Convex Optimization

Czech Academy of Sciences Publication Activity Database

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

2004-01-01

Roč. 11, č. 5-6 (2004), s. 431-453 ISSN 1070-5325 R&D Projects: GA AV ČR IAA1030103 Institutional research plan: CEZ:AV0Z1030915 Keywords : non-linear programming * interior point methods * indefinite systems * indefinite preconditioners * preconditioned conjugate gradient method * merit functions * algorithms * computational experiments Subject RIV: BA - General Mathematics Impact factor: 0.727, year: 2004

Simplified Methods Applied to Nonlinear Motion of Spar Platforms

Energy Technology Data Exchange (ETDEWEB)

Haslum, Herbjoern Alf

2000-07-01

Simplified methods for prediction of motion response of spar platforms are presented. The methods are based on first and second order potential theory. Nonlinear drag loads and the effect of the pumping motion in a moon-pool are also considered. Large amplitude pitch motions coupled to extreme amplitude heave motions may arise when spar platforms are exposed to long period swell. The phenomenon is investigated theoretically and explained as a Mathieu instability. It is caused by nonlinear coupling effects between heave, surge, and pitch. It is shown that for a critical wave period, the envelope of the heave motion makes the pitch motion unstable. For the same wave period, a higher order pitch/heave coupling excites resonant heave response. This mutual interaction largely amplifies both the pitch and the heave response. As a result, the pitch/heave instability revealed in this work is more critical than the previously well known Mathieu's instability in pitch which occurs if the wave period (or the natural heave period) is half the natural pitch period. The Mathieu instability is demonstrated both by numerical simulations with a newly developed calculation tool and in model experiments. In order to learn more about the conditions for this instability to occur and also how it may be controlled, different damping configurations (heave damping disks and pitch/surge damping fins) are evaluated both in model experiments and by numerical simulations. With increased drag damping, larger wave amplitudes and more time are needed to trigger the instability. The pitch/heave instability is a low probability of occurrence phenomenon. Extreme wave periods are needed for the instability to be triggered, about 20 seconds for a typical 200m draft spar. However, it may be important to consider the phenomenon in design since the pitch/heave instability is very critical. It is also seen that when classical spar platforms (constant cylindrical cross section and about 200m draft

Reconstruction of Undersampled Big Dynamic MRI Data Using Non-Convex Low-Rank and Sparsity Constraints

Directory of Open Access Journals (Sweden)

Ryan Wen Liu

2017-03-01

Full Text Available Dynamic magnetic resonance imaging (MRI has been extensively utilized for enhancing medical living environment visualization, however, in clinical practice it often suffers from long data acquisition times. Dynamic imaging essentially reconstructs the visual image from raw (k,t-space measurements, commonly referred to as big data. The purpose of this work is to accelerate big medical data acquisition in dynamic MRI by developing a non-convex minimization framework. In particular, to overcome the inherent speed limitation, both non-convex low-rank and sparsity constraints were combined to accelerate the dynamic imaging. However, the non-convex constraints make the dynamic reconstruction problem difficult to directly solve through the commonly-used numerical methods. To guarantee solution efficiency and stability, a numerical algorithm based on Alternating Direction Method of Multipliers (ADMM is proposed to solve the resulting non-convex optimization problem. ADMM decomposes the original complex optimization problem into several simple sub-problems. Each sub-problem has a closed-form solution or could be efficiently solved using existing numerical methods. It has been proven that the quality of images reconstructed from fewer measurements can be significantly improved using non-convex minimization. Numerous experiments have been conducted on two in vivo cardiac datasets to compare the proposed method with several state-of-the-art imaging methods. Experimental results illustrated that the proposed method could guarantee the superior imaging performance in terms of quantitative and visual image quality assessments.

Functional analysis and applied optimization in Banach spaces applications to non-convex variational models

CERN Document Server

Botelho, Fabio

2014-01-01

This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

Robust Control and Motion Planning for Nonlinear Underactuated Systems Using H infinity Techniques

National Research Council Canada - National Science Library

Toussaint, Gregory

2000-01-01

This thesis presents new techniques for planning and robustly controlling the motion of nonlinear underactuated vehicles when disturbances are present and only imperfect state measurements are available for feedback...

Influence of earthquake strong motion duration on nonlinear structural response

International Nuclear Information System (INIS)

Meskouris, K.

1983-01-01

The effects of motion duration on nonlinear structural response of high-rise, moment resisting frames are studied by subjecting shear beam models of a 10- and a 5-story frame to a series of synthetic accelerograms, all matching the same NEWMARK/HALL design spectrum. Two different hysteretic laws are used for the story springs, and calculations are carried out for target ductility values of 2 and 4. Maximum ductilities reached and energy-based damage indicators (maximum seismically input energy, hysteretically dissipated energy) are evaluated and correlated with the motion characteristics. A reasonable extrapolative determination of structural response characteristics based on these indicators seems possible. (orig.)

A one-layer recurrent neural network for constrained nonconvex optimization.

Science.gov (United States)

Li, Guocheng; Yan, Zheng; Wang, Jun

2015-01-01

In this paper, a one-layer recurrent neural network is proposed for solving nonconvex optimization problems subject to general inequality constraints, designed based on an exact penalty function method. It is proved herein that any neuron state of the proposed neural network is convergent to the feasible region in finite time and stays there thereafter, provided that the penalty parameter is sufficiently large. The lower bounds of the penalty parameter and convergence time are also estimated. In addition, any neural state of the proposed neural network is convergent to its equilibrium point set which satisfies the Karush-Kuhn-Tucker conditions of the optimization problem. Moreover, the equilibrium point set is equivalent to the optimal solution to the nonconvex optimization problem if the objective function and constraints satisfy given conditions. Four numerical examples are provided to illustrate the performances of the proposed neural network.

Chance-Constrained Guidance With Non-Convex Constraints

Science.gov (United States)

Ono, Masahiro

2011-01-01

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of

A modified artificial bee colony based on chaos theory for solving non-convex emission/economic dispatch

International Nuclear Information System (INIS)

Shayeghi, H.; Ghasemi, A.

2014-01-01

Highlights: • This paper presents a developed multi objective CIABC based on CLS theory for solving EED problem. • The EED problem is formulated as a non-convex multi objective optimization problem. • Considered three test systems to demonstrate its efficiency including practical constrains. • The significant improvement in the results comparing the reported literature. - Abstract: In this paper, a modified ABC based on chaos theory namely CIABC is comprehensively enhanced and effectively applied for solving a multi-objective EED problem to minimize three conflicting objective functions with non-smooth and non-convex generator fuel cost characteristics while satisfying the operation constraints. The proposed method uses a Chaotic Local Search (CLS) to enhance the self searching ability of the original ABC algorithm for finding feasible optimal solutions of the EED problem. Also, many linear and nonlinear constraints, such as generation limits, transmission line loss, security constraints and non-smooth cost functions are considered as dynamic operational constraints. Moreover, a method based on fuzzy set theory is employed to extract one of the Pareto-optimal solutions as the best compromise one. The proposed multi objective evolutionary method has been applied to the standard IEEE 30 bus six generators, fourteen generators and 40 thermal generating units, respectively, as small, medium and large test power system. The numerical results obtained with the proposed method based on tables and figures compared with other evolutionary algorithm of scientific literatures. The results regards that the proposed CIABC algorithm surpasses the other available methods in terms of computational efficiency and solution quality

Realising traceable electrostatic forces despite non-linear balance motion

International Nuclear Information System (INIS)

Stirling, Julian; Shaw, Gordon A

2017-01-01

Direct realisation of force, traceable to fundamental constants via electromagnetic balances, is a key goal of the proposed redefinition of the international system of units (SI). This will allow small force metrology to be performed using an electrostatic force balance (EFB) rather than subdivision of larger forces. Such a balance uses the electrostatic force across a capacitor to balance an external force. In this paper we model the capacitance of a concentric cylinder EFB design as a function of the displacement of its free electrode, accounting for the arcuate motion produced by parallelogram linkages commonly used in EFB mechanisms. From this model we suggest new fitting procedures to reduce uncertainties arising from non-linear motion as well as methods to identify misalignment of the mechanism. Experimental studies on both a test capacitor and the NIST EFB validate the model. (paper)

Anti-predatory particle swarm optimization: Solution to nonconvex economic dispatch problems

Energy Technology Data Exchange (ETDEWEB)

Selvakumar, A. Immanuel [Department of Electrical and Electronics Engineering, Karunya Institute of Technology and Sciences, Coimbatore 641114, Tamilnadu (India); Thanushkodi, K. [Department of Electronics and Instrumentation Engineering, Government College of Technology, Coimbatore 641013, Tamilnadu (India)

2008-01-15

This paper proposes a new particle swarm optimization (PSO) strategy namely, anti-predatory particle swarm optimization (APSO) to solve nonconvex economic dispatch problems. In the classical PSO, the movement of a particle (bird) is governed by three behaviors: inertial, cognitive and social. The cognitive and social behaviors are the components of the foraging activity, which help the swarm of birds to locate food. Another activity that is observed in birds is the anti-predatory nature, which helps the swarm to escape from the predators. In this work, the anti-predatory activity is modeled and embedded in the classical PSO to form APSO. This inclusion enhances the exploration capability of the swarm. To validate the proposed APSO model, it is applied to two test systems having nonconvex solution spaces. Satisfactory results are obtained when compared with previous approaches. (author)

The imprint of proper motion of nonlinear structures on the cosmic microwave background

Science.gov (United States)

Tuluie, Robin; Laguna, Pablo

1995-01-01

We investigate the imprint of nonlinear matter condensations on the cosmic microwave background (CMB) in an Omega = 1, cold dark matter (CDM) model universe. Temperature anisotropies are obtained by numerically evolving matter inhomogeneities and CMB photons from the beginning of decoupling until the present epoch. The underlying density field produced by the inhomogeneities is followed from the linear, through the weakly clustered, into the fully nonlinear regime. We concentrate on CMB temperature distortions arising from variations in the gravitational potentials of nonlinear structures. We find two sources of temperature fluctuations produced by time-varying potentials: (1) anisotropies due to intrinsic changes in the gravitational potentials of the inhomogeneities and (2) anisotropies generated by the peculiar, bulk motion of the structures across the microwave sky. Both effects generate CMB anisotropies in the range of 10(exp -7) approximately less than or equal to (Delta T/T) approximately less than or equal to 10(exp -6) on scales of approximately 1 deg. For isolated structures, anisotropies due to proper motion exhibit a dipole-like signature in the CMB sky that in principle could yield information on the transverse velocity of the structures.

Equations of motion for anisotropic nonlinear elastic continuum in gravitational field

International Nuclear Information System (INIS)

Sokolov, S.N.

1994-01-01

Equations of motion for anisotropic nonlinear elastic continuum in the gravitational field are written in the form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors frozen in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given. 47 refs

An Approximate Redistributed Proximal Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions

Directory of Open Access Journals (Sweden)

Jie Shen

2015-01-01

Full Text Available We describe an extension of the redistributed technique form classical proximal bundle method to the inexact situation for minimizing nonsmooth nonconvex functions. The cutting-planes model we construct is not the approximation to the whole nonconvex function, but to the local convexification of the approximate objective function, and this kind of local convexification is modified dynamically in order to always yield nonnegative linearization errors. Since we only employ the approximate function values and approximate subgradients, theoretical convergence analysis shows that an approximate stationary point or some double approximate stationary point can be obtained under some mild conditions.

Complex motion in nonlinear-map model of elevators in energy-saving traffic

Science.gov (United States)

Nagatani, Takashi

2011-05-01

We have studied the dynamic behavior and dynamic transitions of elevators in a system for reducing energy consumption. We present a nonlinear-map model for the dynamics of M elevators. The motion of elevators depends on the loading parameter and their number M. The dependence of the fixed points on the loading parameter is derived. The dynamic transitions occur at 2(M-1) stages with increasing the value of loading parameter. At the dynamic transition point, the motion of elevators changes from a stable state to an unstable state and vice versa. The elevators display periodic motions with various periods in the unstable state. In the unstable state, the number of riding passengers fluctuates in a complex manner over various trips.

Directed motion generated by heat bath nonlinearly driven by external noise

International Nuclear Information System (INIS)

Chaudhuri, J Ray; Barik, D; Banik, S K

2007-01-01

Based on the heat bath system approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system. Making use of the coupling between the heat bath and the external modulation as a small perturbation, we construct a Langevin equation with multiplicative noise- and space-dependent dissipation and the corresponding Fokker-Planck-Smoluchowski equation in the overdamped limit. We examine the thermodynamic consistency condition and explore the possibility of observing a phase-induced current as a consequence of state-dependent diffusion and, necessarily, nonlinear driving of the heat bath by the external noise

Directed motion generated by heat bath nonlinearly driven by external noise

Energy Technology Data Exchange (ETDEWEB)

Chaudhuri, J Ray [Department of Physics, Katwa College, Katwa, Burdwan 713 130, West Bengal (India); Barik, D [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032 (India); Banik, S K [Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0435 (United States)

2007-12-07

Based on the heat bath system approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system. Making use of the coupling between the heat bath and the external modulation as a small perturbation, we construct a Langevin equation with multiplicative noise- and space-dependent dissipation and the corresponding Fokker-Planck-Smoluchowski equation in the overdamped limit. We examine the thermodynamic consistency condition and explore the possibility of observing a phase-induced current as a consequence of state-dependent diffusion and, necessarily, nonlinear driving of the heat bath by the external noise.

Nonlinear Analysis of Two-phase Circumferential Motion in the Ablation Circumstance

Science.gov (United States)

Xiao-liang, Xu; Hai-ming, Huang; Zi-mao, Zhang

2010-05-01

In aerospace craft reentry and solid rocket propellant nozzle, thermal chemistry ablation is a complex process coupling with convection, heat transfer, mass transfer and chemical reaction. Based on discrete vortex method (DVM), thermal chemical ablation model and particle kinetic model, a computational module dealing with the two-phase circumferential motion in ablation circumstance is designed, the ablation velocity and circumferential field can be thus calculated. The calculated nonlinear time series are analyzed in chaotic identification method: relative chaotic characters such as correlation dimension and the maximum Lyapunov exponent are calculated, fractal dimension of vortex bulbs and particles distributions are also obtained, thus the nonlinear ablation process can be judged as a spatiotemporal chaotic process.

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.

Deformation patterning driven by rate dependent non-convex strain gradient plasticity

NARCIS (Netherlands)

Yalcinkaya, T.; Brekelmans, W.A.M.; Geers, M.G.D.

2011-01-01

A rate dependent strain gradient plasticity framework for the description of plastic slip patterning in a system with non-convex energetic hardening is presented. Both the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by

Nonconvex model predictive control for commercial refrigeration

Science.gov (United States)

Gybel Hovgaard, Tobias; Boyd, Stephen; Larsen, Lars F. S.; Bagterp Jørgensen, John

2013-08-01

We consider the control of a commercial multi-zone refrigeration system, consisting of several cooling units that share a common compressor, and is used to cool multiple areas or rooms. In each time period we choose cooling capacity to each unit and a common evaporation temperature. The goal is to minimise the total energy cost, using real-time electricity prices, while obeying temperature constraints on the zones. We propose a variation on model predictive control to achieve this goal. When the right variables are used, the dynamics of the system are linear, and the constraints are convex. The cost function, however, is nonconvex due to the temperature dependence of thermodynamic efficiency. To handle this nonconvexity we propose a sequential convex optimisation method, which typically converges in fewer than 5 or so iterations. We employ a fast convex quadratic programming solver to carry out the iterations, which is more than fast enough to run in real time. We demonstrate our method on a realistic model, with a full year simulation and 15-minute time periods, using historical electricity prices and weather data, as well as random variations in thermal load. These simulations show substantial cost savings, on the order of 30%, compared to a standard thermostat-based control system. Perhaps more important, we see that the method exhibits sophisticated response to real-time variations in electricity prices. This demand response is critical to help balance real-time uncertainties in generation capacity associated with large penetration of intermittent renewable energy sources in a future smart grid.

Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis

Science.gov (United States)

2016-10-11

stationary point. These results are the state of art in complexity analysis of non-convex optimization. “Complexity of Unconstrained L2-Lp Minimization...Parameter Optimized Radiation Therapy ( SPORT )” (M Zarepisheh, Y Ye, S Boyd, R Li, L Xing), Medical Physics 41(6) (2014) 292-292. Station parameter...optimized radiation therapy ( SPORT ) was recently proposed to fully utilize the technical capability of emerging digital linear accelerators, in

Unusual motions due to nonlinear effects in a driven vibrating string

Science.gov (United States)

Hanson, Roger J.

2005-09-01

Usual nonlinear effects observed in a sinusoidally driven vibrating string include generation of motion perpendicular to the driving plane, sudden jumps of amplitude and associated hysteresis, and generation of higher harmonics. In addition, under some conditions, there can be a rich variety of unusual, very complex motions of a point on the string, the pattern of which, together with associated harmonic (and sometimes subharmonic) content, can change dramatically with a slight change in driving frequency or sometimes with constant driving frequency and force. Intrinsic string asymmetries can also have a profound effect on the behavior. In a brass harpsichord string (wire) such asymmetries can cause a small splitting of each natural frequency of free vibration into two closely spaced frequencies (relative separation ~0.2% to 2%, strongly dependent on tension.) The two frequency components are associated, respectively, with the transverse motion along two orthogonal characteristic wire axes. Emphasis will be on display of optically detected unusual motion patterns of a point on the string, including an example of a pattern period of 10 s when driving at 50 Hz. See R. J. Hanson et al., J. Acoust. Soc. Am. 117, 400-412 (2005) for a more complete treatment.

Nonlinear dynamic response of cable-suspended systems under swinging and heaving motion

International Nuclear Information System (INIS)

Cao, Guohua; Wang, Naige; Wang, Lei; Zhu, Zhencai

2017-01-01

In order to enhance the fidelity, convenient and flexibility of swinging motion, the structure of incompletely restrained cablesuspended system controlled by two drums was proposed, and the dynamic response of the system under swinging and heaving motion were investigated in this paper. The cables are spatially discretized using the assumed modes method and the system equations of motion are derived by Lagrange equations of the first kind. Based on geometric boundary conditions and linear complementary theory, the differential algebraic equations are transformed to a set of classical difference equations. Nonlinear dynamic behavior occurs under certain range of rotational velocity and frequency. The results show that asynchronous motion of suspension platform is easily caused imbalance for cable tension. Dynamic response of different swing frequencies were obtained via power frequency analysis, which could be used in the selection of the working frequency of the swing motion. The work will contribute to a better understanding of the swing frequency, cable tension and posture with dynamic characteristics of unilateral geometric and kinematic constraints in this system, and it is also useful to investigate the accuracy and reliability of instruments in future.

Nonlinear dynamic response of cable-suspended systems under swinging and heaving motion

Energy Technology Data Exchange (ETDEWEB)

Cao, Guohua; Wang, Naige; Wang, Lei; Zhu, Zhencai [China University of Mining and Technology, Xuzhou (China)

2017-07-15

In order to enhance the fidelity, convenient and flexibility of swinging motion, the structure of incompletely restrained cablesuspended system controlled by two drums was proposed, and the dynamic response of the system under swinging and heaving motion were investigated in this paper. The cables are spatially discretized using the assumed modes method and the system equations of motion are derived by Lagrange equations of the first kind. Based on geometric boundary conditions and linear complementary theory, the differential algebraic equations are transformed to a set of classical difference equations. Nonlinear dynamic behavior occurs under certain range of rotational velocity and frequency. The results show that asynchronous motion of suspension platform is easily caused imbalance for cable tension. Dynamic response of different swing frequencies were obtained via power frequency analysis, which could be used in the selection of the working frequency of the swing motion. The work will contribute to a better understanding of the swing frequency, cable tension and posture with dynamic characteristics of unilateral geometric and kinematic constraints in this system, and it is also useful to investigate the accuracy and reliability of instruments in future.

Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System

Science.gov (United States)

Amjad, Hussain; Syed Tauseef, Mohyud-Din; Ahmet, Yildirim

2012-03-01

MacMillan's equations are extended to Poincaré's formalism, and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré parameters. The equivalence of the results obtained here with other forms of equations of motion is demonstrated. An illustrative example of the theory is provided as well.

96 International Conference on Nonlinear Programming

CERN Document Server

1998-01-01

About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu­ tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi­ nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi­ hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by...

Relaxation and decomposition methods for mixed integer nonlinear programming

CERN Document Server

Nowak, Ivo; Bank, RE

2005-01-01

This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.

Nonlinear seismic behavior of a CANDU containment building subjected to near-field ground motions

International Nuclear Information System (INIS)

Choi, In Kil; Ahn, Seong Moon; Choun, Young Sun; Seo, Jeong Moon

2004-01-01

The standard response spectrum proposed by US NRC has been used as a design earthquake for the design of Korean nuclear power plant structures. A survey on some of the Quaternary fault segments near Korean nuclear power plants is ongoing. It is likely that these faults will be identified as active ones. If the faults are confirmed as active ones, it will be necessary to reevaluate the seismic safety of the nuclear power plants located near the fault. Near-fault ground motions are the ground motions that occur near an earthquake fault. In general, the near-fault ground motion records exhibit a distinctive long period pulse like time history with very high peak velocities. These features are induced by the slip of the earthquake fault. Near-fault ground motions, which have caused much of the damage in recent major earthquakes, can be characterized by a pulse-like motion that exposes the structure to a high input energy at the beginning of the motion. In this study, nonlinear dynamic time-history analyses were performed to investigate the seismic behavior of a CANDU containment structure subjected to various earthquake ground motions including the near-field ground motions

Reference Information Based Remote Sensing Image Reconstruction with Generalized Nonconvex Low-Rank Approximation

Directory of Open Access Journals (Sweden)

Hongyang Lu

2016-06-01

Full Text Available Because of the contradiction between the spatial and temporal resolution of remote sensing images (RSI and quality loss in the process of acquisition, it is of great significance to reconstruct RSI in remote sensing applications. Recent studies have demonstrated that reference image-based reconstruction methods have great potential for higher reconstruction performance, while lacking accuracy and quality of reconstruction. For this application, a new compressed sensing objective function incorporating a reference image as prior information is developed. We resort to the reference prior information inherent in interior and exterior data simultaneously to build a new generalized nonconvex low-rank approximation framework for RSI reconstruction. Specifically, the innovation of this paper consists of the following three respects: (1 we propose a nonconvex low-rank approximation for reconstructing RSI; (2 we inject reference prior information to overcome over smoothed edges and texture detail losses; (3 on this basis, we combine conjugate gradient algorithms and a single-value threshold (SVT simultaneously to solve the proposed algorithm. The performance of the algorithm is evaluated both qualitatively and quantitatively. Experimental results demonstrate that the proposed algorithm improves several dBs in terms of peak signal to noise ratio (PSNR and preserves image details significantly compared to most of the current approaches without reference images as priors. In addition, the generalized nonconvex low-rank approximation of our approach is naturally robust to noise, and therefore, the proposed algorithm can handle low resolution with noisy inputs in a more unified framework.

Effect of spatial variability of ground motion on non-linear dynamic behavior of cable stayed bridges

Directory of Open Access Journals (Sweden)

Ouanani Mouloud

2018-01-01

Full Text Available This present paper summarizes the main results of incoherence of Spatial Variability of Ground Motion (SVGM component on the non-linear dynamic behavior of a Mila cable stayed bridge. The Hindy and Novack coherence model is developed for the present study in order to examine the SVGM on bridge responses, Nonlinear bridge responses are investigated in terms of transverse displacements and bending moments along the superstructure and substructure of the study bridge, as well as temporal variations of rotational ductility demands at the bridge piers ends under the incoherence SVGM component. The results are systematically compared with those obtained assuming uniform ground motion. As a general trend, it may be concluded that incoherence component of SVGM should be considered for the earthquake response assessments of cable-stayed bridges.

Finite Element Modeling and Analysis of Nonlinear Impact and Frictional Motion Responses Including Fluid—Structure Coupling Effects

Directory of Open Access Journals (Sweden)

Yong Zhao

1997-01-01

Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.

Higher-Order Approximations of Motion of a Nonlinear Oscillator Using the Parameter Expansion Technique

Science.gov (United States)

Ganji, S. S.; Domairry, G.; Davodi, A. G.; Babazadeh, H.; Seyedalizadeh Ganji, S. H.

The main objective of this paper is to apply the parameter expansion technique (a modified Lindstedt-Poincaré method) to calculate the first, second, and third-order approximations of motion of a nonlinear oscillator arising in rigid rod rocking back. The dynamics and frequency of motion of this nonlinear mechanical system are analyzed. A meticulous attention is carried out to the study of the introduced nonlinearity effects on the amplitudes of the oscillatory states and on the bifurcation structures. We examine the synchronization and the frequency of systems using both the strong and special method. Numerical simulations and computer's answers confirm and complement the results obtained by the analytical approach. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. The solutions of this method are compared with the exact ones in order to validate the approach, and assess the accuracy of the solutions. In particular, APL-PM works well for the whole range of oscillation amplitudes and excellent agreement of the approximate frequency with the exact one has been demonstrated. The approximate period derived here is accurate and close to the exact solution. This method has a distinguished feature which makes it simple to use, and also it agrees with the exact solutions for various parameters.

Cohesive granular media modelization with non-convex particles shape: Application to UO2 powder compaction

International Nuclear Information System (INIS)

Saint-Cyr, B.

2011-01-01

We model in this work granular materials composed of non-convex and cohesive aggregates, in view of application to the rheology of UO 2 powders. The effect of non convexity is analyzed in terms of bulk quantities (Coulomb internal friction and cohesion) and micromechanical parameters such as texture anisotropy and force transmission. In particular, we find that the packing fraction evolves in a complex manner with the shape non convexity and the shear strength increases but saturates due to interlocking between the aggregates. We introduce simple models to describe these features in terms of micro-mechanical parameters. Furthermore, a systematic investigation of shearing, uniaxial compaction and simple compression of cohesive packings show that bulk cohesion increases with non-convexity but is strongly influenced by the boundary conditions and shear bands or stress concentration. (author) [fr

Experimental studies of nonlinear beam dynamics

International Nuclear Information System (INIS)

Caussyn, D.D.; Ball, M.; Brabson, B.; Collins, J.; Curtis, S.A.; Derenchuck, V.; DuPlantis, D.; East, G.; Ellison, M.; Ellison, T.; Friesel, D.; Hamilton, B.; Jones, W.P.; Lamble, W.; Lee, S.Y.; Li, D.; Minty, M.G.; Sloan, T.; Xu, G.; Chao, A.W.; Ng, K.Y.; Tepikian, S.

1992-01-01

The nonlinear beam dynamics of transverse betatron oscillations were studied experimentally at the Indiana University Cyclotron Facility cooler ring. Motion in one dimension was measured for betatron tunes near the third, fourth, fifth, and seventh integer resonances. This motion is described by coupling between the transverse modes of motion and nonlinear field errors. The Hamiltonian for nonlinear particle motion near the third- and fourth-integer-resonance conditions has been deduced

Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization

Science.gov (United States)

2016-11-22

structure of the graph, we replace the ℓ1- norm by the nonconvex Capped -ℓ1 norm , and obtain the Generalized Capped -ℓ1 regularized logistic regression...X. M. Yuan. Linearized augmented lagrangian and alternating direction methods for nuclear norm minimization. Mathematics of Computation, 82(281):301...better approximations of ℓ0- norm theoretically and computationally beyond ℓ1- norm , for example, the compressive sensing (Xiao et al., 2011). The

Unified solution of a non-convex SCUC problem using combination of modified Branch-and-Bound method with Quadratic Programming

International Nuclear Information System (INIS)

Shafie-khah, M.; Parsa Moghaddam, M.; Sheikh-El-Eslami, M.K.

2011-01-01

Highlights: → A hybrid SCUC solution is developed to deal with large-scale, real-time and long-term problems. → New formulations are proposed for considering valve point effect and warmth-dependent start-up cost. → A new algorithm is developed for modeling the AC power flow in SCUC problems. → Using the power flow algorithm both steps in traditional SCUC is done simultaneously. → The proposed method provides better solutions than previous ones with a fast speed. - Abstract: In this paper, a new practical method is presented for solving the non-convex security constraint unit commitment (SCUC) problem in power systems. The accuracy of the proposed method is desirable while the shorter computation time makes it useful for SCUC solution of large-scale power systems, real-time market operation and long-term SCUC problems. The proposed framework allows inclusion of the valve point effects, warmth-dependent start-up costs, ramp rates, minimum up/down time constraints, multiple fuels costs, emission costs, prohibited operating zones and AC power flow limits in normal and contingency conditions. To solve the non-convex problem, combination of a modified Branch-and-Bound method with the Quadratic Programming is used as an optimization tool and a developed AC power flow algorithm is applied for considering the security and contingency concerns using the nonlinear/linear AC model. These modifications improve the convergence speed and solution precision of SCUC problem. In the proposed method, in contrast with traditional SCUC algorithms, unit commitment solution, checking and satisfying the security constraints are managed simultaneously. The obtained results are compared with other reported methods for investigating the effectiveness of the proposed method. Also, the proposed method is applied to an Iranian power system including 493 thermal units.

Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

Directory of Open Access Journals (Sweden)

Messaoud Bounkhel

2013-01-01

Full Text Available In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t∈F(t,x(t a.e. on I, x(t∈S, ∀t∈I, x(0=x0∈S, (*, where S is a closed subset in a Banach space , I=[0,T], (T>0, F:I×S→, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x⊂c(tx+xp, ∀(t,x∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+. The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.

Nonlinearity, Viscosity and Air-Compressibility Effects on the Helmholtz Resonant Wave Motion Generated by an Oscillating Twin Body in a Free Surface

Science.gov (United States)

Ananthakrishnan, Palaniswamy

2012-11-01

The problem is of practical relevance in determining the motion response of multi-hull and air-cushion vehicles in high seas and in littoral waters. The linear inviscid problem without surface pressure has been well studied in the past. In the present work, the nonlinear wave-body interaction problem is solved using finite-difference methods based on boundary-fitted coordinates. The inviscid nonlinear problem is tackled using the mixed Eulerian-Lagrangian formulation and the solution of the incompressible Navier-Stokes equations governing the viscous problem using a fractional-step method. The pressure variation in the air cushion is modeled using the isentropic gas equation pVγ = Constant. Results show that viscosity and free-surface nonlinearity significantly affect the hydrodynamic force and the wave motion at the resonant Helmholtz frequency (at which the primary wave motion is the vertical oscillation of the mean surface in between the bodies). Air compressibility suppresses the Helmholtz oscillation and enhances the wave radiation. Work supported by the ONR under the grant N00014-98-1-0151.

Stochastic Blind Motion Deblurring

KAUST Repository

Xiao, Lei

2015-05-13

Blind motion deblurring from a single image is a highly under-constrained problem with many degenerate solutions. A good approximation of the intrinsic image can therefore only be obtained with the help of prior information in the form of (often non-convex) regularization terms for both the intrinsic image and the kernel. While the best choice of image priors is still a topic of ongoing investigation, this research is made more complicated by the fact that historically each new prior requires the development of a custom optimization method. In this paper, we develop a stochastic optimization method for blind deconvolution. Since this stochastic solver does not require the explicit computation of the gradient of the objective function and uses only efficient local evaluation of the objective, new priors can be implemented and tested very quickly. We demonstrate that this framework, in combination with different image priors produces results with PSNR values that match or exceed the results obtained by much more complex state-of-the-art blind motion deblurring algorithms.

Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

International Nuclear Information System (INIS)

Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.

2005-01-01

The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules

Nonparametric instrumental regression with non-convex constraints

International Nuclear Information System (INIS)

Grasmair, M; Scherzer, O; Vanhems, A

2013-01-01

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition. (paper)

Nonparametric instrumental regression with non-convex constraints

Science.gov (United States)

Grasmair, M.; Scherzer, O.; Vanhems, A.

2013-03-01

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition.

Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

International Nuclear Information System (INIS)

Liolios, A.A.; Boglou, A.K.

2003-01-01

The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-θ method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-convex linear complementarity problem is solved with a reduced number of unknowns

Nonlinear finite element analysis of liquid sloshing in complex vehicle motion scenarios

Science.gov (United States)

Nicolsen, Brynne; Wang, Liang; Shabana, Ahmed

2017-09-01

The objective of this investigation is to develop a new total Lagrangian continuum-based liquid sloshing model that can be systematically integrated with multibody system (MBS) algorithms in order to allow for studying complex motion scenarios. The new approach allows for accurately capturing the effect of the sloshing forces during curve negotiation, rapid lane change, and accelerating and braking scenarios. In these motion scenarios, the liquid experiences large displacements and significant changes in shape that can be captured effectively using the finite element (FE) absolute nodal coordinate formulation (ANCF). ANCF elements are used in this investigation to describe complex mesh geometries, to capture the change in inertia due to the change in the fluid shape, and to accurately calculate the centrifugal forces, which for flexible bodies do not take the simple form used in rigid body dynamics. A penalty formulation is used to define the contact between the rigid tank walls and the fluid. A fully nonlinear MBS truck model that includes a suspension system and Pacejka's brush tire model is developed. Specified motion trajectories are used to examine the vehicle dynamics in three different scenarios - deceleration during straight-line motion, rapid lane change, and curve negotiation. It is demonstrated that the liquid sloshing changes the contact forces between the tires and the ground - increasing the forces on certain wheels and decreasing the forces on other wheels. In cases of extreme sloshing, this dynamic behavior can negatively impact the vehicle stability by increasing the possibility of wheel lift and vehicle rollover.

Time history nonlinear earthquake response analysis considering materials and geometrical nonlinearity

International Nuclear Information System (INIS)

Kobayashi, T.; Yoshikawa, K.; Takaoka, E.; Nakazawa, M.; Shikama, Y.

2002-01-01

A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat uplift, were considered. The 'Lattice Model' for the soil-structure interaction model was employed. An earthquake record on soil surface at the site was used as control motion, and deconvoluted to the input motion of the analysis model at GL-52 m with 300 Gal of maximum acceleration. The following two analyses were considered: (A) time history nonlinear, (B) equivalent linear, and the advantage of time history nonlinear earthquake response analysis method is discussed

Single-ion nonlinear mechanical oscillator

International Nuclear Information System (INIS)

Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

2010-01-01

We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

Neuro-genetic hybrid approach for the solution of non-convex economic dispatch problem

International Nuclear Information System (INIS)

Malik, T.N.; Asar, A.U.

2009-01-01

ED (Economic Dispatch) is non-convex constrained optimization problem, and is used for both on line and offline studies in power system operation. Conventionally, it is solved as convex problem using optimization techniques by approximating generator input/output characteristic. Curves of monotonically increasing nature thus resulting in an inaccurate dispatch. The GA (Genetic Algorithm) has been used for the solution of this problem owing to its inherent ability to address the convex and non-convex problems equally. This approach brings the solution to the global minimum region of search space in a short time and then takes longer time to converge to near optimal results. GA based hybrid approaches are used to fine tune the near optimal results produced by GA. This paper proposes NGH (Neuro Genetic Hybrid) approach to solve the economic dispatch with valve point effect. The proposed approach combines the GA with the ANN (Artificial Neural Network) using SI (Swarm Intelligence) learning rule. The GA acts as a global optimizer and the neural network fine tunes the GA results to the desired targets. Three machines standard test system has been tested for validation of the approach. Comparing the results with GA and NGH model based on back-propagation learning, the proposed approach gives contrast improvements showing the promise of the approach. (author)

An efficient approach to the numerical solution of rate-independent problems with nonconvex energies

Czech Academy of Sciences Publication Activity Database

Bartels, S.; Kružík, Martin

2011-01-01

Roč. 9, č. 3 (2011), s. 1275-1300 ISSN 1540-3459 R&D Projects: GA AV ČR IAA100750802 Grant - others:GA ČR(CZ) GAP201/10/0357 Institutional research plan: CEZ:AV0Z10750506 Keywords : numerical solution * nonconvexity Subject RIV: BA - General Mathematics Impact factor: 2.009, year: 2011 http://library.utia.cas.cz/separaty/2011/MTR/kruzik-0364707.pdf

Effective potential for non-convex potentials

International Nuclear Information System (INIS)

Fujimoto, Y.; O'Raifeartaigh, L.; Parravicini, G.

1983-01-01

It is shown that the well-known relationship between the effective potential GAMMA and the vacuum graphs μ of scalar QFT follows directly from the translational invariance of the measure, and that it holds for all values of the fields phi if, and only if, the classical potential is convex. In the non-convex case μ appears to become complex for some values of phi, but it is shown that the complexity is only apparent and is due to the failure of the loop expansion. The effective potential actually remains real and well-defined for all phi, and reduces to μ in the neighbourhood of the classical minima. A number of examples are considered, notably potentials which are spontaneously broken. In particular the mechanism by which a spontaneous breakdown may be generated by radiative corrections is re-investigated and some new insights obtained. Finally, it is shown that the renormalization group equations for the parameters may be obtained by inspection from the effective potential, and among the examples considered are SU(n) fields and supermultiplets. In particular, it is shown that for supermultiplets the effective potential is not only real but positive. (orig.)

A normal form approach to the theory of nonlinear betatronic motion

International Nuclear Information System (INIS)

Bazzani, A.; Todesco, E.; Turchetti, G.; Servizi, G.

1994-01-01

The betatronic motion of a particle in a circular accelerator is analysed using the transfer map description of the magnetic lattice. In the linear case the transfer matrix approach is shown to be equivalent to the Courant-Snyder theory: In the normal coordinates' representation the transfer matrix is a pure rotation. When the nonlinear effects due to the multipolar components of the magnetic field are taken into account, a similar procedure is used: a nonlinear change of coordinates provides a normal form representation of the map, which exhibits explicit symmetry properties depending on the absence or presence of resonance relations among the linear tunes. The use of normal forms is illustrated in the simplest but significant model of a cell with a sextupolar nonlinearity which is described by the quadratic Henon map. After recalling the basic theoretical results in Hamiltonian dynamics, we show how the normal forms describe the different topological structures of phase space such as KAM tori, chains of islands and chaotic regions; a critical comparison with the usual perturbation theory for Hamilton equations is given. The normal form theory is applied to compute the tune shift and deformation of the orbits for the lattices of the SPS and LHC accelerators, and scaling laws are obtained. Finally, the correction procedure of the multipolar errors of the LHC, based on the analytic minimization of the tune shift computed via the normal forms, is described and the results for a model of the LHC are presented. This application, relevant for the lattice design, focuses on the advantages of normal forms with respect to tracking when parametric dependences have to be explored. (orig.)

Quantization of O(N) non-linear sigma models as the stochastic motion on Ssup(N-1)

International Nuclear Information System (INIS)

Aldazabal, G.; Parga, N.

1983-09-01

We obtain the Langevin equations for the stochastic quantization of the O(N) non-linear sigma model by studying the random (Gaussian) motion on the sphere Ssup(N-1). We prove the equivalence of this procedure with a different one where the random forces are elements of the O(N) algebra. A proof that our approach yields in the equilibrium regime the quantum field theory is also given. (author)

Linear decomposition approach for a class of nonconvex programming problems.

Science.gov (United States)

Shen, Peiping; Wang, Chunfeng

2017-01-01

This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

Iterated non-linear model predictive control based on tubes and contractive constraints.

Science.gov (United States)

Murillo, M; Sánchez, G; Giovanini, L

2016-05-01

This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

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.

A canonical eight-dimensional formalism for linear and non-linear classical spin-orbit motion in storage rings

International Nuclear Information System (INIS)

Barber, D.P.; Heinemann, K.; Ripken, G.

1991-05-01

In the following report we begin to reformulate work by Derbenev on the behaviour of coupled quantized spin-orbit motion. To this end we present a classical symplectic treatment of linear and non-linear spin-orbit motion for storage rings using a fully coupled eight-dimensional formalism which generalizes earlier investigations of coupled synchro-betatron oscillations by introducing two additional canonical spin variables which behave, in a small-angle limit, like those already used in linearised spin theory. Thus in addition to the usual x-z-s couplings, both the spin to orbit and orbit to spin coupling are described canonically. Since the spin Hamiltonian can be expanded in a Taylor series in canonical variables, the formalism is convenient for use in 8-dimensional symplectic tracking calculations with the help, for example, of Lie algebra or differential algebra for the study of chaotic spin motion, for construction of spin normal forms and for the study of the effect of Stern-Gerlach forces. (orig.)

Unsupervised markerless 3-DOF motion tracking in real time using a single low-budget camera.

Science.gov (United States)

Quesada, Luis; León, Alejandro J

2012-10-01

Motion tracking is a critical task in many computer vision applications. Existing motion tracking techniques require either a great amount of knowledge on the target object or specific hardware. These requirements discourage the wide spread of commercial applications based on motion tracking. In this paper, we present a novel three degrees of freedom motion tracking system that needs no knowledge on the target object and that only requires a single low-budget camera that can be found installed in most computers and smartphones. Our system estimates, in real time, the three-dimensional position of a nonmodeled unmarked object that may be nonrigid, nonconvex, partially occluded, self-occluded, or motion blurred, given that it is opaque, evenly colored, enough contrasting with the background in each frame, and that it does not rotate. Our system is also able to determine the most relevant object to track in the screen. Our proposal does not impose additional constraints, therefore it allows a market-wide implementation of applications that require the estimation of the three position degrees of freedom of an object.

Improved Accuracy of Nonlinear Parameter Estimation with LAV and Interval Arithmetic Methods

Directory of Open Access Journals (Sweden)

Humberto Muñoz

2009-06-01

Full Text Available The reliable solution of nonlinear parameter es- timation problems is an important computational problem in many areas of science and engineering, including such applications as real time optimization. Its goal is to estimate accurate model parameters that provide the best fit to measured data, despite small- scale noise in the data or occasional large-scale mea- surement errors (outliers. In general, the estimation techniques are based on some kind of least squares or maximum likelihood criterion, and these require the solution of a nonlinear and non-convex optimiza- tion problem. Classical solution methods for these problems are local methods, and may not be reliable for finding the global optimum, with no guarantee the best model parameters have been found. Interval arithmetic can be used to compute completely and reliably the global optimum for the nonlinear para- meter estimation problem. Finally, experimental re- sults will compare the least squares, l2, and the least absolute value, l1, estimates using interval arithmetic in a chemical engineering application.

Equations of motion for a (non-linear) scalar field model as derived from the field equations

International Nuclear Information System (INIS)

Kaniel, S.; Itin, Y.

2006-01-01

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

The coupled nonlinear dynamics of a lift system

Energy Technology Data Exchange (ETDEWEB)

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk [The University of Northampton, School of Science and Technology, Avenue Campus, St George' s Avenue, Northampton (United Kingdom)

2014-12-10

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

Nonlinear Ion Harmonics in the Paul Trap with Added Octopole Field: Theoretical Characterization and New Insight into Nonlinear Resonance Effect.

Science.gov (United States)

Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu

2016-02-01

The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.

Insurance-markets Equilibrium with Sequential Non-convex Straight-time and Over-time Labor Supply

OpenAIRE

Vasilev, Aleksandar

2016-01-01

This note describes the lottery- and insurance-market equilibrium in an economy with non-convex straight-time and overtime employment. In contrast to Hansen and Sargent (1988), the overtime-decision is a sequential one. This requires two separate insurance market to operate, one for straight-time work, and one for overtime. In addi- tion, given that the labor choice for regular and overtime hours is made in succession, the insurance market for overtime needs to open once the insurance market ...

Non-linear Response to a Type of Seismic Input Motion

International Nuclear Information System (INIS)

2011-06-01

This publication reports the results and findings of a coordinated research project on the safety significance of near-field earthquakes in the design of nuclear power plants. It describes the outcome of a benchmark exercise conducted by a number of institutions on the effects of low to moderate magnitude near-field earthquakes, comparing model analytical simulations with the results of a shaking test performed in France on a physical model of a conventional shear-wall structure. The results build the basis for proposals for possible evolution of engineering practices in order to realistically take into account the effects of near-field earthquakes. A CD is attached that contains the List of participants; Summary of the Research Coordination Meetings; Description of the CAMUS data; Description of the Japanese input motions: near-field earthquakes observed recently in Japan; Description of the output requested of the IAEA CRP participants; Summary of the participants' modelling; Results of Benchmark Step 1, 2 and 3; Scientific background on classification of seismic loads as primary or secondary; and Japanese practice on nonlinear seismic response analysis of safety related important structures.

Global Optimization of Nonlinear Blend-Scheduling Problems

Directory of Open Access Journals (Sweden)

Pedro A. Castillo Castillo

2017-04-01

Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.

NONLINEAR ACCELERATOR LATTICES WITH ONE AND TWO ANALYTIC INVARIANTS

International Nuclear Information System (INIS)

Danilov, Viatcheslav V.

2010-01-01

Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler s and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear map produces a chaotic motion and a complex network of stable and unstable resonances with the unit probability. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate space charge effects with relatively small resonances and particle loss. To create such an accelerator lattice one has to find magnetic and electrtic field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents 3 families of integrable nonlinear accelerator lattices, relizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.

A Duality Theory for Non-convex Problems in the Calculus of Variations

Science.gov (United States)

Bouchitté, Guy; Fragalà, Ilaria

2018-02-01

We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).

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.

Linear instability and nonlinear motion of rotating plasma

International Nuclear Information System (INIS)

Liu, J.

1985-01-01

Two coupled nonlinear equations describing the flute dynamics of the magnetically confined low-β collisionless rotating plasma are derived. The linear instability and nonlinear dynamics of the rotating column are analyzed theoretically. In the linear stability analysis, a new sufficient condition of stability is obtained. From the exact solution of eigenvalue equation for Gaussian density profile and uniform rotation of the plasma, the stability of the system strongly depends on the direction of plasma rotation, FLR effect and the location of the conducting wall. An analytic expression showing the finite wall effect on different normal modes is obtained and it explains the different behavior of (1,0) normal mode from other modes. The sheared rotation driven instability is investigated by using three model equilibrium profiles, and the analytic expressions of eigenvalues which includes the wall effect are obtained. The analogy between shear rotation driven instability and the instability driven by sheared plane parallel flow in the inviscid fluid is analyzed. Applying the linear analysis to the central cell of tandem mirror system, the trapped particle instability with only passing electronics is analyzed. For uniform rotation and Gaussian density profile, an analytic expression that determines the stability boundary is found. The nonlinear analysis shows that the nonlinear equations have a solitary vortex solution which is very similar to the vortex solution of nonlinear Rossby wave equation

Nonlinear dynamic modeling of a simple flexible rotor system subjected to time-variable base motions

Science.gov (United States)

Chen, Liqiang; Wang, Jianjun; Han, Qinkai; Chu, Fulei

2017-09-01

Rotor systems carried in transportation system or under seismic excitations are considered to have a moving base. To study the dynamic behavior of flexible rotor systems subjected to time-variable base motions, a general model is developed based on finite element method and Lagrange's equation. Two groups of Euler angles are defined to describe the rotation of the rotor with respect to the base and that of the base with respect to the ground. It is found that the base rotations would cause nonlinearities in the model. To verify the proposed model, a novel test rig which could simulate the base angular-movement is designed. Dynamic experiments on a flexible rotor-bearing system with base angular motions are carried out. Based upon these, numerical simulations are conducted to further study the dynamic response of the flexible rotor under harmonic angular base motions. The effects of base angular amplitude, rotating speed and base frequency on response behaviors are discussed by means of FFT, waterfall, frequency response curve and orbits of the rotor. The FFT and waterfall plots of the disk horizontal and vertical vibrations are marked with multiplications of the base frequency and sum and difference tones of the rotating frequency and the base frequency. Their amplitudes will increase remarkably when they meet the whirling frequencies of the rotor system.

Second-order processing of four-stroke apparent motion.

Science.gov (United States)

Mather, G; Murdoch, L

1999-05-01

In four-stroke apparent motion displays, pattern elements oscillate between two adjacent positions and synchronously reverse in contrast, but appear to move unidirectionally. For example, if rightward shifts preserve contrast but leftward shifts reverse contrast, consistent rightward motion is seen. In conventional first-order displays, elements reverse in luminance contrast (e.g. light elements become dark, and vice-versa). The resulting perception can be explained by responses in elementary motion detectors turned to spatio-temporal orientation. Second-order motion displays contain texture-defined elements, and there is some evidence that they excite second-order motion detectors that extract spatio-temporal orientation following the application of a non-linear 'texture-grabbing' transform by the visual system. We generated a variety of second-order four-stroke displays, containing texture-contrast reversals instead of luminance contrast reversals, and used their effectiveness as a diagnostic test for the presence of various forms of non-linear transform in the second-order motion system. Displays containing only forward or only reversed phi motion sequences were also tested. Displays defined by variation in luminance, contrast, orientation, and size were effective. Displays defined by variation in motion, dynamism, and stereo were partially or wholly ineffective. Results obtained with contrast-reversing and four-stroke displays indicate that only relatively simple non-linear transforms (involving spatial filtering and rectification) are available during second-order energy-based motion analysis.

Construction of the Courant-Snyder invariants for the non-linear equations of motion and criterion for the long-term stability of the beam in a storage ring

International Nuclear Information System (INIS)

Garczynski, V.

1993-01-01

The Courant-Snyder invariants become Lyapunov functions when the β-functions admit non-zero lower, and finite upper bounds. The long-term stability of motion then follows. This alternative criterion for the long-term stability of motion can be generalized to the nonlinear case. A single particle subjected to an arbitrary static magnetic field is considered in some detail, as an example

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

Science.gov (United States)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Estimation of lung motion fields in 4D CT data by variational non-linear intensity-based registration: A comparison and evaluation study

International Nuclear Information System (INIS)

Werner, René; Schmidt-Richberg, Alexander; Handels, Heinz; Ehrhardt, Jan

2014-01-01

Accurate and robust estimation of motion fields in respiration-correlated CT (4D CT) images, usually performed by non-linear registration of the temporal CT frames, is a precondition for the analysis of patient-specific breathing dynamics and subsequent image-supported diagnostics and treatment planning. In this work, we present a comprehensive comparison and evaluation study of non-linear registration variants applied to the task of lung motion estimation in thoracic 4D CT data. In contrast to existing multi-institutional comparison studies (e.g. MIDRAS and EMPIRE10), we focus on the specific but common class of variational intensity-based non-parametric registration and analyze the impact of the different main building blocks of the underlying optimization problem: the distance measure to be minimized, the regularization approach and the transformation space considered during optimization. In total, 90 different combinations of building block instances are compared. Evaluated on proprietary and publicly accessible 4D CT images, landmark-based registration errors (TRE) between 1.14 and 1.20 mm for the most accurate registration variants demonstrate competitive performance of the applied general registration framework compared to other state-of-the-art approaches for lung CT registration. Although some specific trends can be observed, effects of interchanging individual instances of the building blocks on the TRE are in general rather small (no single outstanding registration variant existing); the same level of accuracy is, however, associated with significantly different degrees of motion field smoothness and computational demands. Consequently, the building block combination of choice will depend on application-specific requirements on motion field characteristics. (paper)

Non-linear methods for the quantification of cyclic motion

OpenAIRE

Quintana Duque, Juan Carlos

2016-01-01

Traditional methods of human motion analysis assume that fluctuations in cycles (e.g. gait motion) and repetitions (e.g. tennis shots) arise solely from noise. However, the fluctuations may have enough information to describe the properties of motion. Recently, the fluctuations in motion have been analysed based on the concepts of variability and stability, but they are not used uniformly. On the one hand, these concepts are often mixed in the existing literature, while on the other hand, the...

Qualitative aspects of nonlinear wave motion: Complexity and simplicity

International Nuclear Information System (INIS)

Engelbrecht, J.

1993-01-01

The nonlinear wave processes possess many qualitative properties which cannot be described by linear theories. In this presentation, an attempt is made to systematize the main aspects of this fascinating area. The sources of nonlinearities are analyzed in order to understand why and how the nonlinear mathematical models are formulated. The technique of evolution equations is discussed then as a main mathematical tool to separate multiwave processes into single waves. The evolution equations give concise but in many cases sufficient description of wave processes in solids permitting to analyze spectral changes, phase changes and velocities, coupling of waves, and interaction of nonlinearities with other physical effects of the same order. Several new problems are listed. Knowing the reasons, the seemingly complex problems can be effectively analyzed. 61 refs

Demand-Side Energy Management Based on Nonconvex Optimization in Smart Grid

Directory of Open Access Journals (Sweden)

Kai Ma

2017-10-01

Full Text Available Demand-side energy management is used for regulating the consumers’ energy usage in smart grid. With the guidance of the grid’s price policy, the consumers can change their energy consumption in response. The objective of this study is jointly optimizing the load status and electric supply, in order to make a tradeoff between the electric cost and the thermal comfort. The problem is formulated into a nonconvex optimization model. The multiplier method is used to solve the constrained optimization, and the objective function is transformed to the augmented Lagrangian function without constraints. Hence, the Powell direction acceleration method with advance and retreat is applied to solve the unconstrained optimization. Numerical results show that the proposed algorithm can achieve the balance between the electric supply and demand, and the optimization variables converge to the optimum.

Non-convex polygons clustering algorithm

Directory of Open Access Journals (Sweden)

Kruglikov Alexey

2016-01-01

Full Text Available A clustering algorithm is proposed, to be used as a preliminary step in motion planning. It is tightly coupled to the applied problem statement, i.e. uses parameters meaningful only with respect to it. Use of geometrical properties for polygons clustering allows for a better calculation time as opposed to general-purpose algorithms. A special form of map optimized for quick motion planning is constructed as a result.

A nonlinear analysis of the EHF booster

International Nuclear Information System (INIS)

Colton, E.P.; Shi, D.

1987-01-01

We have analyzed particle motion at 1.2 GeV with assumption of nonlinearities arising from non-linear space charge forces and from the lattice sextupoles which are tuned to cancel the machine chromaticity. In the first case the motion is as expected and there are no problems as long as the x and y betatron tunes are separated by an integer or more. In the second case the motion is stable so long as the betatron amplitudes do not exceed values corresponding to beam normalized emittance of 100 mm-mr; when this occurs the effects of fifth-order betatron resonances are observed. 3 refs

Nonlinear friction model for servo press simulation

Science.gov (United States)

Ma, Ninshu; Sugitomo, Nobuhiko; Kyuno, Takunori; Tamura, Shintaro; Naka, Tetsuo

2013-12-01

The friction coefficient was measured under an idealized condition for a pulse servo motion. The measured friction coefficient and its changing with both sliding distance and a pulse motion showed that the friction resistance can be reduced due to the re-lubrication during unloading process of the pulse servo motion. Based on the measured friction coefficient and its changes with sliding distance and re-lubrication of oil, a nonlinear friction model was developed. Using the newly developed the nonlinear friction model, a deep draw simulation was performed and the formability was evaluated. The results were compared with experimental ones and the effectiveness was verified.

Imitation learning of Non-Linear Point-to-Point Robot Motions using Dirichlet Processes

DEFF Research Database (Denmark)

Krüger, Volker; Tikhanoff, Vadim; Natale, Lorenzo

2012-01-01

In this paper we discuss the use of the infinite Gaussian mixture model and Dirichlet processes for learning robot movements from demonstrations. Starting point of this work is an earlier paper where the authors learn a non-linear dynamic robot movement model from a small number of observations....... The model in that work is learned using a classical finite Gaussian mixture model (FGMM) where the Gaussian mixtures are appropriately constrained. The problem with this approach is that one needs to make a good guess for how many mixtures the FGMM should use. In this work, we generalize this approach...... our algorithm on the same data that was used in [5], where the authors use motion capture devices to record the demonstrations. As further validation we test our approach on novel data acquired on our iCub in a different demonstration scenario in which the robot is physically driven by the human...

E11 and the non-linear dual graviton

Science.gov (United States)

Tumanov, Alexander G.; West, Peter

2018-04-01

The non-linear dual graviton equation of motion as well as the duality relation between the gravity and dual gravity fields are found in E theory by carrying out E11 variations of previously found equations of motion. As a result the equations of motion in E theory have now been found at the full non-linear level up to, and including, level three, which contains the dual graviton field. When truncated to contain fields at levels three and less, and the spacetime is restricted to be the familiar eleven dimensional space time, the equations are equivalent to those of eleven dimensional supergravity.

V S30, slope, H 800 and f 0: performance of various site-condition proxies in reducing ground-motion aleatory variability and predicting nonlinear site response

Science.gov (United States)

Derras, Boumédiène; Bard, Pierre-Yves; Cotton, Fabrice

2017-09-01

The aim of this paper is to investigate the ability of various site-condition proxies (SCPs) to reduce ground-motion aleatory variability and evaluate how SCPs capture nonlinearity site effects. The SCPs used here are time-averaged shear-wave velocity in the top 30 m ( V S30), the topographical slope (slope), the fundamental resonance frequency ( f 0) and the depth beyond which V s exceeds 800 m/s ( H 800). We considered first the performance of each SCP taken alone and then the combined performance of the 6 SCP pairs [ V S30- f 0], [ V S30- H 800], [ f 0-slope], [ H 800-slope], [ V S30-slope] and [ f 0- H 800]. This analysis is performed using a neural network approach including a random effect applied on a KiK-net subset for derivation of ground-motion prediction equations setting the relationship between various ground-motion parameters such as peak ground acceleration, peak ground velocity and pseudo-spectral acceleration PSA ( T), and M w, R JB, focal depth and SCPs. While the choice of SCP is found to have almost no impact on the median ground-motion prediction, it does impact the level of aleatory uncertainty. V S30 is found to perform the best of single proxies at short periods ( T < 0.6 s), while f 0 and H 800 perform better at longer periods; considering SCP pairs leads to significant improvements, with particular emphasis on [ V S30- H 800] and [ f 0-slope] pairs. The results also indicate significant nonlinearity on the site terms for soft sites and that the most relevant loading parameter for characterising nonlinear site response is the "stiff" spectral ordinate at the considered period.[Figure not available: see fulltext.

Structural motion engineering

CERN Document Server

Connor, Jerome

2014-01-01

This innovative volume provides a systematic treatment of the basic concepts and computational procedures for structural motion design and engineering for civil installations. The authors illustrate the application of motion control to a wide spectrum of buildings through many examples. Topics covered include optimal stiffness distributions for building-type structures, the role of damping in controlling motion, tuned mass dampers, base isolation systems, linear control, and nonlinear control. The book's primary objective is the satisfaction of motion-related design requirements, such as restrictions on displacement and acceleration. The book is ideal for practicing engineers and graduate students. This book also: ·         Broadens practitioners' understanding of structural motion control, the enabling technology for motion-based design ·         Provides readers the tools to satisfy requirements of modern, ultra-high strength materials that lack corresponding stiffness, where the motion re...

Hyperbolicity of the Nonlinear Models of Maxwell's Equations

Science.gov (United States)

Serre, Denis

. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.

Applicability of linear and non-linear potential flow models on a Wavestar float

DEFF Research Database (Denmark)

Bozonnet, Pauline; Dupin, Victor; Tona, Paolino

2017-01-01

as a model based on non-linear potential flow theory and weakscatterer hypothesis are successively considered. Simple tests, such as dip tests, decay tests and captive tests enable to highlight the improvements obtained with the introduction of nonlinearities. Float motion under wave actions and without...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces.......Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...

Nonlinear dynamics and astrophysics

International Nuclear Information System (INIS)

Vallejo, J. C.; Sanjuan, M. A. F.

2000-01-01

Concepts and techniques from Nonlinear Dynamics, also known as Chaos Theory, have been applied successfully to several astrophysical fields such as orbital motion, time series analysis or galactic dynamics, providing answers to old questions but also opening a few new ones. Some of these topics are described in this review article, showing the basis of Nonlinear Dynamics, and how it is applied in Astrophysics. (Author)

Optimal exploitation of a renewable resource with stochastic nonconvex technology: An analysis of extinction and survival

International Nuclear Information System (INIS)

Mitra, Tapan; Roy, Santanu

1992-11-01

This paper analyzes the possibilities of extinction and survival of a renewable resource whose technology of reproduction is both stochastic and nonconvex. In particular, the production function is subject to random shocks over time and is allowed to be nonconcave, though it eventually exhibits bounded growth. The existence of a minimum biomass below which the resource can only decrease, is allowed for. Society harvests a part of the current stock every time period over an infinite horizon so as to maximize the expected discounted sum of one period social utilities from the harvested resource. The social utility function is strictly concave. The stochastic process of optimal stocks generated by the optimal stationary policy is analyzed. The nonconvexity in the optimization problem implies that the optimal policy functions are not 'well behaved'. The behaviour of the probability of extinction (and the expected time to extinction), as a function of initial stock, is characterized for various possible configurations of the optimal policy and the technology. Sufficient conditions on the utility and production functions and the rate of impatience, are specified in order to ensure survival of the resource with probability one from some stock level (the minimum safe standard of conservation). Sufficient conditions for almost sure extinction and almost sure survival from all stock levels are also specified. These conditions are related to the corresponding conditions derived in models with deterministic and/or convex technology. 4 figs., 29 refs

Optimal exploitation of a renewable resource with stochastic nonconvex technology: An analysis of extinction and survival

Energy Technology Data Exchange (ETDEWEB)

Mitra, Tapan [Department of Economics, Cornell University, Ithaca, NY (United States); Roy, Santanu [Econometric Institute, Erasmus University, Rotterdam (Netherlands)

1992-11-01

This paper analyzes the possibilities of extinction and survival of a renewable resource whose technology of reproduction is both stochastic and nonconvex. In particular, the production function is subject to random shocks over time and is allowed to be nonconcave, though it eventually exhibits bounded growth. The existence of a minimum biomass below which the resource can only decrease, is allowed for. Society harvests a part of the current stock every time period over an infinite horizon so as to maximize the expected discounted sum of one period social utilities from the harvested resource. The social utility function is strictly concave. The stochastic process of optimal stocks generated by the optimal stationary policy is analyzed. The nonconvexity in the optimization problem implies that the optimal policy functions are not `well behaved`. The behaviour of the probability of extinction (and the expected time to extinction), as a function of initial stock, is characterized for various possible configurations of the optimal policy and the technology. Sufficient conditions on the utility and production functions and the rate of impatience, are specified in order to ensure survival of the resource with probability one from some stock level (the minimum safe standard of conservation). Sufficient conditions for almost sure extinction and almost sure survival from all stock levels are also specified. These conditions are related to the corresponding conditions derived in models with deterministic and/or convex technology. 4 figs., 29 refs.

Nonlinear Vibration and Mode Shapes of FG Cylindrical Shells

Directory of Open Access Journals (Sweden)

Saeed Mahmoudkhani

Full Text Available Abstract The nonlinear vibration and normal mode shapes of FG cylindrical shells are investigated using an efficient analytical method. The equations of motion of the shell are based on the Donnell’s non-linear shallow-shell, and the material is assumed to be gradually changed across the thickness according to the simple power law. The solution is provided by first discretizing the equations of motion using the multi-mode Galerkin’s method. The nonlinear normal mode of the system is then extracted using the invariant manifold approach and employed to decouple the discretized equations. The homotopy analysis method is finally used to determine the nonlinear frequency. Numerical results are presented for the backbone curves of FG cylindrical shells, nonlinear mode shapes and also the nonlinear invariant modal surfaces. The volume fraction index and the geometric properties of the shell are found to be effective on the type of nonlinear behavior and also the nonlinear mode shapes of the shell. The circumferential half-wave numbers of the nonlinear mode shapes are found to change with time especially in a thinner cylinder.

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.

Robot motion control in mobile environment

Institute of Scientific and Technical Information of China (English)

Iliya V Miroshnik; HUANG Xian-lin(黄显林); HE Jie(贺杰)

2003-01-01

With the problem of robot motion control in dynamic environment represented by mobile obstacles,working pieces and external mechanisms considered, a relevant control actions design procedure has been pro-posed to provide coordination of robot motions with respect to the moving external objects so that an extension ofrobot spatial motion techniques and active robotic strategies based on approaches of nonlinear control theory canbe achieved.

Non-linear Response to a Type of Seismic Input Motion. Additional Information

International Nuclear Information System (INIS)

2011-06-01

This publication reports the results and findings of a coordinated research project on the safety significance of near-field earthquakes in the design of nuclear power plants. It describes the outcome of a benchmark exercise conducted by a number of institutions on the effects of low to moderate magnitude near-field earthquakes, comparing model analytical simulations with the results of a shaking test performed in France on a physical model of a conventional shear-wall structure. The results build the basis for proposals for possible evolution of engineering practices in order to realistically take into account the effects of near-field earthquakes. A CD is attached that contains the List of participants; Summary of the Research Coordination Meetings; Description of the Camus data; Description of the Japanese input motions: near-field earthquakes observed recently in Japan; Description of the output requested of the IAEA CRP participants; Summary of the participants' modelling; Results of Benchmark Step 1, 2 and 3; Scientific background on classification of seismic loads as primary or secondary; and Japanese practice on nonlinear seismic response analysis of safety related important structures.

Altitude dependent neutral wind effects on the nonlinear motion of a small barium cloud

International Nuclear Information System (INIS)

Book, D.L.; Ossakow, S.L.; Goldman, S.R.

1975-01-01

The nonlinear motion of a small F region barium release electrostatically coupled to the E region is studied in the presence of a neutral wind with differing values for the E and F regions. In a reference frame moving with the E region neutral wind and F region neutral wind transverse to the background E 0 field is shown to retard or accelerate the evolution of the cloud without otherwise altering the development of the system. When the relative neutral wind has a component parallel to the background E 0 field, there is also a change in the direction of the axis of elongation of the cloud as a function of time, although the final direction is independent of the relative neutral wind. Barium cloud and image behavior are shown to be substantially identical for periodic and Dirichlet boundary conditions

Nonlinear beam dynamics experimental program at SPEAR

International Nuclear Information System (INIS)

Tran, P.; Pellegrini, C.; Cornacchia, M.; Lee, M.; Corbett, W.

1995-01-01

Since nonlinear effects can impose strict performance limitations on modern colliders and storage rings, future performance improvements depend on further understanding of nonlinear beam dynamics. Experimental studies of nonlinear beam motion in three-dimensional space have begun in SPEAR using turn-by-turn transverse and longitudinal phase-space monitors. This paper presents preliminary results from an on-going experiment in SPEAR

Solitary waves on nonlinear elastic rods. I

DEFF Research Database (Denmark)

Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.

1984-01-01

Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction betwe...... nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.......Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...

Nonlinear roll damping of a barge with and without liquid cargo in spherical tanks

Directory of Open Access Journals (Sweden)

Wenhua Zhao

2016-01-01

Full Text Available Damping plays a significant role on the maximum amplitude of a vessel's roll motion, in particular near the resonant frequency. It is a common practice to predict roll damping using a linear radiation–diffraction code and add that to a linearized viscous damping component, which can be obtained through empirical, semi-empirical equations or free decay tests in calm water. However, it is evident that the viscous roll damping is nonlinear with roll velocity and amplitude. Nonlinear liquid cargo motions inside cargo tanks also contribute to roll damping, which when ignored impedes the accurate prediction of maximum roll motions. In this study, a series of free decay model tests is conducted on a barge-like vessel with two spherical tanks, which allows a better understanding of the nonlinear roll damping components considering the effects of the liquid cargo motion. To examine the effects of the cargo motion on the damping levels, a nonlinear model is adopted to calculate the damping coefficients. The liquid cargo motion is observed to affect both the linear and the quadratic components of the roll damping. The flow memory effect on the roll damping is also studied. The nonlinear damping coefficients of the vessel with liquid cargo motions in spherical tanks are obtained, which are expected to contribute in configurations involving spherical tanks.

Non-linear soil-structure interaction

International Nuclear Information System (INIS)

Wolf, J.P.

1984-01-01

The basic equation of motion to analyse the interaction of a non-linear structure and an irregular soil with the linear unbounded soil is formulated in the time domain. The contribution of the unbounded soil involves convolution integrals of the dynamic-stiffness coefficients in the time domain and the corresponding motions. As another possibility, a flexibility formulation fot the contribution of the unbounded soil using the dynamic-flexibility coefficients in the time domain, together with the direct-stiffness method for the structure and the irregular soil can be applied. As an example of a non-linear soil-structure-interaction analysis, the partial uplift of the basemat of a structure is examined. (Author) [pt

Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances

International Nuclear Information System (INIS)

Perez Polo, Manuel F.; Perez Molina, Manuel

2007-01-01

Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations

Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances

Energy Technology Data Exchange (ETDEWEB)

Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com

2007-07-15

Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.

Nonlinear Dynamics of Nanomechanical Resonators

Science.gov (United States)

Ramakrishnan, Subramanian; Gulak, Yuiry; Sundaram, Bala; Benaroya, Haym

2007-03-01

Nanoelectromechanical systems (NEMS) offer great promise for many applications including motion and mass sensing. Recent experimental results suggest the importance of nonlinear effects in NEMS, an issue which has not been addressed fully in theory. We report on a nonlinear extension of a recent analytical model by Armour et al [1] for the dynamics of a single-electron transistor (SET) coupled to a nanomechanical resonator. We consider the nonlinear resonator motion in both (a) the Duffing and (b) nonlinear pendulum regimes. The corresponding master equations are derived and solved numerically and we consider moment approximations as well. In the Duffing case with hardening stiffness, we observe that the resonator is damped by the SET at a significantly higher rate. In the cases of softening stiffness and the pendulum, there exist regimes where the SET adds energy to the resonator. To our knowledge, this is the first instance of a single model displaying both negative and positive resonator damping in different dynamical regimes. The implications of the results for SET sensitivity as well as for, as yet unexplained, experimental results will be discussed. 1. Armour et al. Phys.Rev.B (69) 125313 (2004).

Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems.

Science.gov (United States)

Miró, Anton; Pozo, Carlos; Guillén-Gosálbez, Gonzalo; Egea, Jose A; Jiménez, Laureano

2012-05-10

The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.

Chaos in balance: non-linear measures of postural control predict individual variations in visual illusions of motion.

Directory of Open Access Journals (Sweden)

Deborah Apthorp

Full Text Available Visually-induced illusions of self-motion (vection can be compelling for some people, but they are subject to large individual variations in strength. Do these variations depend, at least in part, on the extent to which people rely on vision to maintain their postural stability? We investigated by comparing physical posture measures to subjective vection ratings. Using a Bertec balance plate in a brightly-lit room, we measured 13 participants' excursions of the centre of foot pressure (CoP over a 60-second period with eyes open and with eyes closed during quiet stance. Subsequently, we collected vection strength ratings for large optic flow displays while seated, using both verbal ratings and online throttle measures. We also collected measures of postural sway (changes in anterior-posterior CoP in response to the same visual motion stimuli while standing on the plate. The magnitude of standing sway in response to expanding optic flow (in comparison to blank fixation periods was predictive of both verbal and throttle measures for seated vection. In addition, the ratio between eyes-open and eyes-closed CoP excursions during quiet stance (using the area of postural sway significantly predicted seated vection for both measures. Interestingly, these relationships were weaker for contracting optic flow displays, though these produced both stronger vection and more sway. Next we used a non-linear analysis (recurrence quantification analysis, RQA of the fluctuations in anterior-posterior position during quiet stance (both with eyes closed and eyes open; this was a much stronger predictor of seated vection for both expanding and contracting stimuli. Given the complex multisensory integration involved in postural control, our study adds to the growing evidence that non-linear measures drawn from complexity theory may provide a more informative measure of postural sway than the conventional linear measures.

Bifurcations and chaos of the nonlinear viscoelastic plates subjected to subsonic flow and external loads

International Nuclear Information System (INIS)

An, Fengxian; Chen, Fangqi

2016-01-01

Highlights: • The subharmonic bifurcations and chaotic motions are studied by means of Melnikov method. • The critical conditions for the occurrence of chaotic motions and subharmonic bifurcations are obtained. • The chaotic features on the system parameters are discussed. • The theoretical predictions are confirmed by numerical simulations. - Abstract: The subharmonic bifurcations and chaotic motions of the nonlinear viscoelastic plates subjected to subsonic flow and external loads are studied by means of Melnikov method. The critical conditions for the occurrence of chaotic motions are obtained. The chaotic features on the system parameters are discussed in detail. The conditions for subharmonic bifurcations are also obtained. For the system with no structural damping, chaotic motions can occur through infinite subharmonic bifurcations of odd orders. Furthermore, we confirm our theoretical predictions by numerical simulations. The theoretical results obtained here can help us to eliminate or suppress large nonlinear vibrations and chaotic motions of the nonlinear viscoelastic plates. Based on Melnikov method, complex dynamical behaviors of the nonlinear viscoelastic plates can be controlled by modifying the system parameters.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

Science.gov (United States)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

International Nuclear Information System (INIS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-01-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix

Scaling earthquake ground motions for performance-based assessment of buildings

Science.gov (United States)

Huang, Y.-N.; Whittaker, A.S.; Luco, N.; Hamburger, R.O.

2011-01-01

The impact of alternate ground-motion scaling procedures on the distribution of displacement responses in simplified structural systems is investigated. Recommendations are provided for selecting and scaling ground motions for performance-based assessment of buildings. Four scaling methods are studied, namely, (1)geometric-mean scaling of pairs of ground motions, (2)spectrum matching of ground motions, (3)first-mode-period scaling to a target spectral acceleration, and (4)scaling of ground motions per the distribution of spectral demands. Data were developed by nonlinear response-history analysis of a large family of nonlinear single degree-of-freedom (SDOF) oscillators that could represent fixed-base and base-isolated structures. The advantages and disadvantages of each scaling method are discussed. The relationship between spectral shape and a ground-motion randomness parameter, is presented. A scaling procedure that explicitly considers spectral shape is proposed. ?? 2011 American Society of Civil Engineers.

Prediction of Above-elbow Motions in Amputees, based on Electromyographic(EMG Signals, Using Nonlinear Autoregressive Exogenous (NARX Model

Directory of Open Access Journals (Sweden)

Ali Akbar Akbari

2014-08-01

Full Text Available Introduction In order to improve the quality of life of amputees, biomechatronic researchers and biomedical engineers have been trying to use a combination of various techniques to provide suitable rehabilitation systems. Diverse biomedical signals, acquired from a specialized organ or cell system, e.g., the nervous system, are the driving force for the whole system. Electromyography(EMG, as an experimental technique,is concerned with the development, recording, and analysis of myoelectric signals. EMG-based research is making progress in the development of simple, robust, user-friendly, and efficient interface devices for the amputees. Materials and Methods Prediction of muscular activity and motion patterns is a common, practical problem in prosthetic organs. Recurrent neural network (RNN models are not only applicable for the prediction of time series, but are also commonly used for the control of dynamical systems. The prediction can be assimilated to identification of a dynamic process. An architectural approach of RNN with embedded memory is Nonlinear Autoregressive Exogenous (NARX model, which seems to be suitable for dynamic system applications. Results Performance of NARX model is verified for several chaotic time series, which are applied as input for the neural network. The results showed that NARX has the potential to capture the model of nonlinear dynamic systems. The R-value and MSE are  and  , respectively. Conclusion  EMG signals of deltoid and pectoralis major muscles are the inputs of the NARX  network. It is possible to obtain EMG signals of muscles in other arm motions to predict the lost functions of the absent arm in above-elbow amputees, using NARX model.

Nonlinear Coupled Dynamics of a Rod Fastening Rotor under Rub-Impact and Initial Permanent Deflection

Directory of Open Access Journals (Sweden)

Liang Hu

2016-10-01

Full Text Available A nonlinear coupled dynamic model of a rod fastening rotor under rub-impact and initial permanent deflection was developed in this paper. The governing motion equation was derived by the D’Alembert principle considering the contact characteristic between disks, nonlinear oil-film force, rub-impact force, unbalance mass, etc. The contact effects between disks was modeled as a flexural spring with cubical nonlinear stiffness. The coupled nonlinear dynamic phenomena of the rub-impact rod fastening rotor bearing system with initial permanent deflection were investigated by the fourth-order Runge-Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, shaft orbit and Poincaré map are used to illustrate the rich diversity of the system response with complicated dynamics. The studies indicate that the coupled dynamic responses of the rod fastening rotor bearing system under rub-impact and initial permanent deflection exhibit a rich nonlinear dynamic diversity, synchronous periodic-1 motion, multiple periodic motion, quasi-periodic motion and chaotic motion can be observed under certain conditions. Larger radial stiffness of the stator will simplify the system motion and make the oil whirl weaker or even disappear at a certain rotating speed. With the increase of initial permanent deflection length, the instability speed of the system gradually rises, and the chaotic motion region gets smaller and smaller. The corresponding results can provide guidance for the fault diagnosis of a rub-impact rod fastening rotor with initial permanent deflection and contribute to the further understanding of the nonlinear dynamic characteristics of the rod fastening rotor bearing system.

Nonlinear dynamics and cavity cooling of levitated nanoparticles

Science.gov (United States)

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

2016-09-01

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

The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

Science.gov (United States)

Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John

1988-01-01

The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

Example-based human motion denoising.

Science.gov (United States)

Lou, Hui; Chai, Jinxiang

2010-01-01

With the proliferation of motion capture data, interest in removing noise and outliers from motion capture data has increased. In this paper, we introduce an efficient human motion denoising technique for the simultaneous removal of noise and outliers from input human motion data. The key idea of our approach is to learn a series of filter bases from precaptured motion data and use them along with robust statistics techniques to filter noisy motion data. Mathematically, we formulate the motion denoising process in a nonlinear optimization framework. The objective function measures the distance between the noisy input and the filtered motion in addition to how well the filtered motion preserves spatial-temporal patterns embedded in captured human motion data. Optimizing the objective function produces an optimal filtered motion that keeps spatial-temporal patterns in captured motion data. We also extend the algorithm to fill in the missing values in input motion data. We demonstrate the effectiveness of our system by experimenting with both real and simulated motion data. We also show the superior performance of our algorithm by comparing it with three baseline algorithms and to those in state-of-art motion capture data processing software such as Vicon Blade.

Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

Directory of Open Access Journals (Sweden)

S. L. Han

2012-01-01

Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach

Directory of Open Access Journals (Sweden)

Olav Slupphaug

2001-01-01

Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.

Nonlinear Non-convex Optimization of Hydraulic Networks

DEFF Research Database (Denmark)

Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef

2013-01-01

Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption in p....... They can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users. The results in this paper show that the power consumption of the pumps is reduced.......Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...

Predictive local receptive fields based respiratory motion tracking for motion-adaptive radiotherapy.

Science.gov (United States)

Yubo Wang; Tatinati, Sivanagaraja; Liyu Huang; Kim Jeong Hong; Shafiq, Ghufran; Veluvolu, Kalyana C; Khong, Andy W H

2017-07-01

Extracranial robotic radiotherapy employs external markers and a correlation model to trace the tumor motion caused by the respiration. The real-time tracking of tumor motion however requires a prediction model to compensate the latencies induced by the software (image data acquisition and processing) and hardware (mechanical and kinematic) limitations of the treatment system. A new prediction algorithm based on local receptive fields extreme learning machines (pLRF-ELM) is proposed for respiratory motion prediction. All the existing respiratory motion prediction methods model the non-stationary respiratory motion traces directly to predict the future values. Unlike these existing methods, the pLRF-ELM performs prediction by modeling the higher-level features obtained by mapping the raw respiratory motion into the random feature space of ELM instead of directly modeling the raw respiratory motion. The developed method is evaluated using the dataset acquired from 31 patients for two horizons in-line with the latencies of treatment systems like CyberKnife. Results showed that pLRF-ELM is superior to that of existing prediction methods. Results further highlight that the abstracted higher-level features are suitable to approximate the nonlinear and non-stationary characteristics of respiratory motion for accurate prediction.

Analytical Solutions to Non-linear Mechanical Oscillation Problems

DEFF Research Database (Denmark)

Kaliji, H. D.; Ghadimi, M.; Barari, Amin

2011-01-01

In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...

Discrete second order trajectory generator with nonlinear constraints

NARCIS (Netherlands)

Morselli, R.; Zanasi, R.; Stramigioli, Stefano

2005-01-01

A discrete second order trajectory generator for motion control systems is presented. The considered generator is a nonlinear system which receives as input a raw reference signal and provides as output a smooth reference signal satisfying nonlinear constraints on the output derivatives as UM-(x) ≤

Economic analysis of price premiums in the presence of non-convexities. Evidence from German electricity markets

Energy Technology Data Exchange (ETDEWEB)

Paschmann, Martin

2017-11-15

Analyzing price data from sequential German electricity markets, namely the day-ahead and intraday auction, a puzzling but apparently systematic pattern of price premiums can be identified. The price premiums are highly correlated with the underlying demand profile. As there is evidence that widespread models for electricity forward premiums are not applicable to the market dynamics under analysis, a theoretical model is developed within this article which reveals that non-convexities in only a subset of sequential markets with differing product granularity may cause systematic price premiums at equilibrium. These price premiums may be bidirectional and reflect a value for additional short-term power supply system flexibility.

Economic analysis of price premiums in the presence of non-convexities. Evidence from German electricity markets

International Nuclear Information System (INIS)

Paschmann, Martin

2017-01-01

Analyzing price data from sequential German electricity markets, namely the day-ahead and intraday auction, a puzzling but apparently systematic pattern of price premiums can be identified. The price premiums are highly correlated with the underlying demand profile. As there is evidence that widespread models for electricity forward premiums are not applicable to the market dynamics under analysis, a theoretical model is developed within this article which reveals that non-convexities in only a subset of sequential markets with differing product granularity may cause systematic price premiums at equilibrium. These price premiums may be bidirectional and reflect a value for additional short-term power supply system flexibility.

Nonlinear Dynamics of Controlled Synchronizations of Manipulator System

Directory of Open Access Journals (Sweden)

Qingkai Han

2014-01-01

Full Text Available The nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.

Features and states of microscopic particles in nonlinear quantum-mechanics systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

In this paper,we present the elementary principles of nonlinear quantum mechanics(NLQM),which is based on some problems in quantum mechanics.We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles.Concretely speaking,we study in this paper the wave-particle duality of the solution of the nonlinear Schr6dinger equation,the stability of microscopic particles described by NLQM,invariances and conservation laws of motion of particles,the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations,the classical rule of microscopic particle motion,the mechanism and rules of particle collision,the features of reflection and the transmission of particles at interfaces,and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles,and so on.We obtained the invariance and conservation laws of mass,energy and momentum and angular momenturn for the microscopic particles,which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions.We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics(LQM).They have a lot of new properties;for example,the particles possess the real wave-corpuscle duality,obey the classical rule of motion and conservation laws of energy,momentum and mass,satisfy minimum uncertainty relation,can be localized due to the nonlinear interaction,and its position and momentum can also be determined,etc.From these studies,we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM.Therefore,the NLQM is a new physical theory,and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems,which can

The study on the non-linear soil structure interaction for nuclear power plants

International Nuclear Information System (INIS)

Tetsuya Hagiwara; Yoshio Kitada

2005-01-01

1. Introduction: JNES is planning a new project to study non-linear soil-structure interaction (SSI) effect under large earthquake ground motions equivalent to and/or over a design earthquake ground motion of S2(The extreme design earthquake). Concerning the SSI test, it is pointed out that handling of the scale effect of the specimen together with the surrounding soil on the earthquake response evaluation of the actual structure is essential issue for the scaled model test. Thus, for the test, the largest specimen possible and the biggest input motion possible are necessary. Taking into account the above issues, new test methodology, which utilizes artificial earthquake ground motion, is considered desirable if it can be performed at a realistic cost. Under this motivation, we have studied the test methodology which applying blasting power as for a big earthquake ground motion. The information from a coal mine company in the U.S.A. indicates that the works performed in the surface coal mine to blast a rock covering a coal layer generates a big artificial ground motion, which is similar to earthquake ground motion. Application of this artificial earthquake ground motion for the SSI test is considered very promising because the blasting work is carried out periodically for mining coal so that we can apply artificial motions generated by the work if we construct a building model at a closed point to the blasting work area. The major purposes of the test will be to understand (a) basic earthquake response characteristics of a Nuclear Power Plant (NPP) reactor building when a large earthquake strikes the NPP site and (b) nonlinear characteristics of SSI phenomenon during a big earthquake. In the paper, we introduce the test method and basic characteristics of measured artificial ground motions generated by the blasting works on an actual site. 2. Conclusion: It was confirmed that the artificial ground motions generated by blasting works have enough acceleration level

Modal-pushover-based ground-motion scaling procedure

Science.gov (United States)

Kalkan, Erol; Chopra, Anil K.

2011-01-01

Earthquake engineering is increasingly using nonlinear response history analysis (RHA) to demonstrate the performance of structures. This rigorous method of analysis requires selection and scaling of ground motions appropriate to design hazard levels. This paper presents a modal-pushover-based scaling (MPS) procedure to scale ground motions for use in a nonlinear RHA of buildings. In the MPS method, the ground motions are scaled to match to a specified tolerance, a target value of the inelastic deformation of the first-mode inelastic single-degree-of-freedom (SDF) system whose properties are determined by the first-mode pushover analysis. Appropriate for first-mode dominated structures, this approach is extended for structures with significant contributions of higher modes by considering elastic deformation of second-mode SDF systems in selecting a subset of the scaled ground motions. Based on results presented for three actual buildings-4, 6, and 13-story-the accuracy and efficiency of the MPS procedure are established and its superiority over the ASCE/SEI 7-05 scaling procedure is demonstrated.

Continuous limit of a crowd motion and herding model: Analysis and numerical simulations

KAUST Repository

Pietschmann, Jan-Frederik; Markowich, Peter Alexander; Burger, Martin

2011-01-01

In this paper we study the continuum limit of a cellular automaton model used for simulating human crowds with herding behaviour. We derive a system of non-linear partial differential equations resembling the Keller-Segel model for chemotaxis, however with a non-monotone interaction. The latter has interesting consequences on the behaviour of the model's solutions, which we highlight in its analysis. In particular we study the possibility of stationary states, the formation of clusters and explore their connection to congestion. We also introduce an efficient numerical simulation approach based on an appropriate hybrid discontinuous Galerkin method, which in particular allows flexible treatment of complicated geometries. Extensive numerical studies also provide a better understanding of the strengths and shortcomings of the herding model, in particular we examine trapping effects of crowds behind nonconvex obstacles. © American Institute of Mathematical Sciences.

Continuous limit of a crowd motion and herding model: Analysis and numerical simulations

KAUST Repository

Pietschmann, Jan-Frederik

2011-11-01

In this paper we study the continuum limit of a cellular automaton model used for simulating human crowds with herding behaviour. We derive a system of non-linear partial differential equations resembling the Keller-Segel model for chemotaxis, however with a non-monotone interaction. The latter has interesting consequences on the behaviour of the model\\'s solutions, which we highlight in its analysis. In particular we study the possibility of stationary states, the formation of clusters and explore their connection to congestion. We also introduce an efficient numerical simulation approach based on an appropriate hybrid discontinuous Galerkin method, which in particular allows flexible treatment of complicated geometries. Extensive numerical studies also provide a better understanding of the strengths and shortcomings of the herding model, in particular we examine trapping effects of crowds behind nonconvex obstacles. © American Institute of Mathematical Sciences.

Vibrational mechanics nonlinear dynamic effects, general approach, applications

CERN Document Server

Blekhman, Iliya I

2000-01-01

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack

Directory of Open Access Journals (Sweden)

Xin Qi

2015-02-01

Full Text Available Bifurcation analysis and stability design for aircraft longitudinal motion are investigated when the nonlinearity in flight dynamics takes place severely at high angle of attack regime. To predict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynamics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurcation and dynamic bifurcation for high-dimensional system. Case study shows that the F-8 longitudinal motion undergoes saddle node bifurcation, Hopf bifurcation, Zero-Hopf bifurcation and branch point bifurcation under certain conditions. Moreover, the Hopf bifurcation renders series of multiple frequency pitch oscillation phenomena, which deteriorate the flight control stability severely. To relieve the adverse effects of these phenomena, a stabilization control based on gain scheduling and polynomial fitting for F-8 longitudinal motion is presented to enlarge the flight envelope. Simulation results validate the effectiveness of the proposed scheme.

Nonlinear quantum dynamics in diatomic molecules: Vibration, rotation and spin

International Nuclear Information System (INIS)

Yang, Ciann-Dong; Weng, Hung-Jen

2012-01-01

Highlights: ► This paper reveals the internal nonlinear dynamics embedded in a molecular quantum state. ► Analyze quantum molecular dynamics in a deterministic way, while preserving the consistency with probability interpretation. ► Molecular vibration–rotation interaction and spin–orbital coupling are considered simultaneously. ► Spin is just the remnant angular motion when orbital angular momentum is zero. ► Spin is the “zero dynamics” of nonlinear quantum dynamics. - Abstract: For a given molecular wavefunction Ψ, the probability density function Ψ ∗ Ψ is not the only information that can be extracted from Ψ. We point out in this paper that nonlinear quantum dynamics of a diatomic molecule, completely consistent with the probability prediction of quantum mechanics, does exist and can be derived from the quantum Hamilton equations of motion determined by Ψ. It can be said that the probability density function Ψ ∗ Ψ is an external representation of the quantum state Ψ, while the related Hamilton dynamics is an internal representation of Ψ, which reveals the internal mechanism underlying the externally observed random events. The proposed internal representation of Ψ establishes a bridge between nonlinear dynamics and quantum mechanics, which allows the methods and tools already developed by the former to be applied to the latter. Based on the quantum Hamilton equations of motion derived from Ψ, vibration, rotation and spin motions of a diatomic molecule and the interactions between them can be analyzed simultaneously. The resulting dynamic analysis of molecular motion is compared with the conventional probability analysis and the consistency between them is demonstrated.

Orbit-attitude coupled motion around small bodies: Sun-synchronous orbits with Sun-tracking attitude motion

Science.gov (United States)

Kikuchi, Shota; Howell, Kathleen C.; Tsuda, Yuichi; Kawaguchi, Jun'ichiro

2017-11-01

The motion of a spacecraft in proximity to a small body is significantly perturbed due to its irregular gravity field and solar radiation pressure. In such a strongly perturbed environment, the coupling effect of the orbital and attitude motions exerts a large influence that cannot be neglected. However, natural orbit-attitude coupled dynamics around small bodies that are stationary in both orbital and attitude motions have yet to be observed. The present study therefore investigates natural coupled motion that involves both a Sun-synchronous orbit and Sun-tracking attitude motion. This orbit-attitude coupled motion enables a spacecraft to maintain its orbital geometry and attitude state with respect to the Sun without requiring active control. Therefore, the proposed method can reduce the use of an orbit and attitude control system. This paper first presents analytical conditions to achieve Sun-synchronous orbits and Sun-tracking attitude motion. These analytical solutions are then numerically propagated based on non-linear coupled orbit-attitude equations of motion. Consequently, the possibility of implementing Sun-synchronous orbits with Sun-tracking attitude motion is demonstrated.

Nonlinear and turbulent processes in physics. Volume 2. Nonlinear effects in various areas of science

Energy Technology Data Exchange (ETDEWEB)

Sagdeev, R Z

1984-01-01

The results of theoretical and experimental investigations of nonlinear and turbulent phenomena from a wide range of fields in physics are presented in reviews and reports. Topics examined include localized vortex formations in an ideal fluid, phase transitions in crystals, spatially nonuniform structures in condensed matter, solitons in molecular systems, the migration of quasi-particles in easily deformed crystals, bifurcations and dissipative structures in distributed kinetic systems, and structures in a nonlinear burning medium. Consideration is given to macroscopic motion generation in nonequilibrium media, the interaction of bulk and surface wave trains, near-threshold instabilities in hydrodynamics, solitons in nonlinear elastic rods with variable characteristics, the generation of solitons and vortices from chaos, and nonlinear electromagnetic-wave dissipation in an electron system.

Modeling nonlinearities in MEMS oscillators.

Science.gov (United States)

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

2013-08-01

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

Full-motion video analysis for improved gender classification

Science.gov (United States)

Flora, Jeffrey B.; Lochtefeld, Darrell F.; Iftekharuddin, Khan M.

2014-06-01

The ability of computer systems to perform gender classification using the dynamic motion of the human subject has important applications in medicine, human factors, and human-computer interface systems. Previous works in motion analysis have used data from sensors (including gyroscopes, accelerometers, and force plates), radar signatures, and video. However, full-motion video, motion capture, range data provides a higher resolution time and spatial dataset for the analysis of dynamic motion. Works using motion capture data have been limited by small datasets in a controlled environment. In this paper, we explore machine learning techniques to a new dataset that has a larger number of subjects. Additionally, these subjects move unrestricted through a capture volume, representing a more realistic, less controlled environment. We conclude that existing linear classification methods are insufficient for the gender classification for larger dataset captured in relatively uncontrolled environment. A method based on a nonlinear support vector machine classifier is proposed to obtain gender classification for the larger dataset. In experimental testing with a dataset consisting of 98 trials (49 subjects, 2 trials per subject), classification rates using leave-one-out cross-validation are improved from 73% using linear discriminant analysis to 88% using the nonlinear support vector machine classifier.

A modal method for finite amplitude, nonlinear sloshing

Indian Academy of Sciences (India)

Abstract. A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential.

Intermittent Motion, Nonlinear Diffusion Equation and Tsallis Formalism

Directory of Open Access Journals (Sweden)

Ervin K. Lenzi

2017-01-01

Full Text Available We investigate an intermittent process obtained from the combination of a nonlinear diffusion equation and pauses. We consider the porous media equation with reaction terms related to the rate of switching the particles from the diffusive mode to the resting mode or switching them from the resting to the movement. The results show that in the asymptotic limit of small and long times, the spreading of the system is essentially governed by the diffusive term. The behavior exhibited for intermediate times depends on the rates present in the reaction terms. In this scenario, we show that, in the asymptotic limits, the distributions for this process are given by in terms of power laws which may be related to the q-exponential present in the Tsallis statistics. Furthermore, we also analyze a situation characterized by different diffusive regimes, which emerges when the diffusive term is a mixing of linear and nonlinear terms.

A modal method for finite amplitude, nonlinear sloshing

Indian Academy of Sciences (India)

A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential. The effects ...

Stochastic motion of particles in tandem mirror devices

International Nuclear Information System (INIS)

Ichikawa, Y.H.; Kamimura, T.

1982-01-01

Stochastic motion of particles in tandem mirror devices is examined on basis of a nonlinear mapping of particle positions on the equatorial plane. Local stability analysis provides detailed informations on particle trajectories. The rate of stochastic plasma diffusion is estimated from numerical observations of motions of particles over a large number of time steps. (author)

Normal form of particle motion under the influence of an ac dipole

Directory of Open Access Journals (Sweden)

R. Tomás

2002-05-01

Full Text Available ac dipoles in accelerators are used to excite coherent betatron oscillations at a drive frequency close to the tune. These beam oscillations may last arbitrarily long and, in principle, there is no significant emittance growth if the ac dipole is adiabatically turned on and off. Therefore the ac dipole seems to be an adequate tool for nonlinear diagnostics provided the particle motion is well described in the presence of the ac dipole and nonlinearities. Normal forms and Lie algebra are powerful tools to study the nonlinear content of an accelerator lattice. In this article a way to obtain the normal form of the Hamiltonian of an accelerator with an ac dipole is described. The particle motion to first order in the nonlinearities is derived using Lie algebra techniques. The dependence of the Hamiltonian terms on the longitudinal coordinate is studied showing that they vary differently depending on the ac dipole parameters. The relation is given between the lines of the Fourier spectrum of the turn-by-turn motion and the Hamiltonian terms.

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...

New Look at Nonlinear Aerodynamics in Analysis of Hypersonic Panel Flutter

Directory of Open Access Journals (Sweden)

Dan Xie

2017-01-01

Full Text Available A simply supported plate fluttering in hypersonic flow is investigated considering both the airflow and structural nonlinearities. Third-order piston theory is used for nonlinear aerodynamic loading, and von Karman plate theory is used for modeling the nonlinear strain-displacement relation. The Galerkin method is applied to project the partial differential governing equations (PDEs into a set of ordinary differential equations (ODEs in time, which is then solved by numerical integration method. In observation of limit cycle oscillations (LCO and evolution of dynamic behaviors, nonlinear aerodynamic loading produces a smaller positive deflection peak and more complex bifurcation diagrams compared with linear aerodynamics. Moreover, a LCO obtained with the linear aerodynamics is mostly a nonsimple harmonic motion but when the aerodynamic nonlinearity is considered more complex motions are obtained, which is important in the evaluation of fatigue life. The parameters of Mach number, dynamic pressure, and in-plane thermal stresses all affect the aerodynamic nonlinearity. For a specific Mach number, there is a critical dynamic pressure beyond which the aerodynamic nonlinearity has to be considered. For a higher temperature, a lower critical dynamic pressure is required. Each nonlinear aerodynamic term in the full third-order piston theory is evaluated, based on which the nonlinear aerodynamic formulation has been simplified.

Nonlinear dynamic analysis of 2-DOF nonlinear vibration isolation floating raft systems with feedback control

International Nuclear Information System (INIS)

Li Yingli; Xu Daolin; Fu Yiming; Zhou Jiaxi

2012-01-01

In this paper, the average method is adopted to analysis dynamic characteristics of nonlinear vibration isolation floating raft system with feedback control. The analytic results show that the purposes of reducing amplitude of oscillation and complicating the motion can be achieved by adjusting properly the system parameters, exciting frequency and control gain. The conclusions can provide some available evidences for the design and improvement of both the passive and active control of the vibration isolation systems. By altering the exciting frequency and control gain, complex motion of the system can be obtained. Numerical simulations show the system exhibits period vibration, double period vibration and quasi-period motion.

Nonlinear instability and convection in a vertically vibrated granular bed

NARCIS (Netherlands)

Shukla, P.; Ansari, I.H.; van der Meer, Roger M.; Lohse, Detlef; Alam, M.

2014-01-01

The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic

Nonlinear damping based semi-active building isolation system

Science.gov (United States)

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

2018-06-01

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

Electron dynamics with radiation and nonlinear wigglers

International Nuclear Information System (INIS)

Jowett, J.M.

1986-06-01

The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches

Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering

Science.gov (United States)

Ablowitz, Mark J.

1994-12-01

Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.

Towards a Robust Solution of the Non-Linear Kinematics for the General Stewart Platform with Estimation of Distribution Algorithms

Directory of Open Access Journals (Sweden)

Eusebio Eduardo Hernández Martinez

2013-01-01

Full Text Available In robotics, solving the direct kinematics problem (DKP for parallel robots is very often more difficult and time consuming than for their serial counterparts. The problem is stated as follows: given the joint variables, the Cartesian variables should be computed, namely the pose of the mobile platform. Most of the time, the DKP requires solving a non-linear system of equations. In addition, given that the system could be non-convex, Newton or Quasi-Newton (Dogleg based solvers get trapped on local minima. The capacity of such kinds of solvers to find an adequate solution strongly depends on the starting point. A well-known problem is the selection of such a starting point, which requires a priori information about the neighbouring region of the solution. In order to circumvent this issue, this article proposes an efficient method to select and to generate the starting point based on probabilistic learning. Experiments and discussion are presented to show the method performance. The method successfully avoids getting trapped on local minima without the need for human intervention, which increases its robustness when compared with a single Dogleg approach. This proposal can be extended to other structures, to any non-linear system of equations, and of course, to non-linear optimization problems.

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

International Nuclear Information System (INIS)

Hedrih, K

2008-01-01

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

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

Science.gov (United States)

Stevanović Hedrih, K.

2008-02-01

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

Bryan's effect and anisotropic nonlinear damping

Science.gov (United States)

Joubert, Stephan V.; Shatalov, Michael Y.; Fay, Temple H.; Manzhirov, Alexander V.

2018-03-01

In 1890, G. H. Bryan discovered the following: "The vibration pattern of a revolving cylinder or bell revolves at a rate proportional to the inertial rotation rate of the cylinder or bell." We call this phenomenon Bryan's law or Bryan's effect. It is well known that any imperfections in a vibratory gyroscope (VG) affect Bryan's law and this affects the accuracy of the VG. Consequently, in this paper, we assume that all such imperfections are either minimised or eliminated by some known control method and that only damping is present within the VG. If the damping is isotropic (linear or nonlinear), then it has been recently demonstrated in this journal, using symbolic analysis, that Bryan's law remains invariant. However, it is known that linear anisotropic damping does affect Bryan's law. In this paper, we generalise Rayleigh's dissipation function so that anisotropic nonlinear damping may be introduced into the equations of motion. Using a mixture of numeric and symbolic analysis on the ODEs of motion of the VG, for anisotropic light nonlinear damping, we demonstrate (up to an approximate average), that Bryan's law is affected by any form of such damping, causing pattern drift, compromising the accuracy of the VG.

Effects produced by oscillations applied to nonlinear dynamic systems: a general approach and examples

DEFF Research Database (Denmark)

Blekhman, I. I.; Sorokin, V. S.

2016-01-01

A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics.......g., the requirement for the involved nonlinearities to be weak. The approach is illustrated by several relevant examples from various fields of science, e.g., mechanics, physics, chemistry and biophysics....... equations). The approach is named as the oscillatory strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that capture the averaged effect of oscillations. The method of direct separation of motions appears to be an efficient...

Theory of motion for monopole-dipole singularities of classical Yang-Mills-Higgs fields. I. Laws of motion

International Nuclear Information System (INIS)

Drechsler, W.; Havas, P.; Rosenblum, A.

1984-01-01

In two recent papers, the general form of the laws of motion for point particles which are multipole sources of the classical coupled Yang-Mills-Higgs fields was determined by Havas, and for the special case of monopole singularities of a Yang-Mills field an iteration procedure was developed by Drechsler and Rosenblum to obtain the equations of motion of mass points, i.e., the laws of motion including the explicit form of the fields of all interacting particles. In this paper we give a detailed derivation of the laws of motion of monopole-dipole singularities of the coupled Yang-Mills-Higgs fields for point particles with mass and spin, following a procedure first applied by Mathisson and developed by Havas. To obtain the equations of motion, a systematic approximation method is developed in the following paper for the solution of the nonlinear field equations and determination of the fields entering the laws of motion found here to any given order in the coupling constant g

The simulation of a non-linear unstable system of motion, utilising the Solid-Works and Matlab/Simulink extended libraries/toolboxes

Directory of Open Access Journals (Sweden)

Zátopek Jiří

2016-01-01

Full Text Available This text discusses the use and integration of various support software tools for the purpose of designing the motion control law governing mechanical structures with strongly non-linear behaviour. The detailed mathematical model is derived using Lagrange Equations of the Second Type. The physical model was designed by using SolidWorks 3D CAD software and a SimMechanics library. It extends Simulink with modelling tools for the simulation of mechanical “multi-domain” physical systems. The visualization of Simulink outputs is performed using the 3D Animation toolbox. Control law - designed on the basis of the mathematical model, is tested for both models (i.e. mathematical and physical and the regulatory processes’ results are compared.

Nonlinear Resonance Analysis of Slender Portal Frames under Base Excitation

Directory of Open Access Journals (Sweden)

Luis Fernando Paullo Muñoz

2017-01-01

Full Text Available The dynamic nonlinear response and stability of slender structures in the main resonance regions are a topic of importance in structural analysis. In complex problems, the determination of the response in the frequency domain indirectly obtained through analyses in time domain can lead to huge computational effort in large systems. In nonlinear cases, the response in the frequency domain becomes even more cumbersome because of the possibility of multiple solutions for certain forcing frequencies. Those solutions can be stable and unstable, in particular saddle-node bifurcation at the turning points along the resonance curves. In this work, an incremental technique for direct calculation of the nonlinear response in frequency domain of plane frames subjected to base excitation is proposed. The transformation of equations of motion to the frequency domain is made through the harmonic balance method in conjunction with the Galerkin method. The resulting system of nonlinear equations in terms of the modal amplitudes and forcing frequency is solved by the Newton-Raphson method together with an arc-length procedure to obtain the nonlinear resonance curves. Suitable examples are presented, and the influence of the frame geometric parameters and base motion on the nonlinear resonance curves is investigated.

Three dimensional monocular human motion analysis in end-effector space

DEFF Research Database (Denmark)

Hauberg, Søren; Lapuyade, Jerome; Engell-Nørregård, Morten Pol

2009-01-01

In this paper, we present a novel approach to three dimensional human motion estimation from monocular video data. We employ a particle filter to perform the motion estimation. The novelty of the method lies in the choice of state space for the particle filter. Using a non-linear inverse kinemati...

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

Science.gov (United States)

Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

2016-06-01

This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

Nonlinear mathematical modeling of vibrating motion of nanomechanical cantilever active probe

Directory of Open Access Journals (Sweden)

Reza Ghaderi

Full Text Available Nonlinear vibration response of nanomechanical cantilever (NMC active probes in atomic force microscope (AFM application has been studied in the amplitude mode. Piezoelectric layer is placed piecewise and as an actuator on NMC. Continuous beam model has been chosen for analysis with regard to the geometric discontinuities of piezoelectric layer attachment and NMC's cross section. The force between the tip and the sample surface is modeled using Leonard-Jones potential. Assuming that cantilever is inclined to the sample surface, the effect of nonlinear force on NMC is considered as a shearing force and the concentrated bending moment is regarded at the end. Nonlinear frequency response of NMC is obtained close to the sample surface using the dynamic modeling. It is then become clear that the distance and angle of NMC, the probe length, and the geometric dimensions of piezoelectric layer can affect frequency response bending of the curve.

Oscillators from nonlinear realizations

Science.gov (United States)

Kozyrev, N.; Krivonos, S.

2018-02-01

We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the so(2, 3) and G 2(2) algebras.

Nonlinear Dynamics of Electrostatically Actuated MEMS Arches

KAUST Repository

Al Hennawi, Qais M.

2015-01-01

In this thesis, we present theoretical and experimental investigation into the nonlinear statics and dynamics of clamped-clamped in-plane MEMS arches when excited by an electrostatic force. Theoretically, we first solve the equation of motion using

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models.

Science.gov (United States)

Pozo, Carlos; Marín-Sanguino, Alberto; Alves, Rui; Guillén-Gosálbez, Gonzalo; Jiménez, Laureano; Sorribas, Albert

2011-08-25

Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Directory of Open Access Journals (Sweden)

Sorribas Albert

2011-08-01

Full Text Available Abstract Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

CERN Document Server

Liolios, A

2003-01-01

The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-theta method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-c...

Seismic response analysis of a nuclear reactor structure considering nonlinear soil-structure interaction

International Nuclear Information System (INIS)

Bhaumik, Lopamudra; Raychowdhury, Prishati

2013-01-01

Highlights: • Seismic response analysis of an internal shearwall of a reactor is done. • Incremental dynamic analysis is performed with 30 recorded ground motions. • Equivalent viscous damping increases up to twice when nonlinear SSI is considered. • Roof drift demand increases up to 25% upon consideration of foundation nonlinearity. • Base shear, base moment and ductility reduce up to 62%, 40%, and 35%, respectively. - Abstract: This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, S a (T 1 )is incremented from 0.1 g to 1.0 g with an increment step of 0.1 g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure

Seismic response analysis of a nuclear reactor structure considering nonlinear soil-structure interaction

Energy Technology Data Exchange (ETDEWEB)

Bhaumik, Lopamudra, E-mail: lbhaumi2@illinois.edu [University of Illinois at Urbana-Champaign (United States); Raychowdhury, Prishati, E-mail: prishati@iitk.ac.in [Indian Institute of Technology Kanpur (India)

2013-12-15

Highlights: • Seismic response analysis of an internal shearwall of a reactor is done. • Incremental dynamic analysis is performed with 30 recorded ground motions. • Equivalent viscous damping increases up to twice when nonlinear SSI is considered. • Roof drift demand increases up to 25% upon consideration of foundation nonlinearity. • Base shear, base moment and ductility reduce up to 62%, 40%, and 35%, respectively. - Abstract: This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, S{sub a}(T{sub 1})is incremented from 0.1 g to 1.0 g with an increment step of 0.1 g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure.

Nonlinear dynamic behaviour of a rotor-foundation system coupled through passive magnetic bearings with magnetic anisotropy - Theory and experiment

DEFF Research Database (Denmark)

Enemark, Søren; Santos, Ilmar F.

2016-01-01

In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy......) of the magnetic field and the weak nonlinearity of the magnetic forces. Through mathematical modelling the nonlinear equations of motion are established for describing the shaft and bearing housing lateral dynamics coupled via the nonlinear and non-uniform magnetic forces. The equations of motion are solved...

Nonlinear Dynamics of a Helicopter Model in Ground Resonance

Science.gov (United States)

Tang, D. M.; Dowell, E. H.

1985-01-01

An approximate theoretical method is presented which determined the limit cycle behavior of a helicopter model which has one or two nonlinear dampers. The relationship during unstable ground resonance oscillations between lagging motion of the blades and fuselage motion is discussed. An experiment was carried out on using a helicopter scale model. The experimental results agree with those of the theoretical analysis.

Inducing in situ, nonlinear soil response applying an active source

Science.gov (United States)

Johnson, P.A.; Bodin, P.; Gomberg, J.; Pearce, F.; Lawrence, Z.; Menq, F.-Y.

2009-01-01

[1] It is well known that soil sites have a profound effect on ground motion during large earthquakes. The complex structure of soil deposits and the highly nonlinear constitutive behavior of soils largely control nonlinear site response at soil sites. Measurements of nonlinear soil response under natural conditions are critical to advancing our understanding of soil behavior during earthquakes. Many factors limit the use of earthquake observations to estimate nonlinear site response such that quantitative characterization of nonlinear behavior relies almost exclusively on laboratory experiments and modeling of wave propagation. Here we introduce a new method for in situ characterization of the nonlinear behavior of a natural soil formation using measurements obtained immediately adjacent to a large vibrator source. To our knowledge, we are the first group to propose and test such an approach. Employing a large, surface vibrator as a source, we measure the nonlinear behavior of the soil by incrementally increasing the source amplitude over a range of frequencies and monitoring changes in the output spectra. We apply a homodyne algorithm for measuring spectral amplitudes, which provides robust signal-to-noise ratios at the frequencies of interest. Spectral ratios are computed between the receivers and the source as well as receiver pairs located in an array adjacent to the source, providing the means to separate source and near-source nonlinearity from pervasive nonlinearity in the soil column. We find clear evidence of nonlinearity in significant decreases in the frequency of peak spectral ratios, corresponding to material softening with amplitude, observed across the array as the source amplitude is increased. The observed peak shifts are consistent with laboratory measurements of soil nonlinearity. Our results provide constraints for future numerical modeling studies of strong ground motion during earthquakes.

Multivariate Autoregressive Model Based Heart Motion Prediction Approach for Beating Heart Surgery

Directory of Open Access Journals (Sweden)

Fan Liang

2013-02-01

Full Text Available A robotic tool can enable a surgeon to conduct off-pump coronary artery graft bypass surgery on a beating heart. The robotic tool actively alleviates the relative motion between the point of interest (POI on the heart surface and the surgical tool and allows the surgeon to operate as if the heart were stationary. Since the beating heart's motion is relatively high-band, with nonlinear and nonstationary characteristics, it is difficult to follow. Thus, precise beating heart motion prediction is necessary for the tracking control procedure during the surgery. In the research presented here, we first observe that Electrocardiography (ECG signal contains the causal phase information on heart motion and non-stationary heart rate dynamic variations. Then, we investigate the relationship between ECG signal and beating heart motion using Granger Causality Analysis, which describes the feasibility of the improved prediction of heart motion. Next, we propose a nonlinear time-varying multivariate vector autoregressive (MVAR model based adaptive prediction method. In this model, the significant correlation between ECG and heart motion enables the improvement of the prediction of sharp changes in heart motion and the approximation of the motion with sufficient detail. Dual Kalman Filters (DKF estimate the states and parameters of the model, respectively. Last, we evaluate the proposed algorithm through comparative experiments using the two sets of collected vivo data.

A test to evaluation non-linear soil structure interaction

International Nuclear Information System (INIS)

Hagiwara, T.; Kitada, Y.

2005-01-01

JNES is planning a new project to study non-linear soil-structure interaction (SSI) effect under large earthquake ground motions equivalent to and/or over a design earthquake ground motion of S2. Concerning the SSI test, it is pointed out that handling of the scale effect of the specimen taking into account the surrounding soil on the earthquake response evaluation to the actual structure is essential issue for the scaled model test. Thus, for the test, the largest specimen possible and the biggest input motion possible are necessary. Taking into account the above issues, new test methodology, which utilizes artificial earthquake ground motion, is considered desirable if it can be performed at a realistic cost. With this motivation, we have studied the test methodology which applying blasting power as for a big earthquake ground motion. The information from a coalmine company in the U.S.A. indicates that the works performed in the surface coalmine to blast a rock covering a coal layer generates a big artificial ground motion, which is similar to earthquake ground motion. Application of this artificial earthquake ground motion for the SSI test is considered very promising because the blasting work is carried out periodically for mining coal so that we can apply artificial motions generated by the work if we construct a building model at a closed point to the blasting work area. The major purposes of the test are to understand (a) basic earthquake response characteristics of a Nuclear Power Plant (NPP) reactor building when a large earthquake strikes the NPP site and (b) nonlinear characteristics of SSI phenomenon during a big earthquake. In the paper of ICONE-13, we will introduce the test method and basic characteristics of measured artificial ground motions generated by the blasting works on an actual site. (authors)

Gaussian particle filter based pose and motion estimation

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

Determination of relative three-dimensional (3D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry.A solution to pose and motion estimation problem that uses two-dimensional (2D) intensity images from a single camera is desirable for real-time applications. The difficulty in performing this measurement is that the process of projecting 3D object features to 2D images is a nonlinear transformation. In this paper, the 3D transformation is modeled as a nonlinear stochastic system with the state estimation providing six degrees-of-freedom motion and position values, using line features in image plane as measuring inputs and dual quaternion to represent both rotation and translation in a unified notation. A filtering method called the Gaussian particle filter (GPF) based on the particle filtering concept is presented for 3D pose and motion estimation of a moving target from monocular image sequences. The method has been implemented with simulated data, and simulation results are provided along with comparisons to the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) to show the relative advantages of the GPF. Simulation results showed that GPF is a superior alternative to EKF and UKF.

Nonlinear electrorheological instability of two Rivlin-Ericksen elastico-viscous fluids

CERN Document Server

El-Dib, Y O

2003-01-01

The behaviour of surface waves propagating between two Rivlin-Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients. This equation is accomplished by utilizing the cubic nonlinearity. The use of the Gardner-Morikawa transformation yields a simplified linear dispersion relation so that the periodic solution for the linear form is utilized. The ...

Discontinuity and complexity in nonlinear physical systems

CERN Document Server

Baleanu, Dumitru; Luo, Albert

2014-01-01

This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

Science.gov (United States)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

Science.gov (United States)

Wu, R. Q.; Zhang, W.; Yao, M. H.

2018-02-01

In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton's second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.

NOLB: Nonlinear Rigid Block Normal Mode Analysis Method

OpenAIRE

Hoffmann , Alexandre; Grudinin , Sergei

2017-01-01

International audience; We present a new conceptually simple and computationally efficient method for nonlinear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a nonlinear extrapolation of motion out of these veloci...

Broad-band simulation of M7.2 earthquake on the North Tehran fault, considering non-linear soil effects

Science.gov (United States)

Majidinejad, A.; Zafarani, H.; Vahdani, S.

2018-05-01

The North Tehran fault (NTF) is known to be one of the most drastic sources of seismic hazard on the city of Tehran. In this study, we provide broad-band (0-10 Hz) ground motions for the city as a consequence of probable M7.2 earthquake on the NTF. Low-frequency motions (0-2 Hz) are provided from spectral element dynamic simulation of 17 scenario models. High-frequency (2-10 Hz) motions are calculated with a physics-based method based on S-to-S backscattering theory. Broad-band ground motions at the bedrock level show amplifications, both at low and high frequencies, due to the existence of deep Tehran basin in the vicinity of the NTF. By employing soil profiles obtained from regional studies, effect of shallow soil layers on broad-band ground motions is investigated by both linear and non-linear analyses. While linear soil response overestimate ground motion prediction equations, non-linear response predicts plausible results within one standard deviation of empirical relationships. Average Peak Ground Accelerations (PGAs) at the northern, central and southern parts of the city are estimated about 0.93, 0.59 and 0.4 g, respectively. Increased damping caused by non-linear soil behaviour, reduces the soil linear responses considerably, in particular at frequencies above 3 Hz. Non-linear deamplification reduces linear spectral accelerations up to 63 per cent at stations above soft thick sediments. By performing more general analyses, which exclude source-to-site effects on stations, a correction function is proposed for typical site classes of Tehran. Parameters for the function which reduces linear soil response in order to take into account non-linear soil deamplification are provided for various frequencies in the range of engineering interest. In addition to fully non-linear analyses, equivalent-linear calculations were also conducted which their comparison revealed appropriateness of the method for large peaks and low frequencies, but its shortage for small to

Nonlinear vibrations of an inclined beam subjected to a moving load

International Nuclear Information System (INIS)

Mamandi, A; Kargarnovin, M H; Younesian, D

2009-01-01

In this paper, the nonlinear dynamic responses of an inclined pinned-pinned Euler-Bernoulli beam with a constant cross section and finite length subjected to a concentrated vertical force traveling with constant velocity is investigated by using the mode summation method. Frequency analysis of the PDE's governing equations of motion for steady-state response is studied by applying multiple scales method. The nonlinear dynamic deflections of the beam are obtained by solving two coupled nonlinear PDE's governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the numerical results are compared with those obtained from traditional linear solution. It is found that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also stability analysis of the steady-state response for the modes equations having quadratic nonlinearity is carried out and it is observed from the amplitude response curves that for the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon are predicted for the longitudinal excitation.

The effect of high-frequency ground motion on the MAPLE-X10 reactor

International Nuclear Information System (INIS)

Bhan, S.; Dunbar, S.

1989-06-01

The effect of high-frequency ground motion on structures and equipment in nuclear reactors is examined by subjecting simple linear models to selected recorded ground motions which exhibit low and high frequencies. Computed damage measures indicate that high-frequency short-duration ground motion, such as that observed in eastern North America, have a minimal effect on structures with low natural frequencies. Response spectra of high-frequency ground motion indicate that higher forces are induced in structures with high natural frequencies as compared to those induced by low-frequency ground motion. However, reported observations of earthquake damage in eastern North America suggest that high-frequency ground motion causes little of no damage to structures. This may be due to the energy absorption capability of structures. It is concluded that the response spectrum representative of ground motion observed in eastern North America may give an over-conservative measure of the response of structures with high natural frequencies, since it does not account for the typically observed short duration of high-frequency ground motion and for the energy absorption capability of structures. Detailed nonlinear analysis of specific structures with high natural frequencies should be performed to better predict the actual response. Recommendations for a nonlinear analysis of typical structures with high natural frequencies are made

In-plane and out-of-plane nonlinear dynamics of an axially moving beam

International Nuclear Information System (INIS)

Farokhi, Hamed; Ghayesh, Mergen H.; Amabili, Marco

2013-01-01

In the present study, the nonlinear forced dynamics of an axially moving beam is investigated numerically taking into account the in-plane and out-of-plane motions. The nonlinear partial differential equations governing the motion of the system are derived via Hamilton’s principle. The Galerkin scheme is then introduced to these partial differential equations yielding a set of second-order nonlinear ordinary differential equations with coupled terms. This set is transformed into a new set of first-order nonlinear ordinary differential equations by means of a change of variables. A direct time integration technique is conducted upon the new set of equations resulting in the bifurcation diagrams of Poincaré maps of the system. The dynamical characteristics of the system are investigated for different system parameters and presented through use of time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms

Randomness control of vehicular motion through a sequence of traffic signals at irregular intervals

International Nuclear Information System (INIS)

Nagatani, Takashi

2010-01-01

We study the regularization of irregular motion of a vehicle moving through the sequence of traffic signals with a disordered configuration. Each traffic signal is controlled by both cycle time and phase shift. The cycle time is the same for all signals, while the phase shift varies from signal to signal by synchronizing with intervals between a signal and the next signal. The nonlinear dynamic model of the vehicular motion is presented by the stochastic nonlinear map. The vehicle exhibits the very complex behavior with varying both cycle time and strength of irregular intervals. The irregular motion induced by the disordered configuration is regularized by adjusting the phase shift within the regularization regions.

Experimental chaos in nonlinear vibration isolation system

International Nuclear Information System (INIS)

Lou Jingjun; Zhu Shijian; He Lin; He Qiwei

2009-01-01

The chaotic vibration isolation method was studied thoroughly from an experimental perspective. The nonlinear load-deflection characteristic of the conical coil spring used in the experiment was surveyed. Chaos and subharmonic responses including period-2 and period-6 motions were observed. The line spectrum reduction and the drop of the acceleration vibration level in chaotic state and that in non-chaotic state were compared, respectively. It was concluded from the experiment that the nonlinear vibration isolation system in chaotic state has strong ability in line spectrum reduction.

Nonlinear and self-consistent treatment of ECRH

Energy Technology Data Exchange (ETDEWEB)

Tsironis, C.; Vlahos, L.

2005-07-01

A self-consistent formulation for the nonlinear interaction of electromagnetic waves with relativistic magnetized electrons is applied for the description of the ECRH. In general, electron-cyclotron absorption is the result of resonances between the cyclotron harmonics and the Doppler-shifted waver frequency. The resonant interaction results to an intense wave-particle energy exchange and an electron acceleration, and for that reason it is widely applied in fusion experiments for plasma heating and current drive. The linear theory, for the wave absorption, as well as the quasilinear theory for the electron distribution function, are the most frequently-used tools for the study of wave-particle interactions. However, in many cases the validity of these theories is violated, namely cases where nonlinear effects, like, e. g. particle trapping in the wave field, are dominant in the particle phase-space. Our model consists of electrons streaming and gyrating in a tokamak plasma slab, which is finite in the directions perpendicular to the main magnetic field. The particles interact with an electromagnetic electron-cyclotron wave of the ordinary (O-) or the extraordinary (X-) mode. A set of nonlinear and relativistic equations is derived, which take into account the effects of the charged particle motions on the wave. These consist of the equations of motion for the plasma electrons in the slab, as well as the wave equation in terms of the vector potential. The effect of the electron motions on the temporal evolution of the wave is reflected in the current density source term. (Author)

Nonlinear and self-consistent treatment of ECRH

International Nuclear Information System (INIS)

Tsironis, C.; Vlahos, L.

2005-01-01

A self-consistent formulation for the nonlinear interaction of electromagnetic waves with relativistic magnetized electrons is applied for the description of the ECRH. In general, electron-cyclotron absorption is the result of resonances between the cyclotron harmonics and the Doppler-shifted waver frequency. The resonant interaction results to an intense wave-particle energy exchange and an electron acceleration, and for that reason it is widely applied in fusion experiments for plasma heating and current drive. The linear theory, for the wave absorption, as well as the quasilinear theory for the electron distribution function, are the most frequently-used tools for the study of wave-particle interactions. However, in many cases the validity of these theories is violated, namely cases where nonlinear effects, like, e. g. particle trapping in the wave field, are dominant in the particle phase-space. Our model consists of electrons streaming and gyrating in a tokamak plasma slab, which is finite in the directions perpendicular to the main magnetic field. The particles interact with an electromagnetic electron-cyclotron wave of the ordinary (O-) or the extraordinary (X-) mode. A set of nonlinear and relativistic equations is derived, which take into account the effects of the charged particle motions on the wave. These consist of the equations of motion for the plasma electrons in the slab, as well as the wave equation in terms of the vector potential. The effect of the electron motions on the temporal evolution of the wave is reflected in the current density source term. (Author)

Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

Directory of Open Access Journals (Sweden)

Qilin Huang

2013-01-01

Full Text Available A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM. Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

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.

Local and global nonlinear dynamics of a parametrically excited rectangular symmetric cross-ply laminated composite plate

International Nuclear Information System (INIS)

Ye Min; Lu Jing; Zhang Wei; Ding Qian

2005-01-01

The present investigation deals with nonlinear dynamic behavior of a parametrically excited simply supported rectangular symmetric cross-ply laminated composite thin plate for the first time. The governing equation of motion for rectangular symmetric cross-ply laminated composite thin plate is derived by using von Karman equation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion. The Galerkin approach is used to obtain a two-degree-of-freedom nonlinear system under parametric excitation. The method of multiple scales is utilized to transform the second-order non-autonomous differential equations to the first-order averaged equations. Using numerical method, the averaged equations are analyzed to obtain the steady state bifurcation responses. The analysis of stability for steady state bifurcation responses in laminated composite thin plate is also given. Under certain conditions laminated composite thin plate may have two or multiple steady state bifurcation solutions. Jumping phenomenon occurs in the steady state bifurcation solutions. The chaotic motions of rectangular symmetric cross-ply laminated composite thin plate are also found by using numerical simulation. The results obtained here demonstrate that the periodic, quasi-periodic and chaotic motions coexist for a parametrically excited fore-edge simply supported rectangular symmetric cross-ply laminated composite thin plate under certain conditions

Live Speech Driven Head-and-Eye Motion Generators.

Science.gov (United States)

Le, Binh H; Ma, Xiaohan; Deng, Zhigang

2012-11-01

This paper describes a fully automated framework to generate realistic head motion, eye gaze, and eyelid motion simultaneously based on live (or recorded) speech input. Its central idea is to learn separate yet interrelated statistical models for each component (head motion, gaze, or eyelid motion) from a prerecorded facial motion data set: 1) Gaussian Mixture Models and gradient descent optimization algorithm are employed to generate head motion from speech features; 2) Nonlinear Dynamic Canonical Correlation Analysis model is used to synthesize eye gaze from head motion and speech features, and 3) nonnegative linear regression is used to model voluntary eye lid motion and log-normal distribution is used to describe involuntary eye blinks. Several user studies are conducted to evaluate the effectiveness of the proposed speech-driven head and eye motion generator using the well-established paired comparison methodology. Our evaluation results clearly show that this approach can significantly outperform the state-of-the-art head and eye motion generation algorithms. In addition, a novel mocap+video hybrid data acquisition technique is introduced to record high-fidelity head movement, eye gaze, and eyelid motion simultaneously.

Success Stories in Control: Nonlinear Dynamic Inversion Control

Science.gov (United States)

Bosworth, John T.

2010-01-01

NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.

Constrained quadratic stabilization of discrete-time uncertain nonlinear multi-model systems using piecewise affine state-feedback

Directory of Open Access Journals (Sweden)

Olav Slupphaug

1999-07-01

Full Text Available In this paper a method for nonlinear robust stabilization based on solving a bilinear matrix inequality (BMI feasibility problem is developed. Robustness against model uncertainty is handled. In different non-overlapping regions of the state-space called clusters the plant is assumed to be an element in a polytope which vertices (local models are affine systems. In the clusters containing the origin in their closure, the local models are restricted to be linear systems. The clusters cover the region of interest in the state-space. An affine state-feedback is associated with each cluster. By utilizing the affinity of the local models and the state-feedback, a set of linear matrix inequalities (LMIs combined with a single nonconvex BMI are obtained which, if feasible, guarantee quadratic stability of the origin of the closed-loop. The feasibility problem is attacked by a branch-and-bound based global approach. If the feasibility check is successful, the Liapunov matrix and the piecewise affine state-feedback are given directly by the feasible solution. Control constraints are shown to be representable by LMIs or BMIs, and an application of the control design method to robustify constrained nonlinear model predictive control is presented. Also, the control design method is applied to a simple example.

On some nonlinear effects in ultrasonic fields

Science.gov (United States)

Tjotta

2000-03-01

Nonlinear effects associated with intense sound fields in fluids are considered theoretically. Special attention is directed to the study of higher effects that cannot be described within the standard propagation models of nonlinear acoustics (the KZK and Burgers equations). The analysis is based on the fundamental equations of motion for a thermoviscous fluid, for which thermal equations of state exist. Model equations are derived and used to analyze nonlinear sources for generation of flow and heat, and other changes in the ambient state of the fluid. Fluctuations in the coefficients of viscosity and thermal conductivity caused by the sound field, are accounted for. Also considered are nonlinear effects induced in the fluid by flexural vibrations. The intensity and absorption of finite amplitude sound waves are calculated, and related to the sources for generation of higher order effects.

A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction

Directory of Open Access Journals (Sweden)

Qiegen Liu

2014-01-01

Full Text Available Nonconvex optimization has shown that it needs substantially fewer measurements than l1 minimization for exact recovery under fixed transform/overcomplete dictionary. In this work, two efficient numerical algorithms which are unified by the method named weighted two-level Bregman method with dictionary updating (WTBMDU are proposed for solving lp optimization under the dictionary learning model and subjecting the fidelity to the partial measurements. By incorporating the iteratively reweighted norm into the two-level Bregman iteration method with dictionary updating scheme (TBMDU, the modified alternating direction method (ADM solves the model of pursuing the approximated lp-norm penalty efficiently. Specifically, the algorithms converge after a relatively small number of iterations, under the formulation of iteratively reweighted l1 and l2 minimization. Experimental results on MR image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed method can efficiently reconstruct MR images from highly undersampled k-space data and presents advantages over the current state-of-the-art reconstruction approaches, in terms of higher PSNR and lower HFEN values.

On evolving deformation microstructures in non-convex partially damaged solids

KAUST Repository

Gurses, Ercan

2011-06-01

The paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic stress potential. The existence of this potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of a principle of minimum incremental work. Mathematical existence theorems of minimizers then induce a definition of the material stability in terms of the sequential weak lower semicontinuity of the incremental functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of weak convexity notions of the stress potential. Furthermore, the variational setting opens up the possibility to analyze the development of deformation microstructures in the post-critical range of unstable inelastic materials based on energy relaxation methods. In partially damaged solids, accumulated damage may yield non-convex stress potentials which indicate instability and formation of fine-scale microstructures. These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we introduce a new isotropic microstructure which provides a simple approximation of the multi-dimensional rank-one convex hull. The development of those isotropic microstructures is investigated for homogeneous and inhomogeneous numerical simulations. © 2011 Elsevier Ltd. All rights reserved.

Interpretation of Fermion system equilibration by energy fluid motion

International Nuclear Information System (INIS)

Jang, S.

1990-01-01

We study the equilibration of fermion system with the help of both linear and non-linear master equations which are originated from the extended time-dependent Hartree-Fock equation of motion. We show how the non-linear master equation for nucleon occupation number transforms into the Navier-Stokes type of one dimensional equation for non-stationary flow of a compressible and viscous fluid. Physical consequences of these equations are investigated by providing illustrative examples

A novel method for non-parametric identification of nonlinear restoring forces in nonlinear vibrations from noisy response data: A conservative system

International Nuclear Information System (INIS)

Jang, T. S.; Kwon, S. H.; Han, S. L.

2009-01-01

A novel procedure is proposed to identify the functional form of nonlinear restoring forces in the nonlinear oscillatory motion of a conservative system. Although the problem of identification has a unique solution, formulation results in a Volterra-type of integral equation of the 'first' kind: the solution lacks stability because the integral equation is the 'first' kind. Thus, the new problem at hand is ill-posed. Inevitable small errors during the identification procedure can make the prediction of nonlinear restoring forces useless. We overcome the difficulty by using a stabilization technique of Landweber's regularization in this study. The capability of the proposed procedure is investigated through numerical examples

Simulation of nonlinear random vibrations using artificial neural networks

Energy Technology Data Exchange (ETDEWEB)

Paez, T.L.; Tucker, S.; O`Gorman, C.

1997-02-01

The simulation of mechanical system random vibrations is important in structural dynamics, but it is particularly difficult when the system under consideration is nonlinear. Artificial neural networks provide a useful tool for the modeling of nonlinear systems, however, such modeling may be inefficient or insufficiently accurate when the system under consideration is complex. This paper shows that there are several transformations that can be used to uncouple and simplify the components of motion of a complex nonlinear system, thereby making its modeling and random vibration simulation, via component modeling with artificial neural networks, a much simpler problem. A numerical example is presented.

Nonlinear operators and their propagators

International Nuclear Information System (INIS)

Schwartz, C.

1997-01-01

Mathematical physicists are familiar with a large set of tools designed for dealing with linear operators, which are so common in both the classical and quantum theories; but many of those tools are useless with nonlinear equations of motion. In this work a general algebra and calculus is developed for working with nonlinear operators: The basic new tool being the open-quotes slash product,close quotes defined by A(1+εB) =A+εA/B+O(ε 2 ). For a generic time development equation, the propagator is constructed and then there follows the formal version of time dependent perturbation theory, in remarkable similarity to the linear situation. A nonperturbative approximation scheme capable of producing high accuracy computations, previously developed for linear operators, is shown to be applicable as well in the nonlinear domain. A number of auxiliary mathematical properties and examples are given. copyright 1997 American Institute of Physics

Dark matter as a non-linear effect of gravitation

International Nuclear Information System (INIS)

Maia, M.D.; Capistrano, A.J.S.

2006-01-01

The rotation curves of stars in disk galaxies are calculated with the Newtonian law of motion applied to a scalar potential derived from the geodesic equation, only, under the slow motion condition, the so-called Nearly Newtonian Gravity (NNG). A nearly Newtonian gravitational potential, Φ NN = -1/2 c 2 (1+g 44 ), is obtained, characterized by an exact solution of Einsteins equations, with the non-linear effects present in the component g 44 . This gravitational field lies somewhere between General Relativity and Newtonian Gravity. Therefore, Einsteins equations and the equivalence principle are preserved, but the general covariance is broken. The resulting curves are remarkably close to the observed rotation curves in spiral galaxies, suggesting that a substantial component of dark matter may be explained by the non-linearity of Einsteins equations. (author)

Unusual motions of a vibrating string

Science.gov (United States)

Hanson, Roger J.

2003-10-01

The actual motions of a sinusoidally driven vibrating string can be very complex due to nonlinear effects resulting from varying tension and longitudinal motion not included in simple linear theory. Commonly observed effects are: generation of motion perpendicular to the driving force, sudden jumps in amplitude, hysteresis, and generation of higher harmonics. In addition, these effects are profoundly influenced by wire asymmetries which in a brass harpsichord wire can cause a small splitting of each natural frequency of free vibration into two closely spaced frequencies (relative separation ~0.2% to 2%), each associated with transverse motion along two orthogonal characteristic wire axes. Some unusual resulting patterns of complex motions of a point on the wire are exhibited on videotape. Examples include: sudden changes of harmonic content, generation of subharmonics, and motion which appears nearly chaotic but which has a pattern period of over 10 s. Another unusual phenomenon due to entirely different causes can occur when a violin string is bowed with a higher than normal force resulting in sounds ranging from about a musical third to a twelfth lower than the sound produced when the string is plucked.

Wideband quin-stable energy harvesting via combined nonlinearity

Directory of Open Access Journals (Sweden)

Chen Wang

2017-04-01

Full Text Available In this work, we propose a wideband quintuple-well potential piezoelectric-based vibration energy harvester using a combined nonlinearity: the magnetic nonlinearity induced by magnetic force and the piecewise-linearity produced by mechanical impact. With extra stable states compared to other multi-stable harvesters, the quin-stable harvester can distribute its potential energy more uniformly, which provides shallower potential wells and results in lower excitation threshold for interwell motion. The mathematical model of this quin-stable harvester is derived and its equivalent piecewise-nonlinear restoring force is measured in the experiment and identified as piecewise polynomials. Numerical simulations and experimental verifications are performed in different levels of sinusoid excitation ranging from 1 to 25 Hz. The results demonstrate that, with lower potential barriers compared with tri-stable counterpart, the quin-stable arrangement can escape potential wells more easily for doing high-energy interwell motion over a wider band of frequencies. Moreover, by utilizing the mechanical stoppers, this harvester can produce significant output voltage under small tip deflections, which results in a high power density and is especially suitable for a compact MEMS approach.

Experimental verification of a bridge-shaped, nonlinear vibration energy harvester

Energy Technology Data Exchange (ETDEWEB)

Gafforelli, Giacomo, E-mail: giacomo.gafforelli@polimi.it; Corigliano, Alberto [Department of Civil and Environmental Engineering, Politecnico di Milano, Milano, 20133 (Italy); Xu, Ruize; Kim, Sang-Gook [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

2014-11-17

This paper reports a comprehensive modeling and experimental characterization of a bridge shaped nonlinear energy harvester. A doubly clamped beam at large deflection requires stretching strain in addition to the bending strain to be geometrically compatible, which stiffens the beam as the beam deflects and transforms the dynamics to a nonlinear regime. The Duffing mode non-linear resonance widens the frequency bandwidth significantly at higher frequencies than the linear resonant frequency. The modeling includes a nonlinear measure of strain coupled with piezoelectric constitutive equations which end up in nonlinear coupling terms in the equations of motion. The main result supports that the power generation is bounded by the mechanical damping for both linear and nonlinear harvesters. Modeling also shows the power generation is over a wider bandwidth in the nonlinear case. A prototype is manufactured and tested to measure the power generation at different load resistances and acceleration amplitudes. The prototype shows a nonlinear behavior with well-matched experimental data to the modeling.

Nonlinear dynamics in the perceptual grouping of connected surfaces.

Science.gov (United States)

Hock, Howard S; Schöner, Gregor

2016-09-01

Evidence obtained using the dynamic grouping method has shown that the grouping of an object's connected surfaces has properties characteristic of a nonlinear dynamical system. When a surface's luminance changes, one of its boundaries is perceived moving across the surface. The direction of this dynamic grouping (DG) motion indicates which of two flanking surfaces has been grouped with the changing surface. A quantitative measure of overall grouping strength (affinity) for adjacent surfaces is provided by the frequency of DG motion perception in directions promoted by the grouping variables. It was found that: (1) variables affecting surface grouping for three-surface objects evolve over time, settling at stable levels within a single fixation, (2) how often DG motion is perceived when a surface's luminance is perturbed (changed) depends on the pre-perturbation affinity state of the surface grouping, (3) grouping variables promoting the same surface grouping combine cooperatively and nonlinearly (super-additively) in determining the surface grouping's affinity, (4) different DG motion directions during different trials indicate that surface grouping can be bistable, which implies that inhibitory interactions have stabilized one of two alternative surface groupings, and (5) when alternative surface groupings have identical affinity, stochastic fluctuations can break the symmetry and inhibitory interactions can then stabilize one of the surface groupings, providing affinity levels are not too high (which results in bidirectional DG motion). A surface-grouping network is proposed within which boundaries vary in salience. Low salience or suppressed boundaries instantiate surface grouping, and DG motion results from changes in boundary salience. Copyright © 2015 Elsevier Ltd. All rights reserved.

A solution to nonlinearity problems

International Nuclear Information System (INIS)

Neuffer, D.V.

1989-01-01

New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron or transport line are presented. In a simplest form, correction elements are places at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule, forming an accurate quasi-local canceling approximation to the nonlinearity. The F, C, and D correctors may also be used to obtain precise control of the horizontal, coupled, and vertical motion. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in beam transport have been obtained. 13 refs., 1 fig., 1 tab

Nonlinear Squeeze Film Dampers without Centralized Springs

Directory of Open Access Journals (Sweden)

Zhu Changsheng

2000-01-01

Full Text Available In this paper, the bifurcation behavior of a flexible rotor supported on nonlinear squeeze film dampers without centralized springs is analyzed numerically by means of rotor trajectories, Poincar maps, bifurcation diagrams and power spectra, based on the short bearing and cavitated film assumptions. It is shown that there also exist two different operations (i.e., socalled bistable operations in some speed regions in the rotor system supported on the nonlinear squeeze film dampers without centralized springs. In the bistable operation speed regions, the rotor system exhibits synchronous, sub-synchronous, sub-super-synchronous and almost-periodic as well as nonperiodic motions. The periodic bifurcation behaviors of the rotor system supported on nonlinear squeeze film dampers without centralized springs are very complex and require further investigations.

Enhancing power generation of floating wave power generators by utilization of nonlinear roll-pitch coupling

Science.gov (United States)

Yerrapragada, Karthik; Ansari, M. H.; Karami, M. Amin

2017-09-01

We propose utilization of the nonlinear coupling between the roll and pitch motions of wave energy harvesting vessels to increase their power generation by orders of magnitude. Unlike linear vessels that exhibit unidirectional motion, our vessel undergoes both pitch and roll motions in response to frontal waves. This significantly magnifies the motion of the vessel and thus improves the power production by several orders of magnitude. The ocean waves result in roll and pitch motions of the vessel, which in turn causes rotation of an onboard pendulum. The pendulum is connected to an electric generator to produce power. The coupled electro-mechanical system is modeled using energy methods. This paper investigates the power generation of the vessel when the ratio between pitch and roll natural frequencies is about 2 to 1. In that case, a nonlinear energy transfer occurs between the roll and pitch motions, causing the vessel to perform coupled pitch and roll motion even though it is only excited in the pitch direction. It is shown that co-existence of pitch and roll motions significantly enhances the pendulum rotation and power generation. A method for tuning the natural frequencies of the vessel is proposed to make the energy generator robust to variations of the frequency of the incident waves. It is shown that the proposed method enhances the power output of the floating wave power generators by multiple orders of magnitude. A small-scale prototype is developed for the proof of concept. The nonlinear energy transfer and the full rotation of the pendulum in the prototype are observed in the experimental tests.

Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint

Science.gov (United States)

Bullock, S. J.; Peterson, L. D.

1994-01-01

The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.

Approximate Integrals of rf-driven Particle Motion in Magnetic Field

International Nuclear Information System (INIS)

Dodin, I.Y.; Fisch, N.J.

2004-01-01

For a particle moving in nonuniform magnetic field under the action of an rf wave, ponderomotive effects result from rf-driven oscillations nonlinearly coupled with Larmor rotation. Using Lagrangian and Hamiltonian formalism, we show how, despite this coupling, two independent integrals of the particle motion are approximately conserved. Those are the magnetic moment of free Larmor rotation and the quasi-energy of the guiding center motion parallel to the magnetic field. Under the assumption of non-resonant interaction of the particle with the rf field, these integrals represent adiabatic invariants of the particle motion

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...

Active and Nonlinear Microrheology of Dense Colloidal Suspensions

OpenAIRE

Harrer, Christian Josef

2013-01-01

In this work, we have investigated active and nonlinear microrheology of dense colloidal suspensions, i.e., the forced motion of a singled-out tracer particle by an external force, both in the framework of MCT and via event-driven Brownian Dynamics simulations.

Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts

International Nuclear Information System (INIS)

Luo, Albert C.J.; Chen Lidi

2005-01-01

In this paper, an idealized, piecewise linear system is presented to model the vibration of gear transmission systems. Periodic motions in a generalized, piecewise linear oscillator with perfectly plastic impacts are predicted analytically. The analytical predictions of periodic motion are based on the mapping structures, and the generic mappings based on the discontinuous boundaries are developed. This method for the analytical prediction of the periodic motions in non-smooth dynamic systems can give all possible periodic motions based on the adequate mapping structures. The stability and bifurcation conditions for specified periodic motions are obtained. The periodic motions and grazing motion are demonstrated. This model is applicable to prediction of periodic motion in nonlinear dynamics of gear transmission systems

On MHD nonlinear stretching flow of Powell–Eyring nanomaterial

Directory of Open Access Journals (Sweden)

Tasawar Hayat

Full Text Available This communication addresses the magnetohydrodynamic (MHD flow of Powell–Eyring nanomaterial bounded by a nonlinear stretching sheet. Novel features regarding thermophoresis and Brownian motion are taken into consideration. Powell–Eyring fluid is electrically conducted subject to non-uniform applied magnetic field. Assumptions of small magnetic Reynolds number and boundary layer approximation are employed in the mathematical development. Zero nanoparticles mass flux condition at the sheet is selected. Adequate transformation yield nonlinear ordinary differential systems. The developed nonlinear systems have been computed through the homotopic approach. Effects of different pertinent parameters on velocity, temperature and concentration fields are studied and analyzed. Further numerical data of skin friction and heat transfer rate is also tabulated and interpreted. Keywords: Powell–Eyring fluid, Magnetohydrodynamics, Nanomaterial, Nonlinear stretching surface

Five parameters for the evaluation of the soil nonlinearity during the Ms8.0 Wenchuan Earthquake using the HVSR method

Science.gov (United States)

Ren, Yefei; Wen, Ruizhi; Yao, Xinxin; Ji, Kun

2017-08-01

The consideration of soil nonlinearity is important for the accurate estimation of the site response. To evaluate the soil nonlinearity during the 2008 Ms8.0 Wenchuan Earthquake, 33 strong-motion records obtained from the main shock and 890 records from 157 aftershocks were collected for this study. The horizontal-to-vertical spectral ratio (HVSR) method was used to calculate five parameters: the ratio of predominant frequency (RFp), degree of nonlinearity (DNL), absolute degree of nonlinearity (ADNL), frequency of nonlinearity (fNL), and percentage of nonlinearity (PNL). The purpose of this study was to evaluate the soil nonlinearity level of 33 strong-motion stations and to investigate the characteristics, performance, and effective usage of these five parameters. Their correlations with the peak ground acceleration (PGA), peak ground velocity (PGV), average uppermost 30-m shear-wave velocity ( V S30), and maximum amplitude of HVSR ( A max) were investigated. The results showed that all five parameters correlate well with PGA and PGV. The DNL, ADNL, and PNL also show a good correlation with A max, which means that the degree of soil nonlinearity not only depends on the ground-motion amplitude (e.g., PGA and PGV) but also on the site condition. The fNL correlates with PGA and PGV but shows no correlation with either A max or V S30, implying that the frequency width affected by the soil nonlinearity predominantly depends on the ground-motion amplitude rather than the site condition. At 16 of the 33 stations analyzed in this study, the site response showed evident (i.e., strong and medium) nonlinearity during the main shock of the Wenchuan Earthquake, where the ground-motion level was almost beyond the threshold of PGA > 200 cm/s2 or PGV > 15 cm/s. The site response showed weak and no nonlinearity at the other 14 and 3 stations. These results also confirm that RFp, DNL, ADNL, and PNL are effective in identifying the soil nonlinearity behavior. The identification

Nonlinear generalization of the quasiparticle random phase approximation for description of anharmonic effects in vibrational spectra: Application to the even Ni isotopes

International Nuclear Information System (INIS)

Li, C.T.; Klein, A.

1979-01-01

The theory of anharmonic nuclear vibrational motion (nonlinear equations-of-motion method) developed in the preceding paper is applied to atsup 60,62,64atNi, which exhibit one and two phonon quadrupole collective states. A model Hamiltonian consisting of a modified pairing plus quadrupole interaction is studied first by comparing the results of the nonlinear equations-of-motion method with those of an exact diagonalization. Contrary to popular opinion, the model chosen fails to produce a vibrational spectrum, except in the case of 60 Ni, and as a consequence, the nonlinear equations-of-motion method, designed specifically to describe vibrational spectra, accords well with the exact calculations only for this case. A simple method is then described, within the framework of the nonlinear equations-of-motion method, for refining the model Hamiltonian so as to bring it into accord with experiment. In practice, it is found that a simple additional parameter in the Hamiltonian suffices to yield descriptions of the quadrupole states in Ni isotopes comparable in precision to the most up-to-date versions (modified, adjusted, etc.) of the surface delta interaction model

Nonlinear (Anharmonic Casimir Oscillator

Directory of Open Access Journals (Sweden)

Habibollah Razmi

2011-01-01

Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.

Nonlinear dynamic analysis of atomic force microscopy under deterministic and random excitation

International Nuclear Information System (INIS)

Pishkenari, Hossein Nejat; Behzad, Mehdi; Meghdari, Ali

2008-01-01

The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. This paper is devoted to the analysis of nonlinear behavior of amplitude modulation (AM) and frequency modulation (FM) modes of atomic force microscopy. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Using perturbation methods such as averaging, and Fourier transform nonlinear equations of motion are analytically solved and the advantageous results are extracted from this nonlinear analysis. The results of the proposed techniques for AM-AFM, clearly depict the existence of two stable and one unstable (saddle) solutions for some of exciting parameters under deterministic vibration. The basin of attraction of two stable solutions is different and dependent on the exciting frequency. From this analysis the range of the frequency which will result in a unique periodic response can be obtained and used in practical experiments. Furthermore the analytical responses determined by perturbation techniques can be used to detect the parameter region where the chaotic motion is avoided. On the other hand for FM-AFM, the relation between frequency shift and the system parameters can be extracted and used for investigation of the system nonlinear behavior. The nonlinear behavior of the oscillating tip can easily explain the observed shift of frequency as a function of tip sample distance. Also in this paper we have investigated the AM-AFM system response under a random excitation. Using two different methods we have obtained the statistical properties of the tip motion. The results show that we can use the mean square value of tip motion to image the sample when the excitation signal is random

Nonlinear dynamic analysis of atomic force microscopy under deterministic and random excitation

Energy Technology Data Exchange (ETDEWEB)

Pishkenari, Hossein Nejat [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Behzad, Mehdi [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)], E-mail: m_behzad@sharif.edu; Meghdari, Ali [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)

2008-08-15

The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. This paper is devoted to the analysis of nonlinear behavior of amplitude modulation (AM) and frequency modulation (FM) modes of atomic force microscopy. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Using perturbation methods such as averaging, and Fourier transform nonlinear equations of motion are analytically solved and the advantageous results are extracted from this nonlinear analysis. The results of the proposed techniques for AM-AFM, clearly depict the existence of two stable and one unstable (saddle) solutions for some of exciting parameters under deterministic vibration. The basin of attraction of two stable solutions is different and dependent on the exciting frequency. From this analysis the range of the frequency which will result in a unique periodic response can be obtained and used in practical experiments. Furthermore the analytical responses determined by perturbation techniques can be used to detect the parameter region where the chaotic motion is avoided. On the other hand for FM-AFM, the relation between frequency shift and the system parameters can be extracted and used for investigation of the system nonlinear behavior. The nonlinear behavior of the oscillating tip can easily explain the observed shift of frequency as a function of tip sample distance. Also in this paper we have investigated the AM-AFM system response under a random excitation. Using two different methods we have obtained the statistical properties of the tip motion. The results show that we can use the mean square value of tip motion to image the sample when the excitation signal is random.

Stability of the Minimizers of Least Squares with a Non-Convex Regularization. Part I: Local Behavior

International Nuclear Information System (INIS)

Durand, S.; Nikolova, M.

2006-01-01

Many estimation problems amount to minimizing a piecewise C m objective function, with m ≥ 2, composed of a quadratic data-fidelity term and a general regularization term. It is widely accepted that the minimizers obtained using non-convex and possibly non-smooth regularization terms are frequently good estimates. However, few facts are known on the ways to control properties of these minimizers. This work is dedicated to the stability of the minimizers of such objective functions with respect to variations of the data. It consists of two parts: first we consider all local minimizers, whereas in a second part we derive results on global minimizers. In this part we focus on data points such that every local minimizer is isolated and results from a C m-1 local minimizer function, defined on some neighborhood. We demonstrate that all data points for which this fails form a set whose closure is negligible

Nonlinear flight dynamics and stability of hovering model insects

Science.gov (United States)

Liang, Bin; Sun, Mao

2013-01-01

Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier–Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect. PMID:23697714

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.

Nonlinear analysis of a rotor-bearing system using describing functions

Science.gov (United States)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Seismic Response of Power Transmission Tower-Line System Subjected to Spatially Varying Ground Motions

Directory of Open Access Journals (Sweden)

Li Tian

2010-01-01

Full Text Available The behavior of power transmission tower-line system subjected to spatially varying base excitations is studied in this paper. The transmission towers are modeled by beam elements while the transmission lines are modeled by cable elements that account for the nonlinear geometry of the cables. The real multistation data from SMART-1 are used to analyze the system response subjected to spatially varying ground motions. The seismic input waves for vertical and horizontal ground motions are also generated based on the Code for Design of Seismic of Electrical Installations. Both the incoherency of seismic waves and wave travel effects are accounted for. The nonlinear time history analytical method is used in the analysis. The effects of boundary conditions, ground motion spatial variations, the incident angle of the seismic wave, coherency loss, and wave travel on the system are investigated. The results show that the uniform ground motion at all supports of system does not provide the most critical case for the response calculations.

Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

Science.gov (United States)

Tobita, Miwa; Omura, Yoshiharu

2018-03-01

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.

Energy Technology Data Exchange (ETDEWEB)

Robinson, Brandon [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Rocha da Costa, Leandro Jose [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Poirel, Dominique [Royal Military College of Canada, Kingston (Canada). Dept. of Mechanical and Aerospace Engineering; Pettit, Chris [US Naval Academy, Annapolis, MD (United States). Dept. of Mechanical and Aerospace Engineering; Khalil, Mohammad [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sarkar, Abhijit [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering

2017-09-01

Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

Directory of Open Access Journals (Sweden)

Y. N. Pavlov

2015-01-01

Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

Nonlinearity induced synchronization enhancement in mechanical oscillators

Science.gov (United States)

Czaplewski, David A.; Lopez, Omar; Guest, Jeffrey R.; Antonio, Dario; Arroyo, Sebastian I.; Zanette, Damian H.

2018-05-08

An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein, are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.

Some nonlinear problems in the manipulation of beams

International Nuclear Information System (INIS)

Sessler, A.M.

1990-01-01

An overview is given of nonlinear problems that arise in the manipulation of beams. Beams can be made of material particles or photons, can be intense or dilute, can be energetic or not, and they can be propagating in vacuum or in a medium. The nonlinear aspects of the motion are different in each case, and this diversity of behavior is categorized. Many examples are given, which serves to illustrate the categorization and, furthermore, display the richness of behavior encountered in the physics of beams. 25 refs., 5 figs

Estimation of strong motions on free rock surface. Identification of soil structures and strong motions on free rock surface in Kashiwazaki-Kariwa nuclear power plant during the 2007 Niigataken Chuetsu-oki earthquake

International Nuclear Information System (INIS)

Saguchi, Koichiro; Masaki, Kazuaki; Irikura, Kojiro

2009-01-01

Very strong ground motions (maximum acceleration 993 cm/s 2 in the borehole seismometer point of -255m in depth) were observed in the Kashiwazaki Kariwa Nuclear Power Plant during the Niigataken Chuetsu-oki Earthquake on July 16, 2007. In this study, we tried to develop new method, which can simulate waveforms on free rock surface by using the bore hole records. We identified the underground structure model at the Service Hall from aftershock records observed in vertical array, using the simulated annealing method (Ingber(1989)). Based on numerical experiments it is identified that S-wave velocity and Q values of individual layers are inverted very well. Strong motion records of main shock observed by the bore hole seismometers were simulated by using one-dimensional multiple reflection method. In this study, non-linear effect is considered by introducing non-linear coefficient c(f) for under coming wave from surface. The maximum acceleration and phase characteristics in simulated waveforms are similar to the observed one. It means that our method is useful for simulate strong motion in non-linear region. Finally, strong motions on the free rock surface at the Service Hall during the main shock are simulated. The maximum acceleration of EW component on free rock surface is estimated to be 1,207 cm/s 2 . (author)

A method for regulating strong nonlinear vibration energy of the flexible arm

Directory of Open Access Journals (Sweden)

Yushu Bian

2015-07-01

Full Text Available For an oscillating system, large amplitude indicates strong vibration energy. In this article, modal interaction is used as a useful means to regulate strong nonlinear vibration energy of the flexible arm undergoing rigid motion. A method is put forward to migrate and dissipate vibration energy based on modal interaction. By means of multiple-scale perturbation analysis, it is proven that internal resonance can be successfully established between modes of the flexible arm and the vibration absorber. Through examples and analyses, it is verified that this control method is effective in regulating strong vibration energy and can be used to suppress strong nonlinear vibration of the flexible arm undergoing rigid motion.

Nonlinear Synchronization for Automatic Learning of 3D Pose Variability in Human Motion Sequences

Directory of Open Access Journals (Sweden)

Mozerov M

2010-01-01

Full Text Available A dense matching algorithm that solves the problem of synchronizing prerecorded human motion sequences, which show different speeds and accelerations, is proposed. The approach is based on minimization of MRF energy and solves the problem by using Dynamic Programming. Additionally, an optimal sequence is automatically selected from the input dataset to be a time-scale pattern for all other sequences. The paper utilizes an action specific model which automatically learns the variability of 3D human postures observed in a set of training sequences. The model is trained using the public CMU motion capture dataset for the walking action, and a mean walking performance is automatically learnt. Additionally, statistics about the observed variability of the postures and motion direction are also computed at each time step. The synchronized motion sequences are used to learn a model of human motion for action recognition and full-body tracking purposes.

Fragility curves for bridges under differential support motions

DEFF Research Database (Denmark)

Konakli, Katerina

2012-01-01

This paper employs the notion of fragility to investigate the seismic vulnerability of bridges subjected to spatially varying support motions. Fragility curves are developed for four highway bridges in California with vastly different structural characteristics. The input in this analysis consists...... of simulated ground motion arrays with temporal and spectral nonstationarities, and consistent with prescribed spatial variation patterns. Structural damage is quantified through displacement ductility demands obtained from nonlinear time-history analysis. The potential use of the ‘equal displacement’ rule...... to approximately evaluate displacement demands from analysis of the equivalent linear systems is examined....

Nonclassical properties of a contradirectional nonlinear optical coupler

Energy Technology Data Exchange (ETDEWEB)

Thapliyal, Kishore [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); Pathak, Anirban, E-mail: anirban.pathak@gmail.com [Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP-201307 (India); RCPTM, Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Science of the Czech Republic, Faculty of Science, Palacky University, 17. listopadu 12, 771 46 Olomouc (Czech Republic); Sen, Biswajit [Department of Physics, Vidyasagar Teachers' Training College, Midnapore 721101 (India); Perřina, Jan [RCPTM, Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Science of the Czech Republic, Faculty of Science, Palacky University, 17. listopadu 12, 771 46 Olomouc (Czech Republic); Department of Optics, Palacky University, 17. listopadu 12, 771 46 Olomouc (Czech Republic)

2014-10-24

We investigate the nonclassical properties of output fields propagated through a contradirectional asymmetric nonlinear optical coupler consisting of a linear waveguide and a nonlinear (quadratic) waveguide operated by second harmonic generation. In contrast to the earlier results, all the initial fields are considered weak and a completely quantum-mechanical model is used here to describe the system. Perturbative solutions of Heisenberg's equations of motion for various field modes are obtained using Sen–Mandal technique. Obtained solutions are subsequently used to show the existence of single-mode and intermodal squeezing, single-mode and intermodal antibunching, two-mode and multi-mode entanglement in the output of contradirectional asymmetric nonlinear optical coupler. Further, existence of higher order nonclassicality is also established by showing the existence of higher order antibunching, higher order squeezing and higher order entanglement. Variation of observed nonclassical characters with different coupling constants and phase mismatch is discussed. - Highlights: • Nonclassicalities in fields propagating through a directional coupler is studied. • Completely quantum-mechanical description of the coupler is provided. • Analytic solutions of Heisenberg equations of motion for various modes are obtained. • Existence of lower order and higher order entanglement is shown. • Variation of nonclassicalities with phase-mismatch and coupling constants is studied.

Recent advance in nonlinear aeroelastic analysis and control of the aircraft

Directory of Open Access Journals (Sweden)

Xiang Jinwu

2014-02-01

Full Text Available A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the two dimensional airfoil, the wing, and the full aircraft. Different nonlinearities encountered in aeroelastic systems are discussed firstly, where the emphases is placed on new nonlinear model to describe tested nonlinear relationship. Research techniques, especially new theoretical methods and aeroelastic flutter control methods are investigated in detail. The route to chaos and the cause of chaotic motion of two-dimensional aeroelastic system are summarized. Various structural modeling methods for the high-aspect-ratio wing with geometric nonlinearity are discussed. Accordingly, aerodynamic modeling approaches have been developed for the aeroelastic modeling of nonlinear high-aspect-ratio wings. Nonlinear aeroelasticity about high-altitude long-endurance (HALE and fight aircrafts are studied separately. Finally, conclusions and the challenges of the development in nonlinear aeroelasticity are concluded. Nonlinear aeroelastic problems of morphing wing, energy harvesting, and flapping aircrafts are proposed as new directions in the future.

Non-linear effects in the radiolysis-optically detected ESR of radical-ion pairs in liquid and glassy solutions. Reactions and motion of organic radicals as studied by ESR and OD ESR spectroscopy

International Nuclear Information System (INIS)

Antzutkin, O.

1992-01-01

This thesis is divided into two sections. The first part covers an introduction to the Optically Detected Electron Spin Resonance (OD ESR) spectroscopy and a short description of the OD ESR spectrometer built in Linkoeping University in 1991. In the second section the following topics are discussed: Non-linear effects in OD ESR spectroscopy and Reactions and motion of organic radicals trapped in freon matrices. (19 refs.)

Perturbation methods and closure approximations in nonlinear systems

International Nuclear Information System (INIS)

Dubin, D.H.E.

1984-01-01

In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed

Self versus environment motion in postural control.

Directory of Open Access Journals (Sweden)

Kalpana Dokka

2010-02-01

Full Text Available To stabilize our position in space we use visual information as well as non-visual physical motion cues. However, visual cues can be ambiguous: visually perceived motion may be caused by self-movement, movement of the environment, or both. The nervous system must combine the ambiguous visual cues with noisy physical motion cues to resolve this ambiguity and control our body posture. Here we have developed a Bayesian model that formalizes how the nervous system could solve this problem. In this model, the nervous system combines the sensory cues to estimate the movement of the body. We analytically demonstrate that, as long as visual stimulation is fast in comparison to the uncertainty in our perception of body movement, the optimal strategy is to weight visually perceived movement velocities proportional to a power law. We find that this model accounts for the nonlinear influence of experimentally induced visual motion on human postural behavior both in our data and in previously published results.

Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas

International Nuclear Information System (INIS)

Perelomova, A.

2010-01-01

Two dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place, are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into thermal mode and internal vibrational degrees of freedom of a relaxing gas. The final dynamic equations are instantaneous; they include a quadratic nonlinear acoustic source, reflecting the nonlinear character of interaction of low-frequency acoustic and non-acoustic motions of the fluid. All types of sound, periodic or aperiodic, may serve as an acoustic source of both phenomena. The low-frequency sound is considered in this study. Some conclusions about temporal behavior of non-acoustic modes caused by periodic and aperiodic sound are made. Under certain conditions, acoustic cooling takes place instead of heating. (author)

Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

CERN Document Server

El-Dib, Y O

2003-01-01

In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...

Quantum control of ultra-cold atoms: uncovering a novel connection between two paradigms of quantum nonlinear dynamics

DEFF Research Database (Denmark)

Wang, Jiao; Mouritzen, Anders Sørrig; Gong, Jiangbin

2009-01-01

Controlling the translational motion of cold atoms using optical lattice potentials is of both theoretical and experimental interest. By designing two on-resonance time sequences of kicking optical lattice potentials, a novel connection between two paradigms of nonlinear mapping systems, i.e. the...... sequences of control fields. Extensions of this study are also discussed. The results are intended to open up a new generation of cold-atom experiments of quantum nonlinear dynamics.......Controlling the translational motion of cold atoms using optical lattice potentials is of both theoretical and experimental interest. By designing two on-resonance time sequences of kicking optical lattice potentials, a novel connection between two paradigms of nonlinear mapping systems, i...

Nonlinearity without superluminality

International Nuclear Information System (INIS)

Kent, Adrian

2005-01-01

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schroedinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality

An optimal control strategy for two-dimensional motion camouflage with non-holonimic constraints.

Science.gov (United States)

Rañó, Iñaki

2012-07-01

Motion camouflage is a stealth behaviour observed both in hover-flies and in dragonflies. Existing controllers for mimicking motion camouflage generate this behaviour on an empirical basis or without considering the kinematic motion restrictions present in animal trajectories. This study summarises our formal contributions to solve the generation of motion camouflage as a non-linear optimal control problem. The dynamics of the system capture the kinematic restrictions to motion of the agents, while the performance index ensures camouflage trajectories. An extensive set of simulations support the technique, and a novel analysis of the obtained trajectories contributes to our understanding of possible mechanisms to obtain sensor based motion camouflage, for instance, in mobile robots.

Separation of variables for the nonlinear wave equation in polar coordinates

International Nuclear Information System (INIS)

Shermenev, Alexander

2004-01-01

Some classical types of nonlinear wave motion in polar coordinates are studied within quadratic approximation. When the nonlinear quadratic terms in the wave equation are arbitrary, the usual perturbation techniques used in polar coordinates leads to overdetermined systems of linear algebraic equations for the unknown coefficients. However, we show that these overdetermined systems are compatible with the special case of the nonlinear shallow water equation and express explicitly the coefficients of the first two harmonics as polynomials of the Bessel functions of radius and of the trigonometric functions of angle. It gives a series of solutions to the nonlinear shallow water equation that are periodic in time and found with the same accuracy as the equation is derived

SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÖDINGER

Directory of Open Access Journals (Sweden)

T B Prayitno

2012-02-01

Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master Schrödinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution can’t be normalized.   Keywords : harmonic oscillator, nonlinear Schrödinger.

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

Science.gov (United States)

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

Human responses at work may exhibit nonlinear properties where small changes in the initial task conditions can lead to large changes in system behavior. Therefore, it is important to study such nonlinearity to gain a better understanding of human performance under a variety of physical, perceptual, and cognitive tasks conditions. The main objective of this study was to investigate whether the human trunk kinematics data during a manual lifting task exhibits nonlinear behavior in terms of determinist chaos. Data related to kinematics of the trunk with respect to the pelvis were collected using Industrial Lumbar Motion Monitor (ILMM), and analyzed applying the nonlinear dynamical systems methodology. Nonlinear dynamics quantifiers of Lyapunov exponents and Kaplan-Yorke dimensions were calculated and analyzed under different task conditions. The study showed that human trunk kinematics during manual lifting exhibits chaotic behavior in terms of trunk sagittal angular displacement, velocity and acceleration. The findings support the importance of accounting for nonlinear dynamical properties of biomechanical responses to lifting tasks.

Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities

Directory of Open Access Journals (Sweden)

Akira Abe

2010-01-01

and are the driving and natural frequencies, respectively. The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms. The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions. The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.

Bottom boundary layer forced by finite amplitude long and short surface waves motions

Science.gov (United States)

Elsafty, H.; Lynett, P.

2018-04-01

A multiple-scale perturbation approach is implemented to solve the Navier-Stokes equations while including bottom boundary layer effects under a single wave and under two interacting waves. In this approach, fluid velocities and the pressure field are decomposed into two components: a potential component and a rotational component. In this study, the two components are exist throughout the entire water column and each is scaled with appropriate length and time scales. A one-way coupling between the two components is implemented. The potential component is assumed to be known analytically or numerically a prior, and the rotational component is forced by the potential component. Through order of magnitude analysis, it is found that the leading-order coupling between the two components occurs through the vertical convective acceleration. It is shown that this coupling plays an important role in the bottom boundary layer behavior. Its effect on the results is discussed for different wave-forcing conditions: purely harmonic forcing and impurely harmonic forcing. The approach is then applied to derive the governing equations for the bottom boundary layer developed under two interacting wave motions. Both motions-the shorter and the longer wave-are decomposed into two components, potential and rotational, as it is done in the single wave. Test cases are presented wherein two different wave forcings are simulated: (1) two periodic oscillatory motions and (2) short waves interacting with a solitary wave. The analysis of the two periodic motions indicates that nonlinear effects in the rotational solution may be significant even though nonlinear effects are negligible in the potential forcing. The local differences in the rotational velocity due to the nonlinear vertical convection coupling term are found to be on the order of 30% of the maximum boundary layer velocity for the cases simulated in this paper. This difference is expected to increase with the increase in wave

Response analysis of a nuclear containment structure with nonlinear soil-structure interaction under bi-directional ground motion

Science.gov (United States)

Kumar, Santosh; Raychowdhury, Prishati; Gundlapalli, Prabhakar

2015-06-01

Design of critical facilities such as nuclear power plant requires an accurate and precise evaluation of seismic demands, as any failure of these facilities poses immense threat to the community. Design complexity of these structures reinforces the necessity of a robust 3D modeling and analysis of the structure and the soil-foundation interface. Moreover, it is important to consider the multiple components of ground motion during time history analysis for a realistic simulation. Present study is focused on investigating the seismic response of a nuclear containment structure considering nonlinear Winkler-based approach to model the soil-foundation interface using a distributed array of inelastic springs, dashpots and gap elements. It is observed from this study that the natural period of the structure increases about 10 %, whereas the force demands decreases up to 24 % by considering the soil-structure interaction. Further, it is observed that foundation deformations, such as rotation and sliding are affected by the embedment ratio, indicating an increase of up to 56 % in these responses for a reduction of embedment from 0.5 to 0.05× the width of the footing.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev ...

Indian Academy of Sciences (India)

Aly R Seadawy

2017-09-13

Sep 13, 2017 ... We considered the two-dimensional DASWs in colli- sionless, unmagnetized cold plasma consisting of dust fluid, ions and electrons. The dynamics of DASWs is governed by the normalized fluid equations of nonlin- ear continuity (1), nonlinear motion of system (2) and. (3) and linear Poisson equation (4) as.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

Science.gov (United States)

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

2016-10-21

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

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Science.gov (United States)

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

2016-10-01

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

Nonlinear transport properties of non-ideal systems

International Nuclear Information System (INIS)

Pavlov, G A

2009-01-01

The theory of nonlinear transport is elaborated to determine the Burnett transport properties of non-ideal multi-element plasma and neutral systems. The procedure for the comparison of the phenomenological conservation equations of a continuous dense medium and the microscopic equations for dynamical variable operators is used for the definition of these properties. The Mori algorithm is developed to derive the equations of motion of dynamical value operators of a non-ideal system in the form of the generalized nonlinear Langevin equations. In consequence, the microscopic expressions of transport coefficients corresponding to second-order thermal disturbances (temperature, mass velocity, etc) have been found in the long wavelength and low frequency limits

An efficient formulation for linear and geometric non-linear membrane elements

Directory of Open Access Journals (Sweden)

Mohammad Rezaiee-Pajand

Full Text Available Utilizing the straingradient notation process and the free formulation, an efficient way of constructing membrane elements will be proposed. This strategy can be utilized for linear and geometric non-linear problems. In the suggested formulation, the optimization constraints of insensitivity to distortion, rotational invariance and not having parasitic shear error are employed. In addition, the equilibrium equations will be established based on some constraints among the strain states. The authors' technique can easily separate the rigid body motions, and those belong to deformational motions. In this article, a novel triangular element, named SST10, is formulated. This element will be used in several plane problems having irregular mesh and complicated geometry with linear and geometrically nonlinear behavior. The numerical outcomes clearly demonstrate the efficiency of the new formulation.

Study on the Nonlinear Characteristics of a Rotating Flexible Blade with Dovetail Interface Feature

Directory of Open Access Journals (Sweden)

Chaofeng Li

2018-01-01

Full Text Available A dynamic model is proposed in this paper for analyzing the nonlinear characteristics of a flexible blade. The dynamical equation of motion for a rotational flexible blade in a centrifugal force field is established based on the finite element method. A macro-stick-slip mechanical model of dry friction is established to simulate the constraint condition of the flexible blade. The combined motion of the external excitation and friction produces a piecewise linear vibration which is actually nonlinear. The numerical integration method is employed to calculate the vibration reduction characteristics of the nonlinear constrained rotating blade. The results show that the nonlinear dry friction force produced by the dovetail interface plays an important role in vibration reduction. And the effect of dry friction vibration reduction is significant when the rotating speed is slow or the friction coefficient is small. Besides, the magnitude of external excitation also has a great impact on the state of the friction. Therefore, some relevant experimental researches should be done in the future.

Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material

Directory of Open Access Journals (Sweden)

M. Awais

2018-03-01

Full Text Available The present analysis is related to the dynamics of polymeric liquids (Oldroyd-B model with the presence of nanoparticles. The rheological system is considered under the application of nonlinear thermal radiations. Energy and concentration equations are presented when thermophoresis and Brownian motion effects are present. Bidirectional form of stretching is considered to interpret the three-dimensional flow dynamics of polymeric liquid. Making use of the similarity transformations, problem is reduced into ordinary differential system which is approximated by using HAM. Influence of physical parameters including Deborah number, thermophoresis and Brownian motion on velocity, temperature and mass fraction expressions are plotted and analyzed. Numerical values for local Sherwood and Nusselt numbers are presented and discussed. Keywords: Nanoparticles, Polymeric liquid, Oldroyd-B model, Nonlinear thermal radiation

Effect of strong-focusing field distortions on particle motion in a linear accelerator

International Nuclear Information System (INIS)

Bondarev, B.I.; Durkin, A.P.; Solov'ev, L.Yu.

1979-01-01

The increased sensitivity of quadrupole focusing channel used in the highenergetic part of the linear accelerator makes it necessary to pay serious attention to the effect of various distortions of focusing fields on the transverse motion of the beam. The distortions may cause the inadmissible losses of particles in the accelerator. To achieve this aim the main equation of disturbed motion of particles in the linear accelerator, obtained by analogy with the cyclic accelerator theory is presented. The investigation of the solutions of this equation has permitted to obtain the analytical formulas for the estimation of the beam size increase under the effect of focusing field distortions of various types, such as structural non-linearity, gradient errors, random non-linearity, channel axis deformation. While studying the effect of structural non-linearity considered are the resonance effects and obtained are the relations describing the maximum beam size increase in the channel of the linear accelerator in the presence and in the absence of the resonance

Effect of vertical ground motion on earthquake-induced derailment of railway vehicles over simply-supported bridges

Science.gov (United States)

Jin, Zhibin; Pei, Shiling; Li, Xiaozhen; Liu, Hongyan; Qiang, Shizhong

2016-11-01

The running safety of railway vehicles on bridges can be negatively affected by earthquake events. This phenomenon has traditionally been investigated with only the lateral ground excitation component considered. This paper presented results from a numerical investigation on the contribution of vertical ground motion component to the derailment of vehicles on simply-supported bridges. A full nonlinear wheel-rail contact model was used in the investigation together with the Hertzian contact theory and nonlinear creepage theory, which allows the wheel to jump vertically and separate from the rail. The wheel-rail relative displacement was used as the criterion for derailment events. A total of 18 ground motion records were used in the analysis to account for the uncertainty of ground motions. The results showed that inclusion of vertical ground motion will likely increase the chance of derailment. It is recommended to include vertical ground motion component in earthquake induced derailment analysis to ensure conservative estimations. The derailment event on bridges was found to be more closely related to the deck acceleration rather than the ground acceleration.

The redesign of a warranty distribution network with recovery processes

NARCIS (Netherlands)

Ashayeri, J.; Ma, N.; Sotirov, R.

A warranty distribution network provides aftersales warranty services to customers and resembles a closed-loop supply chain network with specific challenges for reverse flows management like recovery, repair, and reflow of refurbished products. We present here a nonlinear and nonconvex mixed integer

Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations

International Nuclear Information System (INIS)

Brizard, Alain J.

2000-01-01

A new variational principle for the nonlinear gyrokinetic Vlasov--Maxwell equations is presented. This Eulerian variational principle uses constrained variations for the gyrocenter Vlasov distribution in eight-dimensional extended phase space and turns out to be simpler than the Lagrangian variational principle recently presented by H. Sugama [Phys. Plasmas 7, 466 (2000)]. A local energy conservation law is then derived explicitly by the Noether method. In future work, this new variational principle will be used to derive self-consistent, nonlinear, low-frequency Vlasov--Maxwell bounce-gyrokinetic equations, in which the fast gyromotion and bounce-motion time scales have been eliminated

Discretization model for nonlinear dynamic analysis of three dimensional structures

International Nuclear Information System (INIS)

Hayashi, Y.

1982-12-01

A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt

A variational treatment of material configurations with application to interface motion and microstructural evolution

Science.gov (United States)

Teichert, Gregory H.; Rudraraju, Shiva; Garikipati, Krishna

2017-02-01

We present a unified variational treatment of evolving configurations in crystalline solids with microstructure. The crux of our treatment lies in the introduction of a vector configurational field. This field lies in the material, or configurational, manifold, in contrast with the traditional displacement field, which we regard as lying in the spatial manifold. We identify two distinct cases which describe (a) problems in which the configurational field's evolution is localized to a mathematically sharp interface, and (b) those in which the configurational field's evolution can extend throughout the volume. The first case is suitable for describing incoherent phase interfaces in polycrystalline solids, and the latter is useful for describing smooth changes in crystal structure and naturally incorporates coherent (diffuse) phase interfaces. These descriptions also lead to parameterizations of the free energies for the two cases, from which variational treatments can be developed and equilibrium conditions obtained. For sharp interfaces that are out-of-equilibrium, the second law of thermodynamics furnishes restrictions on the kinetic law for the interface velocity. The class of problems in which the material undergoes configurational changes between distinct, stable crystal structures are characterized by free energy density functions that are non-convex with respect to configurational strain. For physically meaningful solutions and mathematical well-posedness, it becomes necessary to incorporate interfacial energy. This we have done by introducing a configurational strain gradient dependence in the free energy density function following ideas laid out by Toupin (1962, Elastic materials with couple-stresses. Arch. Ration. Mech. Anal., 11, 385-414). The variational treatment leads to a system of partial differential equations governing the configuration that is coupled with the traditional equations of nonlinear elasticity. The coupled system of equations governs

Nonlinear analysis of doubly curved shells: An analytical approach

Indian Academy of Sciences (India)

Е10Ж. 0rЕs└1Ж. iY j. И Й0rs. iY j└1 З 0rs. iY jЗ1Кa2jX. Е11Ж. Nonlinearity in the governing equations of motion is due to the product of the dependent variables. The quadratic extrapolation technique is used for the linearization and a typical nonlinear function Gj can be expressed at any step j as,. Gj И Е0rЖJЕ0sЖJ. И. И.

The landscape of nonlinear structural dynamics: an introduction.

Science.gov (United States)

Butlin, T; Woodhouse, J; Champneys, A R

2015-09-28

Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner's guide to what hitherto might seem like a vast and complex research landscape. © 2015 The Authors.

Effects of Second-Order Sum- and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

Science.gov (United States)

Wang, Bin; Tang, Yougang; Li, Yan; Cai, Runbo

2018-04-01

This paper presents a study on the motion response of a tension-leg platform (TLP) under first- and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function (QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.

Two-dimensional nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed

International Nuclear Information System (INIS)

Ghayesh, Mergen H.; Amabili, Marco; Farokhi, Hamed

2013-01-01

In the present study, the coupled nonlinear dynamics of an axially moving viscoelastic beam with time-dependent axial speed is investigated employing a numerical technique. The equations of motion for both the transverse and longitudinal motions are obtained using Newton’s second law of motion and the constitutive relations. A two-parameter rheological model of the Kelvin–Voigt energy dissipation mechanism is employed in the modelling of the viscoelastic beam material, in which the material time derivative is used in the viscoelastic constitutive relation. The Galerkin method is then applied to the coupled nonlinear equations, which are in the form of partial differential equations, resulting in a set of nonlinear ordinary differential equations (ODEs) with time-dependent coefficients due to the axial acceleration. A change of variables is then introduced to this set of ODEs to transform them into a set of first-order ordinary differential equations. A variable step-size modified Rosenbrock method is used to conduct direct time integration upon this new set of first-order nonlinear ODEs. The mean axial speed and the amplitude of the speed variations, which are taken as bifurcation parameters, are varied, resulting in the bifurcation diagrams of Poincaré maps of the system. The dynamical characteristics of the system are examined more precisely via plotting time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms (FFTs)

Effects of structural nonlinearity and foundation sliding on probabilistic response of a nuclear structure

International Nuclear Information System (INIS)

Hashemi, Alidad; Elkhoraibi, Tarek; Ostadan, Farhang

2015-01-01

Highlights: • Probabilistic SSI analysis including structural nonlinearity and sliding are shown. • Analysis is done for a soil and a rock site and probabilistic demands are obtained. • Structural drift ratios and In-structure response spectra are evaluated. • Structural nonlinearity significantly impacts local demands in the structure. • Sliding generally reduces seismic demands and can be accommodated in design. - Abstract: This paper examines the effects of structural nonlinearity and foundation sliding on the results of probabilistic structural analysis of a typical nuclear structure where structural nonlinearity, foundation sliding and soil-structure interaction (SSI) are explicitly included. The evaluation is carried out for a soil and a rock site at 10"4, 10"5, and 10"6 year return periods (1E − 4, 1E − 5, and 1E − 6 hazard levels, respectively). The input motions at each considered hazard level are deaggregated into low frequency (LF) and high frequency (HF) motions and a sample size of 30 is used for uncertainty propagation. The statistical distribution of structural responses including story drifts, and in-structure response spectra (ISRS) as well as foundation sliding displacements are examined. The probabilistic implementation of explicit structural nonlinearity and foundation sliding in combination with the SSI effects are demonstrated using nonlinear response history analysis (RHA) of the structure with the foundation motions obtained from elastic SSI analyses, which are applied as input to fixed-base inelastic analyses. This approach quantifies the expected structural nonlinearity and sliding for the particular structural configuration and provides a robust analytical basis for the estimation of the probabilistic distribution of selected demands parameters both at the design level and beyond design level seismic input. For the subject structure, the inclusion of foundation sliding in the analysis is found to have reduced both

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

Science.gov (United States)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

Science.gov (United States)

Sakaguchi, Hidetsugu; Ishibashi, Kazuya

2018-06-01

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

Science.gov (United States)

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

The optimal solution of a non-convex state-dependent LQR problem and its applications.

Directory of Open Access Journals (Sweden)

Xudan Xu

Full Text Available This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR problem, in which the control penalty weighting matrix [Formula: see text] in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting [Formula: see text]. It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting [Formula: see text], in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.

Nonlinear acoustic/seismic waves in earthquake processes

International Nuclear Information System (INIS)

Johnson, Paul A.

2012-01-01

Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering—one of the most fascinating topics in seismology today—which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering of the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge—the granular material located between the fault blocks—is key to the triggering phenomenon.

Existence of solutions for second-order evolution inclusions

Directory of Open Access Journals (Sweden)

Nikolaos S. Papageorgiou

1994-01-01

Full Text Available In this paper we examine second-order nonlinear evolution inclusions and prove two existence theorems; one with a convex-valued orientor field and the other with a nonconvex-valued field. An example of a hyperbolic partial differential inclusion is also presented.

Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation

International Nuclear Information System (INIS)

Ji, J.C.; Hansen, Colin H.

2005-01-01

The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions

Algebraic motion of vertically displacing plasmas

Science.gov (United States)

Pfefferlé, D.; Bhattacharjee, A.

2018-02-01

The vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear "sinking" behaviour shown to be algebraic and decelerating. The acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quench dynamics precipitating loss of plasma current.

On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

Energy Technology Data Exchange (ETDEWEB)

Hayat, Tasawar [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Aziz, Arsalan [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Ahmad, Bashir [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)

2016-06-15

This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter. - Highlights: • Constitutive relation for second grade fluid is employed. • Flow is caused by a nonlinear stretching surface. • Magnetic field applied is in transverse direction. • Nanofluid model consists of Brownian motion and thermophoresis. • Magnetic Reynolds number is assumed small.

On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

International Nuclear Information System (INIS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir

2016-01-01

This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter. - Highlights: • Constitutive relation for second grade fluid is employed. • Flow is caused by a nonlinear stretching surface. • Magnetic field applied is in transverse direction. • Nanofluid model consists of Brownian motion and thermophoresis. • Magnetic Reynolds number is assumed small.

On the Nonlinear Dynamics of a Doubly Clamped Microbeam near Primary Resonance

KAUST Repository

Jaber, Nizar; Masri, Karim M.; Younis, Mohammad I.

2017-01-01

This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency-response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of DC bias revealing hardening, mixed, and softening behavior of the microbeam. A multi-mode Galerkin model combined with a shooting technique are implemented to generate the frequency response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show good agreement with the experimental data.

On the Nonlinear Dynamics of a Doubly Clamped Microbeam near Primary Resonance

KAUST Repository

Jaber, Nizar

2017-04-07

This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency-response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of DC bias revealing hardening, mixed, and softening behavior of the microbeam. A multi-mode Galerkin model combined with a shooting technique are implemented to generate the frequency response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show good agreement with the experimental data.

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.

Nonlinear damping for vibration isolation of microsystems using shear thickening fluid

Science.gov (United States)

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

2013-06-01

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

Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

Directory of Open Access Journals (Sweden)

Alex Elías-Zúñiga

2013-01-01

oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.

Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application.

Science.gov (United States)

Sakai, Kenshi; Upadhyaya, Shrinivasa K; Andrade-Sanchez, Pedro; Sviridova, Nina V

2017-03-01

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Nonlinear realizations, the orbit method and Kohn's theorem

OpenAIRE

Andrzejewski, K.; Gonera, J.; Kosinski, P.

2012-01-01

The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart lift.

Nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas

International Nuclear Information System (INIS)

Shukla, P.K.

1993-01-01

The nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas is considered. Stimulated scattering mechanisms involving electromagnetic and acoustic waves in an unmagnetized plasma are investigated. The growth rate and threshold for three-wave decay interactions as well as modulational and filamentation instabilities are presented. Furthermore, the electromagnetic wave modulation theory is generalized for weakly ionized collisional magnetoplasmas. Here, the radiation envelope is generally governed by a nonlinear Schroedinger equation. Accounting for the dependence of the attachment frequency on the radiation intensity, ponderomotive force, as well as the differential Joule heating nonlinearity, the authors derive the equations for the nonthermal electron density and temperature perturbations. The various nonlinear terms in the electron motion are compared. The problems of self-focusing and wave localization are discussed. The relevance of the investigation to ionospheric modification by powerful electromagnetic waves is pointed out

Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

Directory of Open Access Journals (Sweden)

Yaobing Zhao

2014-01-01

Full Text Available This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively. Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented. Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration. Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods. The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios. Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.

Dissipation and nuclear collective motion

International Nuclear Information System (INIS)

Hofmann, Helmut; Jensen, A.S.; Ngo, Christian; Siemens, P.J.; California Univ., Berkeley

1979-01-01

This contribution is intended to give a brief summary of a forthcoming paper which shall review extensively the linear response theory for dissipation and statistical fluctuations as well as its application to heavy-ion collisions. It shall contain new results on the following subjects: numerical computations of response functions and transport coefficients; dissipation in a self-consistent treatment of harmonic vibrations; introduction of collective variables within a quantum theory. The method used consists of an extended version of the Bohm and Pines treatment of the electron gas. It allows to deduce a quantum Hamiltonian for the collective and intrinsic motion including coupling terms; discussion and solution of a quantal Master equation for non-linear collective motion. Additionally, a somewhat elaborate discussion of the problems of irreversibility is given, especially in connection to a treatment within the moving basis

Geometrical nonlinear free vibration of multi-layered graphene sheets

International Nuclear Information System (INIS)

Wang Jinbao; He Xiaoqiao; Kitipornchai, S; Zhang Hongwu

2011-01-01

A nonlinear continuum model is developed for the nonlinear vibration analysis of multi-layered graphene sheets (MLGSs), in which the nonlinear van der Waals (vdW) interaction between any two layers is formulated explicitly. The nonlinear equations of motion are studied by the harmonic-balance methods. Based on the present model, the nonlinear stiffened amplitude-frequency relations of double-layered graphene sheets (DLGSs) are investigated in the spectral neighbourhood of lower frequencies. The influence of the vdW interaction on the vibration properties of DLGSs is well illustrated by plotting the resulting modes' shapes, in which in-phase and anti-phase vibrations of DLGSs are studied. In particular, the large-amplitude vibration which associates with the anti-phase resonant frequencies, separating DLGS into single-layered GSs, is a promising application that needs to be explored further. In contrast, the vibration modes that are associated with the resonant frequencies are nonidentical and give various vibration patterns, which indicates that MLGSs are highly suited to being used as high-frequency resonators.

Motions of deformable inclusions in a horizontally oscillating vessel with a compressible fluid

DEFF Research Database (Denmark)

Demidov, I.V.; Sorokin, Vladislav

2016-01-01

The paper is concerned with the analysis of rigid particle and compressible gas bubble motion in a horizontally oscillating vessel with a compressible fluid. A nonlinear differential equation describing motion of inclusions with respect to the vessel is derived and solved by the method of direct...... of the bubbles which are affected by the negligible vibrational force is found. Also an approximate expression has been obtained for the average velocity of bubble׳s motion in the fluid; relationship between this velocity and bubble radius and vibration parameters has been revealed. A simple physical explanation...

Nonlinear streak computation using boundary region equations

Energy Technology Data Exchange (ETDEWEB)

Martin, J A; Martel, C, E-mail: juanangel.martin@upm.es, E-mail: carlos.martel@upm.es [Depto. de Fundamentos Matematicos, E.T.S.I Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid (Spain)

2012-08-01

The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier-Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)

Two-Step System Identification and Primitive-Based Motion Planning for Control of Small Unmanned Aerial Vehicles

Science.gov (United States)

Grymin, David J.

This dissertation addresses motion planning, modeling, and feedback control for autonomous vehicle systems. A hierarchical approach for motion planning and control of nonlinear systems operating in obstacle environments is presented. To reduce computation time during the motion planning process, dynamically feasible trajectories are generated in real-time through concatenation of pre-specified motion primitives. The motion planning task is posed as a search over a directed graph, and the applicability of informed graph search techniques is investigated. Specifically, a locally greedy algorithm with effective backtracking ability is developed and compared to weighted A* search. The greedy algorithm shows an advantage with respect to solution cost and computation time when larger motion primitive libraries that do not operate on a regular state lattice are utilized. Linearization of the nonlinear system equations about the motion primitive library results in a hybrid linear time-varying model, and an optimal control algorithm using the l 2-induced norm as the performance measure is applied to ensure that the system tracks the desired trajectory. The ability of the resulting controller to closely track the trajectory obtained from the motion planner, despite various disturbances and uncertainties, is demonstrated through simulation. Additionally, an approach for obtaining dynamically feasible reference trajectories and feedback controllers for a small unmanned aerial vehicle (UAV) based on an aerodynamic model derived from flight tests is presented. The modeling approach utilizes the two step method (TSM) with stepwise multiple regression to determine relevant explanatory terms for the aerodynamic models. Dynamically feasible trajectories are then obtained through the solution of an optimal control problem using pseudospectral optimal control software. Discretetime feedback controllers are then obtained to regulate the vehicle along the desired reference trajectory

Geometric phases for nonlinear coherent and squeezed states

International Nuclear Information System (INIS)

Yang Dabao; Chen Ying; Chen Jingling; Zhang Fulin

2011-01-01

The geometric phases for standard coherent states which are widely used in quantum optics have attracted considerable attention. Nevertheless, few physicists consider the counterparts of nonlinear coherent states, which are useful in the description of the motion of a trapped ion. In this paper, the non-unitary and non-cyclic geometric phases for two nonlinear coherent and one squeezed states are formulated, respectively. Moreover, some of their common properties are discussed, such as gauge invariance, non-locality and nonlinear effects. The nonlinear functions have dramatic impacts on the evolution of the corresponding geometric phases. They speed the evolution up or down. So this property may have an application in controlling or measuring geometric phase. For the squeezed case, when the squeezed parameter r → ∞, the limiting value of the geometric phase is also determined by a nonlinear function at a given time and angular velocity. In addition, the geometric phases for standard coherent and squeezed states are obtained under a particular condition. When the time evolution undergoes a period, their corresponding cyclic geometric phases are achieved as well. And the distinction between the geometric phases of the two coherent states may be regarded as a geometric criterion.

Breaking of ensembles of linear and nonlinear oscillators

International Nuclear Information System (INIS)

Buts, V.A.

2016-01-01

Some results concerning the study of the dynamics of ensembles of linear and nonlinear oscillators are stated. It is shown that, in general, a stable ensemble of linear oscillator has a limited number of oscillators. This number has been defined for some simple models. It is shown that the features of the dynamics of linear oscillators can be used for conversion of the low-frequency energy oscillations into high frequency oscillations. The dynamics of coupled nonlinear oscillators in most cases is chaotic. For such a case, it is shown that the statistical characteristics (moments) of chaotic motion can significantly reduce potential barriers that keep the particles in the capture region

Dynamic nonlinear elasticity in geo materials

International Nuclear Information System (INIS)

Ostrovsky, L.A.; Johnson, P.A.

2001-01-01

The nonlinear elastic behaviour of earth materials is an extremely rich topic, one that has broad implications to earth and materials sciences, including strong ground motion, rock physics, nondestructive evaluation and materials science. The mechanical properties of rock appear to place it in a broader class of materials, it can be named the Structural nonlinear elasticity class (also Mesoscopic/nano scale elasticity, or MS/NSE class). These terms are in contrast to materials that display classical, Atomic Elasticity, such as most fluids and monocrystalline solids. The difference between these two categories of materials is both in intensity and origin of their nonlinear response. The nonlinearity of atomic elastic materials is due to the atomic/molecular lattice anharmonicity. The latter is relatively small because the intermolecular forces are extremely strong. In contrast, the materials considered below contain small soft features that it is called the bond system (cracks, grain contacts, dislocations, etc.) within a hard matrix and relaxation (slow dynamical effects) are characteristic, non of which appear in atomic elastic materials. The research begins with a brief historical background from nonlinear acoustics to the recent developments in rock nonlinearity. This is followed by an overview of some representative laboratory measurements which serve as primary indicators of nonlinear behaviour, followed by theoretical development, and finally, mention a variety of observations of nonlinearity under field conditions and applications to nondestructive testing of materials. The goal is not to survey all papers published in the are but to demonstrate some experimental and theoretical results and ideas that will the reader to become oriented in this broad and rapidly growing area bridging macro-, meso- and microscale (nano scale) phenomena in physics, materials science, and geophysics

Nonlinear convective flow of Powell-Erying magneto nanofluid with Newtonian heating

Directory of Open Access Journals (Sweden)

Sajid Qayyum

Full Text Available Objective of present article is to describe magnetohydrodynamic (MHD non-linear convective flow of Powell-Erying nanofluid over a stretching surface. Characteristics of Newtonian heat and mass conditions in this attempt is given attention. Heat and mass transfer analysis is examined in the frame of thermal radiation and chemical reaction. Brownian motion and thermophoresis concept is introduced due to presence of nanoparticles. Nonlinear equations of momentum, energy and concentration are transformed into dimensionless expression by invoking suitable variables. The series solutions are obtained through homotopy analysis method (HAM. Impact of embedded variables on the velocity, temperature and nanoparticles concentration is graphically presented. Numerical values of skin friction coefficient, local Nusselt and Sherwood numbers are computed and analyzed. It is concluded that velocity field enhances for fluid variable while reverse situation is noticed regarding Hartman number. Temperature and heat transfer rate behave quite reverse for Prandtl number. It is also noted that the concentration and local Sherwood number have opposite behavior in the frame of Brownian motion. Keywords: Powell-Erying nanofluid, Magnetohydrodynamic (MHD, Nonlinear convection, Thermal radiation, Chemical reaction, Newtonian heat and mass conditions

Linear and non-linear calculations of the hose instability in the ion-focused regime

International Nuclear Information System (INIS)

Buchanan, H.L.

1982-01-01

A simple model is adopted to study the hose instability of an intense relativistic electron beam in a partially neutralized, low density ion channel (ion focused regime). Equations of motion for the beam and the channel are derived and linearized to obtain an approximate dispersion relation. The non-linear equations of motion are then solved numerically and the results compared to linearized data

A Hybrid Optimization Method for Reactive Power and Voltage Control Considering Power Loss Minimization

DEFF Research Database (Denmark)

Liu, Chengxi; Qin, Nan; Bak, Claus Leth

2015-01-01

This paper proposes a hybrid optimization method to optimally control the voltage and reactive power with minimum power loss in transmission grid. This approach is used for the Danish automatic voltage control (AVC) system which is typically a non-linear non-convex problem mixed with both...

Motion control of servo cylinder using neural network

International Nuclear Information System (INIS)

Hwang, Un Kyoo; Cho, Seung Ho

2004-01-01

In this paper, a neural network controller that can be implemented in parallel with a PD controller is suggested for motion control of a hydraulic servo cylinder. By applying a self-excited oscillation method, the system design parameters of open loop transfer function of servo cylinder system are identified. Based on system design parameters, the PD gains are determined for the desired closed loop characteristics. The neural network is incorporated with PD control in order to compensate the inherent nonlinearities of hydraulic servo system. As an application example, a motion control using PD-NN has been performed and proved its superior performance by comparing with that of a PD control

Complex motion of a vehicle through a series of signals controlled by power-law phase

Science.gov (United States)

Nagatani, Takashi

2017-07-01

We study the dynamic motion of a vehicle moving through the series of traffic signals controlled by the position-dependent phase of power law. All signals are controlled by both cycle time and position-dependent phase. The dynamic model of the vehicular motion is described in terms of the nonlinear map. The vehicular motion varies in a complex manner by varying cycle time for various values of the power of the position-dependent phase. The vehicle displays the periodic motion with a long cycle for the integer power of the phase, while the vehicular motion exhibits the very complex behavior for the non-integer power of the phase.

Current-induced domain wall motion in magnetic nanowires with spatial variation

International Nuclear Information System (INIS)

Ieda, Jun'ichi; Sugishita, Hiroki; Maekawa, Sadamichi

2010-01-01

We model current-induced domain wall motion in magnetic nanowires with the variable width. Employing the collective coordinate method we trace the wall dynamics. The effect of the width modulation is implemented by spatial dependence of an effective magnetic field. The wall destination in the potential energy landscape due to the magnetic anisotropy and the spatial nonuniformity is obtained as a function of the current density. For a nanowire of a periodically modulated width, we identify three (pinned, nonlinear, and linear) current density regimes for current-induced wall motion. The threshold current densities depend on the pulse duration as well as the magnitude of wire modulation. In the nonlinear regime, application of ns order current pulses results in wall displacement which opposes or exceeds the prediction of the spin transfer mechanism. The finding explains stochastic nature of the domain wall displacement observed in recent experiments.

Allocation of resources in the presence of indivisibilities: Scarf's problem revisited

International Nuclear Information System (INIS)

Bjoerndal, Mette; Joernsten, Kurt

2004-06-01

In his article ''The Allocation of Resources in the Presence of Indivisibilities,'' Scarf points out that the major problem presented to economic theory by the presence of indivisibilities is the impossibility of detecting optimality at the level of the firm, or the economy as a whole, using the creation of profitability based on competitive linear prices. In the absence of such competitive prices, Scarf instead introduces a quantity test. Further development of the quantity test idea has lead to algorithms that are used to solve parametric integer programming problems. However, the quantity test is not a fully acceptable replacement of prices to analyse markets with indivisibilities. Recently, O'Neill et al. have suggested a new scheme that generates discriminatory equilibrium prices in markets with non-convexities- In this paper we elaborate this idea even further and use it to generate non-linear price functions that can be interpreted as a non-linear pricing scheme for markets with non-convexities. (Author)

On the integration of equations of motion for particle-in-cell codes

International Nuclear Information System (INIS)

Fuchs, V.; Gunn, J.P.

2006-01-01

An area-preserving implementation of the 2nd order Runge-Kutta integration method for equations of motion is presented. For forces independent of velocity the scheme possesses the same numerical simplicity and stability as the leapfrog method, and is not implicit for forces which do depend on velocity. It can be therefore easily applied where the leapfrog method in general cannot. We discuss the stability of the new scheme and test its performance in calculations of particle motion in three cases of interest. First, in the ubiquitous and numerically demanding example of nonlinear interaction of particles with a propagating plane wave, second, in the case of particle motion in a static magnetic field and, third, in a nonlinear dissipative case leading to a limit cycle. We compare computed orbits with exact orbits and with results from the leapfrog and other low-order integration schemes. Of special interest is the role of intrinsic stochasticity introduced by time differencing, which can destroy orbits of an otherwise exactly integrable system and therefore constitutes a restriction on the applicability of an integration scheme in such a context [A. Friedman, S.P. Auerbach, J. Comput. Phys. 93 (1991) 171]. In particular, we show that for a plane wave the new scheme proposed herein can be reduced to a symmetric standard map. This leads to the nonlinear stability condition Δt ω B ≤ 1, where Δt is the time step and ω B the particle bounce frequency

Quantum-classical correspondence in multimensional nonlinear systems: Anderson localization and "superdiffusive" solitons

KAUST Repository

Brambila, Danilo; Fratalocchi, Andrea

2012-01-01

We have theoretically studied Anderson localization in a 2D+1 nonlinear kicked rotor model. The system shows a very rich dynamical behavior, where the Anderson localization is suppressed and soliton wave-particles undergo a superdiffusive motion.

Nonlinear Klein-Gordon soliton mechanics

International Nuclear Information System (INIS)

Reinisch, G.

1992-01-01

Nonlinear Klein-Gordon solitary waves - or solitons in a loose sense - in n+1 dimensions, driven by very general external fields which must only satisfy continuity - together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom - which may be conservative or not - of the second Newton's law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force is derivable from a potential energy, we recover the generalized Ehrenfest theorem which was itself the extension to such systems of the well-known Ehrenfest theorem in quantum mechanics. This review paper first displays a few (of one-dimensional sine-Gordon type) typical examples of the basic difficulties related to the trial construction of solitary-waves is proved and the derivation of the previous sine-Gordon examples from this theorem is displayed. Two-dimensional nonlinear solitary-wave patterns are considered, as well as a special emphasis is put on the applications to space-time complexity of 1-dim. sine-Gordon systems

Linearization of Euclidean Norm Dependent Inequalities Applied to Multibeam Satellites Design

OpenAIRE

Camino , Jean-Thomas; Artigues , Christian; Houssin , Laurent; Mourgues , Stéphane

2016-01-01

Euclidean norm computations over continuous variables appear naturally in the constraints or in the objective of many problems in the optimization literature, possibly defining non-convex feasible regions or cost functions. When some other variables have discrete domains, it positions the problem in the challenging Mixed Integer Nonlinear Programming (MINLP) class. For any MINLP where the nonlinearity is only present in the form of inequality constraints involving the Euclidean norm, we propo...

Polarization dynamics in nonlinear anisotropic fibers

International Nuclear Information System (INIS)

Komarov, Andrey; Komarov, Konstantin; Meshcheriakov, Dmitry; Amrani, Foued; Sanchez, Francois

2010-01-01

We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincare sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincare sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi's functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered.

Chaotic behavior of earthquakes induced by a nonlinear magma up flow

International Nuclear Information System (INIS)

Pelap, F.B.; Kagho, L.Y.; Fogang, C.F.

2016-01-01

This paper considers the dynamics of a modified 1D nonlinear spring-block model for earthquake subjected to the strengths induced by the motion of the tectonic plates and the up flow of magma during volcanism. Based on the multiple time scales method, we establish that after the slip, the fault remains active and the frictions increase with the power of the earthquake. We also obtain in the non-resonance case that the appearing probability of an event decreases with these frictions. In the resonance case, the dynamics of harmonic oscillations show that the rocks constituting the block will fracture or resist to the effects induced by the magma motion. Our analytical investigations are complemented by numerical simulations from which it appears that, for given values of the magma thrust strength magnitude, the friction coefficient, the quadratic and cubic nonlinear parameters, the system exhibits chaotic behavior.

Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

International Nuclear Information System (INIS)

Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

2011-01-01

This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.

System Reduction in Nonlinear Multibody Dynamics of Wind Turbines

DEFF Research Database (Denmark)

Holm-Jørgensen, Kristian; Nielsen, Søren R.K.; Rubak, Rune

2007-01-01

In this paper the system reduction in nonlinear multibody dynamics of wind turbines is investigated for various updating schemes of the moving frame of reference. In one case, the moving frame of reference is updated to a stiff body, relative to which the elastic deformations are fixed at one end....... In the other case, the stiff body motion is defined as the chord line connecting the end points of the beam, and the elastic deformations are simply supported at the end points. The system reduction is performed by discretizing the spatial motion into a set of rigid body modes and linear elastic eigenmodes...

Travelling Solitons in the Damped Driven Nonlinear Schroedinger Equation

CERN Document Server

Barashenkov, I V

2003-01-01

The well-known effect of the linear damping on the moving nonlinear Schrodinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable.

Travelling solitons in the damped driven nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Barashenkov, I.V.; Zemlyanaya, E.V.

2003-01-01

The well known effect of the linear damping on the moving nonlinear Schroedinger soliton (even when there is energy supply via the spatially homogeneous driving) is to quench its momentum to zero. Surprisingly, the zero momentum does not necessarily mean zero velocity. We show that two or more parametrically driven damped solitons can form a complex travelling with zero momentum at a nonzero constant speed. All travelling complexes we have found so far, turned out to be unstable. Thus, the parametric driving is capable of sustaining the uniform motion of damped solitons, but some additional agent is required to make this motion stable

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

International Nuclear Information System (INIS)

Yang, J H; Yang, J; Kitipornchai, S

2012-01-01

This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)

An experimental study on the long-term stability of particle motion in hadron storage rings

International Nuclear Information System (INIS)

Fischer, W.

1995-12-01

Nonlinear magnetic fields in conjunction with tune modulation may lead to chaotic particle motion and thereby limit the dynamic aperture in hadron storage rings. This is on particular interest for high energy storage rings with superconducting magnets at injection energy where magnetic field errors and the beam size have their maximum values. At the CERN SPS a dynamic aperture experiment was performed with the aim of finding the relevant effects for the stability of single particle motion in hadron storage rings. Experimental results are compared to long-term particle tracking to test to which extent computer programs can predict the dynamic aperture under well known conditions. In addition, detailed investigations of the loss mechanisms were pursued to improve the phenomenological understanding of the intricate details of particle motion in phase space. In a complementary experiment at the HERA proton ring at injection energy the dynamic aperture was measured under normal operating conditions. The computer simulations for these measurements included a very detailed model of the nonlinear fields which were measured for each individual magnet. Simulation results for the LHC are shown that estimate the effect of tune ripple of different strength on the dynamic aperture for different sets of random nonlinear field errors. (orig.)

Real-time tumor motion estimation using respiratory surrogate via memory-based learning

International Nuclear Information System (INIS)

Li Ruijiang; Xing Lei; Lewis, John H; Berbeco, Ross I

2012-01-01

Respiratory tumor motion is a major challenge in radiation therapy for thoracic and abdominal cancers. Effective motion management requires an accurate knowledge of the real-time tumor motion. External respiration monitoring devices (optical, etc) provide a noninvasive, non-ionizing, low-cost and practical approach to obtain the respiratory signal. Due to the highly complex and nonlinear relations between tumor and surrogate motion, its ultimate success hinges on the ability to accurately infer the tumor motion from respiratory surrogates. Given their widespread use in the clinic, such a method is critically needed. We propose to use a powerful memory-based learning method to find the complex relations between tumor motion and respiratory surrogates. The method first stores the training data in memory and then finds relevant data to answer a particular query. Nearby data points are assigned high relevance (or weights) and conversely distant data are assigned low relevance. By fitting relatively simple models to local patches instead of fitting one single global model, it is able to capture highly nonlinear and complex relations between the internal tumor motion and external surrogates accurately. Due to the local nature of weighting functions, the method is inherently robust to outliers in the training data. Moreover, both training and adapting to new data are performed almost instantaneously with memory-based learning, making it suitable for dynamically following variable internal/external relations. We evaluated the method using respiratory motion data from 11 patients. The data set consists of simultaneous measurement of 3D tumor motion and 1D abdominal surface (used as the surrogate signal in this study). There are a total of 171 respiratory traces, with an average peak-to-peak amplitude of ∼15 mm and average duration of ∼115 s per trace. Given only 5 s (roughly one breath) pretreatment training data, the method achieved an average 3D error of 1.5 mm and 95

Real-time tumor motion estimation using respiratory surrogate via memory-based learning

Science.gov (United States)

Li, Ruijiang; Lewis, John H.; Berbeco, Ross I.; Xing, Lei

2012-08-01

Respiratory tumor motion is a major challenge in radiation therapy for thoracic and abdominal cancers. Effective motion management requires an accurate knowledge of the real-time tumor motion. External respiration monitoring devices (optical, etc) provide a noninvasive, non-ionizing, low-cost and practical approach to obtain the respiratory signal. Due to the highly complex and nonlinear relations between tumor and surrogate motion, its ultimate success hinges on the ability to accurately infer the tumor motion from respiratory surrogates. Given their widespread use in the clinic, such a method is critically needed. We propose to use a powerful memory-based learning method to find the complex relations between tumor motion and respiratory surrogates. The method first stores the training data in memory and then finds relevant data to answer a particular query. Nearby data points are assigned high relevance (or weights) and conversely distant data are assigned low relevance. By fitting relatively simple models to local patches instead of fitting one single global model, it is able to capture highly nonlinear and complex relations between the internal tumor motion and external surrogates accurately. Due to the local nature of weighting functions, the method is inherently robust to outliers in the training data. Moreover, both training and adapting to new data are performed almost instantaneously with memory-based learning, making it suitable for dynamically following variable internal/external relations. We evaluated the method using respiratory motion data from 11 patients. The data set consists of simultaneous measurement of 3D tumor motion and 1D abdominal surface (used as the surrogate signal in this study). There are a total of 171 respiratory traces, with an average peak-to-peak amplitude of ∼15 mm and average duration of ∼115 s per trace. Given only 5 s (roughly one breath) pretreatment training data, the method achieved an average 3D error of 1.5 mm and 95

Learning Inverse Rig Mappings by Nonlinear Regression.

Science.gov (United States)

Holden, Daniel; Saito, Jun; Komura, Taku

2017-03-01

We present a framework to design inverse rig-functions-functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.

The importance of stimulus noise analysis for self-motion studies.

Directory of Open Access Journals (Sweden)

Alessandro Nesti

Full Text Available Motion simulators are widely employed in basic and applied research to study the neural mechanisms of perception and action during inertial stimulation. In these studies, uncontrolled simulator-introduced noise inevitably leads to a disparity between the reproduced motion and the trajectories meticulously designed by the experimenter, possibly resulting in undesired motion cues to the investigated system. Understanding actual simulator responses to different motion commands is therefore a crucial yet often underestimated step towards the interpretation of experimental results. In this work, we developed analysis methods based on signal processing techniques to quantify the noise in the actual motion, and its deterministic and stochastic components. Our methods allow comparisons between commanded and actual motion as well as between different actual motion profiles. A specific practical example from one of our studies is used to illustrate the methodologies and their relevance, but this does not detract from its general applicability. Analyses of the simulator's inertial recordings show direction-dependent noise and nonlinearity related to the command amplitude. The Signal-to-Noise Ratio is one order of magnitude higher for the larger motion amplitudes we tested, compared to the smaller motion amplitudes. Simulator-introduced noise is found to be primarily of deterministic nature, particularly for the stronger motion intensities. The effect of simulator noise on quantification of animal/human motion sensitivity is discussed. We conclude that accurate recording and characterization of executed simulator motion are a crucial prerequisite for the investigation of uncertainty in self-motion perception.

Sampling-Based Motion Planning Algorithms for Replanning and Spatial Load Balancing

Energy Technology Data Exchange (ETDEWEB)

Boardman, Beth Leigh [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-10-12

The common theme of this dissertation is sampling-based motion planning with the two key contributions being in the area of replanning and spatial load balancing for robotic systems. Here, we begin by recalling two sampling-based motion planners: the asymptotically optimal rapidly-exploring random tree (RRT*), and the asymptotically optimal probabilistic roadmap (PRM*). We also provide a brief background on collision cones and the Distributed Reactive Collision Avoidance (DRCA) algorithm. The next four chapters detail novel contributions for motion replanning in environments with unexpected static obstacles, for multi-agent collision avoidance, and spatial load balancing. First, we show improved performance of the RRT* when using the proposed Grandparent-Connection (GP) or Focused-Refinement (FR) algorithms. Next, the Goal Tree algorithm for replanning with unexpected static obstacles is detailed and proven to be asymptotically optimal. A multi-agent collision avoidance problem in obstacle environments is approached via the RRT*, leading to the novel Sampling-Based Collision Avoidance (SBCA) algorithm. The SBCA algorithm is proven to guarantee collision free trajectories for all of the agents, even when subject to uncertainties in the knowledge of the other agents’ positions and velocities. Given that a solution exists, we prove that livelocks and deadlock will lead to the cost to the goal being decreased. We introduce a new deconfliction maneuver that decreases the cost-to-come at each step. This new maneuver removes the possibility of livelocks and allows a result to be formed that proves convergence to the goal configurations. Finally, we present a limited range Graph-based Spatial Load Balancing (GSLB) algorithm which fairly divides a non-convex space among multiple agents that are subject to differential constraints and have a limited travel distance. The GSLB is proven to converge to a solution when maximizing the area covered by the agents. The analysis

Influences of the Control on the Nonlinear Vibrations of a Variable Compression Ratio Mechanism

Directory of Open Access Journals (Sweden)

Mănescu Bogdan

2018-01-01

Full Text Available For the mechanism described in references the study of the nonlinear vibrations is performed considering a multibody approach for the elements of the mechanism and different laws of motion for the control element. A great attention is paid to the equilibrium of the motion. The influence of different parameters of control is highlighted in the paper. The results are numerically validated.

Quasistatic nonlinear viscoelasticity and gradient flows

OpenAIRE

Ball, John M.; Şengül, Yasemin

2014-01-01

We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is λ-convex, which allows for solid phase transformations. We formulate this problem as a gradient flow, leading to existence and uniqueness of solutions. By approximating general initial data by those in which the deformation gradient takes only finitely many values, we show that under suitable hypotheses on the stored-energy function the d...

Extension of the Method of Direct Separation of Motions for Problems of Oscillating Action on Dynamical Systems

DEFF Research Database (Denmark)

Blekhman, Iliya I.; Sorokin, Vladislav

2016-01-01

A general approach to study oscillating action on nonlinear dynamical systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics equations). The approach...... is named as the Oscillatory Strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that represent the averaged effect of the oscillating action. The method of direct separation of motions (MDSM) appears to be an efficient...

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

International Nuclear Information System (INIS)

Donoso, Guillermo; Ladera, Celso L

2012-01-01

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

Nonlinear stage of a Z-pinch instability

International Nuclear Information System (INIS)

Garanin, S.F.; Chernyshev, Y.D.

1987-01-01

The nonlinear evolution of the sausage instability is analyzed for a Z-pinch with a fully developed skin effect in the current. Two-dimensional numerical calculations carried out on the sausage instability show that its occurrence leads to a stage describable by a self-similar solution when the length of the neck is fixed and the plasma compression is isentropic. At a perturbation wavelength small in comparison with the pinch radius, this stage is preceded by a stage which reduces to a nonlinear Rayleigh--Taylor instability. The dynamics of the motion of magnetic field ''bubbles'' and of plasma ''jets'' is analyzed in this case. The plasma jets emerging from the pinch do not block the pinch from the current source

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.

Modern aspects of nonlinear convection and magnetic field in flow of thixotropic nanofluid over a nonlinear stretching sheet with variable thickness

Science.gov (United States)

Hayat, Tasawar; Qayyum, Sajid; Alsaedi, Ahmed; Ahmad, Bashir

2018-05-01

Main objective of present analysis is to study the magnetohydrodynamic (MHD) nonlinear convective flow of thixotropic nanofluid. Flow is due to nonlinear stretching surface with variable thickness. Nonlinear thermal radiation and heat generation/absorption are utilized in the energy expression. Convective conditions and zero mass flux at sheet are considered. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Appropriate transformations are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been scrutinized through homotopic algorithm. Behavior of various sundry variables on velocity, temperature, nanoparticle concentration, skin friction coefficient and local Nusselt number are displayed through graphs. It is concluded that qualitative behaviors of temperature and thermal layer thickness are similar for radiation and temperature ratio variables. Moreover an enhancement in heat generation/absorption show rise to thermal field.

Conservation laws with non-convex flux and applications to two-phase flow in porous media

Energy Technology Data Exchange (ETDEWEB)

Tegnander, Cathrine

1998-12-31

This thesis deals with conservation laws, which form a family of partial differential equations (PDEs) describing conservation of mass, momentum and energy. The first part studies some theoretical aspects of conservation laws: (1) Scalar hyperbolic conservation laws with a non-convex flux function, where time dependent decay estimates are mainly obtained by a front tracking technique, (2) Convergence of solutions for a finite difference scheme given by a class of one dimensional parabolic systems. The second part of the thesis applies the theory to multiphase flow in porous media. A number of mathematical models for multiphase flow in groundwater are studied. Techniques to improve the study of simulations of oil, gas and water phases in reservoirs such as in the North Sea are discussed. Upscaling of a refinement of the permeability field is evaluated using a flow simulation. This is done by a study of the preserving of the rank of a number of realizations with respect to the cumulative production parameter. Finally, the importance of selection of numerical methods in the simulations are exemplified by considering various splitting techniques. The numerical methods of front tracking and finite difference schemes and finite element methods are used. 98 refs., 24 figs., 18 tabs.

Nonlinear dynamic response of cantilever beam tip during atomic force microscopy (AFM) nanolithography of copper surface

International Nuclear Information System (INIS)

Yeh, Y-L; Jang, M-J; Wang, C-C; Lin, Y-P; Chen, K-S

2008-01-01

This paper investigates the nonlinear dynamic response of an atomic force microscope (AFM) cantilever beam tip during the nanolithography of a copper (Cu) surface using a high-depth feed. The dynamic motion of the tip is modeled using a combined approach based on Newton's law and empirical observations. The cutting force is determined from experimental observations of the piling height on the Cu surface and the rotation angle of the cantilever beam tip. It is found that the piling height increases linearly with the cantilever beam carrier velocity. Furthermore, the cantilever beam tip is found to execute a saw tooth motion. Both this motion and the shear cutting force are nonlinear. The elastic modulus in the y direction is variable. Finally, the velocity of the cantilever beam tip as it traverses the specimen surface has a discrete characteristic rather than a smooth, continuous profile

Influence of Variable Acceleration on Parametric Roll Motion of a Container Ship

Directory of Open Access Journals (Sweden)

Emre PEŞMAN

2016-09-01

Full Text Available Ship operators increase or decrease thrust force of ships to avoid parametric roll motion. These operations cause varying acceleration values. In this study, influence of variable acceleration and deceleration of ships on roll motion is investigated in longitudinal waves. The method which is referred as simple model is utilized for analysis. Simple Model is one degree of freedom nonlinear parametric roll motion equation which contains changing velocity and restoring moment in waves with respect to time. Ship velocities in waves are predicted by XFlow software for various thrust forces. Results indicate that variable acceleration has significant effect on parametric roll phenomenon.

Nonlinear Time Domain Seismic Soil-Structure Interaction (SSI) Deep Soil Site Methodology Development

International Nuclear Information System (INIS)

Spears, Robert Edward; Coleman, Justin Leigh

2015-01-01

Currently the Department of Energy (DOE) and the nuclear industry perform seismic soil-structure interaction (SSI) analysis using equivalent linear numerical analysis tools. For lower levels of ground motion, these tools should produce reasonable in-structure response values for evaluation of existing and new facilities. For larger levels of ground motion these tools likely overestimate the in-structure response (and therefore structural demand) since they do not consider geometric nonlinearities (such as gaping and sliding between the soil and structure) and are limited in the ability to model nonlinear soil behavior. The current equivalent linear SSI (SASSI) analysis approach either joins the soil and structure together in both tension and compression or releases the soil from the structure for both tension and compression. It also makes linear approximations for material nonlinearities and generalizes energy absorption with viscous damping. This produces the potential for inaccurately establishing where the structural concerns exist and/or inaccurately establishing the amplitude of the in-structure responses. Seismic hazard curves at nuclear facilities have continued to increase over the years as more information has been developed on seismic sources (i.e. faults), additional information gathered on seismic events, and additional research performed to determine local site effects. Seismic hazard curves are used to develop design basis earthquakes (DBE) that are used to evaluate nuclear facility response. As the seismic hazard curves increase, the input ground motions (DBE's) used to numerically evaluation nuclear facility response increase causing larger in-structure response. As ground motions increase so does the importance of including nonlinear effects in numerical SSI models. To include material nonlinearity in the soil and geometric nonlinearity using contact (gaping and sliding) it is necessary to develop a nonlinear time domain methodology. This

Effect of Ground Motion Directionality on Fragility Characteristics of a Highway Bridge

Directory of Open Access Journals (Sweden)

Swagata Banerjee Basu

2011-01-01

Full Text Available It is difficult to incorporate multidimensional effect of the ground motion in the design and response analysis of structures. The motion trajectory in the corresponding multi-dimensional space results in time variant principal axes of the motion and defies any meaningful definition of directionality of the motion. However, it is desirable to consider the directionality of the ground motion in assessing the seismic damageability of bridges which are one of the most vulnerable components of highway transportation systems. This paper presents a practice-oriented procedure in which the structure can be designed to ensure the safety under single or a pair of independent orthogonal ground motions traveling horizontally with an arbitrary direction to structural axis. This procedure uses nonlinear time history analysis and accounts for the effect of directionality in the form of fragility curves. The word directionality used here is different from “directivity” used in seismology to mean a specific characteristic of seismic fault movement.

Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict

NARCIS (Netherlands)

Wagener, F.

2009-01-01

Outcomes of the shallow lake interest conflict are presented in a number of different contexts: quasi-static and dynamic social planning, and quasi-static one-shot and repeated non-cooperative play. As the underlying dynamics are non-convex, the analysis uses geometrical-numerical methods: the

Coherent Lagrangian swirls among submesoscale motions.

Science.gov (United States)

Beron-Vera, F J; Hadjighasem, A; Xia, Q; Olascoaga, M J; Haller, G

2018-03-05

The emergence of coherent Lagrangian swirls (CLSs) among submesoscale motions in the ocean is illustrated. This is done by applying recent nonlinear dynamics tools for Lagrangian coherence detection on a surface flow realization produced by a data-assimilative submesoscale-permitting ocean general circulation model simulation of the Gulf of Mexico. Both mesoscale and submesoscale CLSs are extracted. These extractions prove the relevance of coherent Lagrangian eddies detected in satellite-altimetry-based geostrophic flow data for the arguably more realistic ageostrophic multiscale flow.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

Science.gov (United States)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

Global format for energy-momentum based time integration in nonlinear dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2014-01-01

A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...

Sliding mode control for uncertain unified chaotic systems with input nonlinearity

International Nuclear Information System (INIS)

Chiang, T.-Y.; Hung, M.-L.; Yan, J.-J.; Yang, Y.-S.; Chang, J.-F.

2007-01-01

This paper investigates the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Using the sliding mode control technique, a robust control law is established which stabilizes the uncertain unified chaotic systems even when the nonlinearity in the actuators is present. A novel adaptive switching surface is introduced to simplify the task of assigning the stability of the closed-loop system in the sliding mode motion. An illustrative example is given to demonstrate the effectiveness of the proposed sliding mode control design

Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver

Science.gov (United States)

Scott, Matthew T.; Mccune, James E.

1988-01-01

This paper presents a nonlinear theory of forces and moment acting on a two-dimensional airfoil in unsteady potential flow. Results are obtained for cases of both large and small amplitude motion. The analysis, which is based on an extension of Wagner's integral equation to the nonlinear regime, takes full advantage of the trailing wake's tendency to deform under local velocities. Interactive computational results are presented that show examples of wake-induced lift and moment augmentation on the order of 20 percent of quasi-static values. The expandability and flexibility of the present computational method are noted, as well as the relative speed with which solutions are obtained.

Superworld volume dynamics of super branes from nonlinear realizations

International Nuclear Information System (INIS)

Bellucci, S.; Ivanov, E.; Krivonos, S.

2000-01-01

Based on the concept of the partial breaking of global supersymmetry (PBGS), it has been derived the world volume superfield equations of motion for N=1, D=4 supermembrane, as well as for the space-time filling D2- and D3-branes, from nonlinear realizations of the corresponding supersymmetries. It has been argued that it is of no need to take care of the relevant automorphism groups when being interested in the dynamical equations. This essentially facilitates computations. As a by-product, it has been obtained a new polynomial representation for the d=3,4 Born-Infeld equations, with merely a cubic nonlinearity

Assessment of modal-pushover-based scaling procedure for nonlinear response history analysis of ordinary standard bridges

Science.gov (United States)

Kalkan, E.; Kwong, N.

2012-01-01

The earthquake engineering profession is increasingly utilizing nonlinear response history analyses (RHA) to evaluate seismic performance of existing structures and proposed designs of new structures. One of the main ingredients of nonlinear RHA is a set of ground motion records representing the expected hazard environment for the structure. When recorded motions do not exist (as is the case in the central United States) or when high-intensity records are needed (as is the case in San Francisco and Los Angeles), ground motions from other tectonically similar regions need to be selected and scaled. The modal-pushover-based scaling (MPS) procedure was recently developed to determine scale factors for a small number of records such that the scaled records provide accurate and efficient estimates of “true” median structural responses. The adjective “accurate” refers to the discrepancy between the benchmark responses and those computed from the MPS procedure. The adjective “efficient” refers to the record-to-record variability of responses. In this paper, the accuracy and efficiency of the MPS procedure are evaluated by applying it to four types of existing Ordinary Standard bridges typical of reinforced concrete bridge construction in California. These bridges are the single-bent overpass, multi-span bridge, curved bridge, and skew bridge. As compared with benchmark analyses of unscaled records using a larger catalog of ground motions, it is demonstrated that the MPS procedure provided an accurate estimate of the engineering demand parameters (EDPs) accompanied by significantly reduced record-to-record variability of the EDPs. Thus, it is a useful tool for scaling ground motions as input to nonlinear RHAs of Ordinary Standard bridges.

Practical guidelines to select and scale earthquake records for nonlinear response history analysis of structures

Science.gov (United States)

Kalkan, Erol; Chopra, Anil K.

2010-01-01

Earthquake engineering practice is increasingly using nonlinear response history analysis (RHA) to demonstrate performance of structures. This rigorous method of analysis requires selection and scaling of ground motions appropriate to design hazard levels. Presented herein is a modal-pushover-based scaling (MPS) method to scale ground motions for use in nonlinear RHA of buildings and bridges. In the MPS method, the ground motions are scaled to match (to a specified tolerance) a target value of the inelastic deformation of the first-'mode' inelastic single-degree-of-freedom (SDF) system whose properties are determined by first-'mode' pushover analysis. Appropriate for first-?mode? dominated structures, this approach is extended for structures with significant contributions of higher modes by considering elastic deformation of second-'mode' SDF system in selecting a subset of the scaled ground motions. Based on results presented for two bridges, covering single- and multi-span 'ordinary standard' bridge types, and six buildings, covering low-, mid-, and tall building types in California, the accuracy and efficiency of the MPS procedure are established and its superiority over the ASCE/SEI 7-05 scaling procedure is demonstrated.

Linear Algebraic Method for Non-Linear Map Analysis

International Nuclear Information System (INIS)

Yu, L.; Nash, B.

2009-01-01

We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.

Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma

Energy Technology Data Exchange (ETDEWEB)

Zhen, Hui-Ling; Tian, Bo, E-mail: tian-bupt@163.com; Wang, Yu-Feng; Liu, De-Yin [State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China)

2015-03-15

For the interaction between the high-frequency Langmuir waves and low-frequency ion-acoustic waves in the plasma, the Zakharov equations are studied in this paper. Via the Hirota method, we obtain the soliton solutions, based on which the soliton propagation is presented. It is found that with λ increasing, the amplitude of u decreases, whereas that of v remains unchanged, where λ is the ion-acoustic speed, u is the slowly-varying envelope of the Langmuir wave, and v is the fluctuation of the equilibrium ion density. Both the head-on and bound-state interactions between the two solitons are displayed. We observe that with λ decreasing, the interaction period of u decreases, while that of v keeps unchanged. It is found that the Zakharov equations cannot admit any chaotic motions. With the external perturbations taken into consideration, the perturbed Zakharov equations are studied for us to see the associated chaotic motions. Both the weak and developed chaotic motions are investigated, and the difference between them roots in the relative magnitude of the nonlinearities and perturbations. The chaotic motions are weakened with λ increasing, or else, strengthened. Periodic motion appears when the nonlinear terms and external perturbations are balanced. With such a balance kept, one period increases with λ increasing.

Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation

Energy Technology Data Exchange (ETDEWEB)

Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, A.; Alhuthali, M.S. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)

2015-07-01

Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect. - Highlights: • Three-dimensional boundary layer flow of viscoelastic nanofluid is examined. • Nonlinear thermal radiation is analyzed. • Brownian motion and thermophoresis effects are present. • Recently developed condition requiring zero nanoparticle mass flux is implemented. • Construction of convergent solutions of nonlinear flow is possible.

Nonlinear Dynamic Characteristics of the Railway Vehicle

Science.gov (United States)

Uyulan, Çağlar; Gokasan, Metin

2017-06-01

The nonlinear dynamic characteristics of a railway vehicle are checked into thoroughly by applying two different wheel-rail contact model: a heuristic nonlinear friction creepage model derived by using Kalker 's theory and Polach model including dead-zone clearance. This two models are matched with the quasi-static form of the LuGre model to obtain more realistic wheel-rail contact model. LuGre model parameters are determined using nonlinear optimization method, which it's objective is to minimize the error between the output of the Polach and Kalker model and quasi-static LuGre model for specific operating conditions. The symmetric/asymmetric bifurcation attitude and stable/unstable motion of the railway vehicle in the presence of nonlinearities which are yaw damping forces in the longitudinal suspension system are analyzed in great detail by changing the vehicle speed. Phase portraits of the lateral displacement of the leading wheelset of the railway vehicle are drawn below and on the critical speeds, where sub-critical Hopf bifurcation take place, for two wheel-rail contact model. Asymmetric periodic motions have been observed during the simulation in the lateral displacement of the wheelset under different vehicle speed range. The coexistence of multiple steady states cause bounces in the amplitude of vibrations, resulting instability problems of the railway vehicle. By using Lyapunov's indirect method, the critical hunting speeds are calculated with respect to the radius of the curved track parameter changes. Hunting, which is defined as the oscillation of the lateral displacement of wheelset with a large domain, is described by a limit cycle-type oscillation nature. The evaluated accuracy of the LuGre model adopted from Kalker's model results for prediction of critical speed is higher than the results of the LuGre model adopted from Polach's model. From the results of the analysis, the critical hunting speed must be resolved by investigating the track tests

Three-dimensional nonlinear H-infinity guidance design and H-infinity-based pursuit-evasion game

Science.gov (United States)

Chen, Hsin-Yuan; Yang, Chi-Ching

2001-08-01

There are five features in this approach: (1) The complete nonlinear dynamics of the pursuit-evasion motion is considered in 3D spherical coordinate system. Neither linearization nor small signal assumptions are made. (2) The nonlinear H-infinity guidance design is derived analytically and expressed in a very simple form. (3) Unlike adaptive control concept, implementation of the proposed H(infinity ) guidance design does not need the information on target acceleration while ensuring acceptable intercept performance for arbitrary targets with the finite acceleration. (4) The derived guidance design exhibits strong robustness against variations in target acceleration. (5) Finally the issues related to the validation of the control law using Hardware In The Loop simulation are presented. The effects of the Flight Motion Simulator static and dynamic accuracies (time delay etc...) are discussed.

Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay

Science.gov (United States)

Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai

2016-08-01

In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.

A Modal-Based Substructure Method Applied to Nonlinear Rotordynamic Systems

Directory of Open Access Journals (Sweden)

Helmut J. Holl

2009-01-01

Full Text Available The discretisation of rotordynamic systems usually results in a high number of coordinates, so the computation of the solution of the equations of motion is very time consuming. An efficient semianalytic time-integration method combined with a substructure technique is given, which accounts for nonsymmetric matrices and local nonlinearities. The partitioning of the equation of motion into two substructures is performed. Symmetric and linear background systems are defined for each substructure. The excitation of the substructure comes from the given excitation force, the nonlinear restoring force, the induced force due to the gyroscopic and circulatory effects of the substructure under consideration and the coupling force of the substructures. The high effort for the analysis with complex numbers, which is necessary for nonsymmetric systems, is omitted. The solution is computed by means of an integral formulation. A suitable approximation for the unknown coordinates, which are involved in the coupling forces, has to be introduced and the integration results in Green's functions of the considered substructures. Modal analysis is performed for each linear and symmetric background system of the substructure. Modal reduction can be easily incorporated and the solution is calculated iteratively. The numerical behaviour of the algorithm is discussed and compared to other approximate methods of nonlinear structural dynamics for a benchmark problem and a representative example.

Lagrangian speckle model and tissue-motion estimation--theory.

Science.gov (United States)

Maurice, R L; Bertrand, M

1999-07-01

It is known that when a tissue is subjected to movements such as rotation, shearing, scaling, etc., changes in speckle patterns that result act as a noise source, often responsible for most of the displacement-estimate variance. From a modeling point of view, these changes can be thought of as resulting from two mechanisms: one is the motion of the speckles and the other, the alterations of their morphology. In this paper, we propose a new tissue-motion estimator to counteract these speckle decorrelation effects. The estimator is based on a Lagrangian description of the speckle motion. This description allows us to follow local characteristics of the speckle field as if they were a material property. This method leads to an analytical description of the decorrelation in a way which enables the derivation of an appropriate inverse filter for speckle restoration. The filter is appropriate for linear geometrical transformation of the scattering function (LT), i.e., a constant-strain region of interest (ROI). As the LT itself is a parameter of the filter, a tissue-motion estimator can be formulated as a nonlinear minimization problem, seeking the best match between the pre-tissue-motion image and a restored-speckle post-motion image. The method is tested, using simulated radio-frequency (RF) images of tissue undergoing axial shear.

Induced dynamic nonlinear ground response at Gamer Valley, California

Science.gov (United States)

Lawrence, Z.; Bodin, P.; Langston, C.A.; Pearce, F.; Gomberg, J.; Johnson, P.A.; Menq, F.-Y.; Brackman, T.

2008-01-01

We present results from a prototype experiment in which we actively induce, observe, and quantify in situ nonlinear sediment response in the near surface. This experiment was part of a suite of experiments conducted during August 2004 in Garner Valley, California, using a large mobile shaker truck from the Network for Earthquake Engineering Simulation (NEES) facility. We deployed a dense accelerometer array within meters of the mobile shaker truck to replicate a controlled, laboratory-style soil dynamics experiment in order to observe wave-amplitude-dependent sediment properties. Ground motion exceeding 1g acceleration was produced near the shaker truck. The wave field was dominated by Rayleigh surface waves and ground motions were strong enough to produce observable nonlinear changes in wave velocity. We found that as the force load of the shaker increased, the Rayleigh-wave phase velocity decreased by as much as ???30% at the highest frequencies used (up to 30 Hz). Phase velocity dispersion curves were inverted for S-wave velocity as a function of depth using a simple isotropic elastic model to estimate the depth dependence of changes to the velocity structure. The greatest change in velocity occurred nearest the surface, within the upper 4 m. These estimated S-wave velocity values were used with estimates of surface strain to compare with laboratory-based shear modulus reduction measurements from the same site. Our results suggest that it may be possible to characterize nonlinear soil properties in situ using a noninvasive field technique.

Scattered Data Processing Approach Based on Optical Facial Motion Capture

Directory of Open Access Journals (Sweden)

Qiang Zhang

2013-01-01

Full Text Available In recent years, animation reconstruction of facial expressions has become a popular research field in computer science and motion capture-based facial expression reconstruction is now emerging in this field. Based on the facial motion data obtained using a passive optical motion capture system, we propose a scattered data processing approach, which aims to solve the common problems of missing data and noise. To recover missing data, given the nonlinear relationships among neighbors with the current missing marker, we propose an improved version of a previous method, where we use the motion of three muscles rather than one to recover the missing data. To reduce the noise, we initially apply preprocessing to eliminate impulsive noise, before our proposed three-order quasi-uniform B-spline-based fitting method is used to reduce the remaining noise. Our experiments showed that the principles that underlie this method are simple and straightforward, and it delivered acceptable precision during reconstruction.

Incremental Dynamic Analysis of Koyna Dam under Repeated Ground Motions

Science.gov (United States)

Zainab Nik Azizan, Nik; Majid, Taksiah A.; Nazri, Fadzli Mohamed; Maity, Damodar; Abdullah, Junaidah

2018-03-01

This paper discovers the incremental dynamic analysis (IDA) of concrete gravity dam under single and repeated earthquake loadings to identify the limit state of the dam. Seven ground motions with horizontal and vertical direction as seismic input considered in the nonlinear dynamic analysis based on the real repeated earthquake in the worldwide. All the ground motions convert to respond spectrum and scaled according to the developed elastic respond spectrum in order to match the characteristic of the ground motion to the soil type. The scaled was depends on the fundamental period, T1 of the dam. The Koyna dam has been selected as a case study for the purpose of the analysis by assuming that no sliding and rigid foundation, has been estimated. IDA curves for Koyna dam developed for single and repeated ground motions and the performance level of the dam identifies. The IDA curve of repeated ground motion shown stiffer rather than single ground motion. The ultimate state displacement for a single event is 45.59mm and decreased to 39.33mm under repeated events which are decreased about 14%. This showed that the performance level of the dam based on seismic loadings depend on ground motion pattern.

Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts

International Nuclear Information System (INIS)

Emans, Joseph; Wiercigroch, Marian; Krivtsov, Anton M.

2005-01-01

The nonlinear analysis of a common beam system was performed, and the method for such, outlined and presented. Nonlinear terms for the governing dynamic equations were extracted and the behaviour of the system was investigated. The analysis was carried out with and without physically realistic parameters, to show the characteristics of the system, and the physically realistic responses. Also, the response as part of a more complex system was considered, in order to investigate the cumulative effects of nonlinearities. Chaos, as well as periodic motion was found readily for the physically unrealistic parameters. In addition, nonlinear behaviour such as co-existence of attractors was found even at modest oscillation levels during investigations with realistic parameters. When considered as part of a more complex system with further nonlinearities, comparisons with linear beam theory show the classical approach to be lacking in accuracy of qualitative predictions, even at weak oscillations

A dynamic load estimation method for nonlinear structures with unscented Kalman filter

Science.gov (United States)

Guo, L. N.; Ding, Y.; Wang, Z.; Xu, G. S.; Wu, B.

2018-02-01

A force estimation method is proposed for hysteretic nonlinear structures. The equation of motion for the nonlinear structure is represented in state space and the state variable is augmented by the unknown the time history of external force. Unscented Kalman filter (UKF) is improved for the force identification in state space considering the ill-condition characteristic in the computation of square roots for the covariance matrix. The proposed method is firstly validated by a numerical simulation study of a 3-storey nonlinear hysteretic frame excited by periodic force. Each storey is supposed to follow a nonlinear hysteretic model. The external force is identified and the measurement noise is considered in this case. Then a case of a seismically isolated building subjected to earthquake excitation and impact force is studied. The isolation layer performs nonlinearly during the earthquake excitation. Impact force between the seismically isolated structure and the retaining wall is estimated with the proposed method. Uncertainties such as measurement noise, model error in storey stiffness and unexpected environmental disturbances are considered. A real-time substructure testing of an isolated structure is conducted to verify the proposed method. In the experimental study, the linear main structure is taken as numerical substructure while the one of the isolations with additional mass is taken as the nonlinear physical substructure. The force applied by the actuator on the physical substructure is identified and compared with the measured value from the force transducer. The method proposed in this paper is also validated by shaking table test of a seismically isolated steel frame. The acceleration of the ground motion as the unknowns is identified by the proposed method. Results from both numerical simulation and experimental studies indicate that the UKF based force identification method can be used to identify external excitations effectively for the nonlinear

Motion of a Rigid Body Supported at One Point by a Rotating Arm

Directory of Open Access Journals (Sweden)

Jeffrey D. Stoen

1993-01-01

Full Text Available This article details a scheme for evaluating the stability of motions of a system consisting of a rigid body connected at one point to a rotating arm. The nonlinear equations of motion for the system are formulated, and a method for finding exact solutions representing motions that resemble a state of rest is presented. The equations are then linearized and roots of the eigensystem are classified and used to construct stability diagrams that facilitate the assessment of effects of varying the body's mass properties and system geometry, changing the position of the attachment joint, and adding energy dissipation in the joint.

Effects of nonlinearity in the materials used for the semi-rigid pedicle screw systems on biomechanical behaviors of the lumbar spine after surgery

International Nuclear Information System (INIS)

Kim, Hyun; Lee, Sung-Jae; Lim, Do-Hyung; Oh, Hyun-Ju; Lee, Kwon-Yong

2011-01-01

Recently, various types of semi-rigid pedicle screw fixation systems have been developed for the surgical treatment of the lumbar spine. They were introduced to address the adverse issues commonly found in traditional rigid spinal fusion--abnormally large motion at the adjacent level and subsequent degeneration. The semi-rigid system uses more compliant materials (nitinol or polymers) and/or changes in rod design (coiled or twisted rods) as compared to the conventional rigid straight rods made of Ti alloys (E = 114 GPa, υ = 0.32). However, biomechanical studies on the semi-rigid pedicle screw systems were usually limited to linear modeling of the implant and anatomic elements, which may not be capable of reflecting realistic post-operative motions of the spine. In this study, we evaluated the effects of nonlinearity in materials used for semi-rigid pedicle screw fixation systems to evaluate the changes in biomechanical behaviors using finite element analysis. Changes in range of motion (ROM) and center of rotation (COR) were assessed at the operated and adjacent levels. Actual load-displacement results of the semi-rigid rod from mechanical test were carried out to reflect the nonlinearity of the implant. In addition, nonlinear material properties of various spinal ligaments studies were used for the finite element modeling. The post-operative models were constructed by modifying the previously validated intact model of the L1-S1 spine. Eight different post-operative models were made to address the effects of nonlinearity-with a traditional stiffness modulus rod (with linear ligaments, case 1; with nonlinear ligaments, case 5), with a rigid rod (with linear ligaments, case 2; with nonlinear ligaments, case 6), with a soft rod (with linear ligaments, case 3; with nonlinear ligaments, case 7), and with a nonlinear rod (with linear ligaments, case 4; with nonlinear ligaments, case 8). To simulate the load on the lumbar spine in a neutral posture, follower load (400 N

Effect of weak nonlinearities on the plane waves in a plasma stream

International Nuclear Information System (INIS)

Seshadri, S.R.

1976-01-01

The effect of weak nonlinearities on the monochromatic plane waves in a cold infinite plasma stream is investigated for the case in which the waves are progressing parallel to the drift velocity. The fast and the slow space-charge waves undergo amplitude-dependent frequency and wave number shifts. There is a long time slow modulation of the amplitude of the electromagnetic mode which becomes unstable to this nonlinear wave modulation. The importance of using the relativistically correct equation of motion for predicting correctly the modulational stability of the electromagnetic mode is pointed out. (author)

Experimental analysis of nonlinear oscillations in the undergraduate physics laboratory

International Nuclear Information System (INIS)

Moreno, R; Page, A; Riera, J; Hueso, J L

2014-01-01

In this paper, we present a simple experiment to introduce the nonlinear behaviour of oscillating systems in the undergraduate physics laboratory. The transverse oscillations of a spring allow reproduction of three totally different scenarios: linear oscillations, nonlinear oscillations reducible to linear for small displacements, and intrinsically nonlinear oscillations. The chosen approach consists of measuring the displacements using video photogrammetry and computing the velocities and the accelerations by means of a numerical differentiation algorithm. In this way, one can directly check the differential equation of the motion without having to integrate it, or perform an experimental study of the potential energy in each of the analysed scenarios. This experiment allows first year students to reflect on the consequences and the limits of the linearity assumption for small displacements that is so often made in technical studies. (paper)

Nonlinear dynamics of vortices in ultraclean type-II superconductors: Integrable wave equations in cylindrical geometry

International Nuclear Information System (INIS)

Coffey, M.W.

1996-01-01

Due to their short coherence lengths and relatively large energy gaps, the high-transition temperature superconductors are very likely candidates as ultraclean materials at low temperature. This class of materials features significantly modified vortex dynamics, with very little dissipation at low temperature. The motion is then dominated by wave propagation, being in general nonlinear. Here two-dimensional vortex motion is investigated in the ultraclean regime for a superconductor described in cylindrical geometry. The small-amplitude limit is assumed, and the focus is on the long-wavelength limit. Results for both zero and nonzero Hall force are presented, with the effects of nonlocal vortex interaction and vortex inertia being included within London theory. Linear and nonlinear problems are studied, with a predisposition toward the more analytically tractable situations. For a nonlinear problem in 2+1 dimensions, the cylindrical Kadomtsev-Petviashvili equation is derived. Hall angle measurements on high-T c superconductors indicate the need to investigate the properties of such a completely integrable wave equation. copyright 1996 The American Physical Society

Extrinsic contribution to the non-linearity in a PZT disc

Energy Technology Data Exchange (ETDEWEB)

Perez, Rafel [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Albareda, Alfons [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Garcia, Jose E [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Tiana, Jordi [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Ringgaard, Erling [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark); Wolny, Wanda W [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark)

2004-10-07

Non-linear increases in elastic, piezoelectric (direct and reverse) and dielectric coefficients have been measured under a high electrical field or under high mechanical stress. The permittivity and reverse piezoelectric coefficient can be measured by applying a high voltage at a low frequency, while the elastic compliance and direct piezoelectric coefficient can be measured at the first radial resonance frequency in order to apply a high stress. The non-linear behaviour has been analysed at the radial resonance of a disc. In all the materials tested, the results show that there is a close relation between the non-linear increments of the different coefficients. An empirical model has been proposed in order to describe and understand these relations. It is assumed that either the strain or the electrical displacement is produced by intrinsic and extrinsic processes, but only the latter, which consist mainly in the motion of domain walls, contribute to the non-linearity. The model enables us to find the domain wall contribution to elastic, piezoelectric and dielectric non-linearities, and allows us to compare the amplitudes of the fields and stresses that produce the same displacement of domain walls.

Effect of stopover on motion of two competing elevators in peak traffic

Science.gov (United States)

Nagatani, Takashi

2016-02-01

We study the dynamic motion of two competing elevators when elevators stop over at some floors. We present the dynamic model of elevators to take into account the stopover effect. The dynamics of the elevator traffic system is described by a pair of deterministic nonlinear maps. The motion of two elevators is determined by the five parameters: the numbers of stopovers at two elevators, the fraction of passengers choosing the first elevator, the fraction of passengers choosing the second elevator, and the inflow rate. The dynamics of two elevators depends highly on these parameters. The motion of two elevators displays a complex behavior by a neck-and-neck race between two elevators. We explore the dependence of elevator motion on the fractions of two kinds of passengers, the numbers of stopover floors, and the inflow rate.

Beating Heart Motion Accurate Prediction Method Based on Interactive Multiple Model: An Information Fusion Approach

Science.gov (United States)

Xie, Weihong; Yu, Yang

2017-01-01

Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG) in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM) estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively “switch” from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly. PMID:29124062

Beating Heart Motion Accurate Prediction Method Based on Interactive Multiple Model: An Information Fusion Approach

Directory of Open Access Journals (Sweden)

Fan Liang

2017-01-01

Full Text Available Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively “switch” from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly.

Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms

Directory of Open Access Journals (Sweden)

Alex Elías-Zúñiga

2013-01-01

Full Text Available In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others.

A non-linear canonical formalism for the coupled synchro-betatron motion of protons with arbitrary energy

International Nuclear Information System (INIS)

Barber, D.P.; Ripken, G.; Schmidt, F.

1987-05-01

We investigate the motion of protons of arbitrary energy (below and above transition energy) in a storage ring. The motion is described both in terms of the fully six-dimensional formalism with the canonical variables x, p x , z, p z , σ = s - v 0 . t, η = ΔE/E 0 = p σ and in terms of a dispersion formalism with new variables x, p x , z, p z , σ, p σ . Since the dispersion function is introduced into the equations of motion via a canonical transformation the symplectic structure of these equations is completely preserved. In this formulation it is then possible to define three uncoupled linear (unperturbed) oscillation modes which are described by phase ellipses. Perturbations manifest themselves as deviations from these ellipses. The equations of motion are solved within the framework of the fully six-dimensional formalism. (orig.)

Data and performance profiles applying an adaptive truncation criterion, within linesearch-based truncated Newton methods, in large scale nonconvex optimization

Directory of Open Access Journals (Sweden)

Andrea Caliciotti

2018-04-01

Full Text Available In this paper, we report data and experiments related to the research article entitled “An adaptive truncation criterion, for linesearch-based truncated Newton methods in large scale nonconvex optimization” by Caliciotti et al. [1]. In particular, in Caliciotti et al. [1], large scale unconstrained optimization problems are considered by applying linesearch-based truncated Newton methods. In this framework, a key point is the reduction of the number of inner iterations needed, at each outer iteration, to approximately solving the Newton equation. A novel adaptive truncation criterion is introduced in Caliciotti et al. [1] to this aim. Here, we report the details concerning numerical experiences over a commonly used test set, namely CUTEst (Gould et al., 2015 [2]. Moreover, comparisons are reported in terms of performance profiles (Dolan and Moré, 2002 [3], adopting different parameters settings. Finally, our linesearch-based scheme is compared with a renowned trust region method, namely TRON (Lin and Moré, 1999 [4].

Combined effects of traveling seismic waves and soil nonlinearity on nuclear power plant response

International Nuclear Information System (INIS)

Lee, T.H.; Charman, C.M.

1981-01-01

The effects of ground motion nonuniformity on the seismic input have been actively studied in recent years by considering the passage of traveling seismic waves. These studies gave rise to a new class of soil-structure interaction problems in which the seismic input is modified as a result of the spatial variations of ground motion. The phenomena were usually studied by using the elastic half-space simulation or discrete spring-models for modeling the soil medium. Finite element methods were also used recently on a limited scope. Results obtained from these investigations are often manifested by an attenuation of translational excitation along with an addition of rotational ground motion input. The decrease in structural response resulting from the input loss in the translational component was often insignificant since the response reduction tends to be offset by the effects from rotational input. The traveling wave effects have, so far, been investigated within the framework of linear theory with soil nonlinearity ignored. Conversely, the incorporation of soil nonlinearity in soil-structure interaction analyses has been done without including wave effect. Seismic analyses considering the hysteretic behavior of soil have been performed using highly idealized models for steady-state solution. More elaborate nonlinear seismic models deal with only the strain-dependent soil modulus rather than the transient unloading-reloading type of hysteretic characteristics of soil under a time-function input of earthquake trace. Apparently, the traveling wave effect and soil nonlinearity have been separately treated in the past. The purpose of this paper is to demonstrate that these two major effects can be combined in one model such that the influence of wave passage is reflected through the hysteretic behavior of soil particles, and thereby achieving significant reduction in seismic loads. (orig./RW)

Biology-Inspired Robust Dive Plane Control of Non-Linear AUV Using Pectoral-Like Fins

Directory of Open Access Journals (Sweden)

Subramanian Ramasamy

2010-01-01

Full Text Available The development of a control system for the dive plane control of non-linear biorobotic autonomous underwater vehicles, equipped with pectoral-like fins, is the subject of this paper. Marine animals use pectoral fins for swimming smoothly. The fins are assumed to be oscillating with a combined pitch and heave motion and therefore produce unsteady control forces. The objective is to control the depth of the vehicle. The mean angle of pitch motion of the fin is used as a control variable. A computational-fluid-dynamics-based parameterisation of the fin forces is used for control system design. A robust servo regulator for the control of the depth of the vehicle, based on the non-linear internal model principle, is derived. For the control law derivation, an exosystem of third order is introduced, and the non-linear time-varying biorobotic autonomous underwater vehicle model, including the fin forces, is represented as a non-linear autonomous system in an extended state space. The control system includes the internal model of a k-fold exosystem, where k is a positive integer chosen by the designer. It is shown that in the closed-loop system, all the harmonic components of order up to k of the tracking error are suppressed. Simulation results are presented which show that the servo regulator accomplishes accurate depth control despite uncertainties in the model parameters.

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...

Documentation for assessment of modal pushover-based scaling procedure for nonlinear response history analysis of "ordinary standard" bridges

Science.gov (United States)

Kalkan, Erol; Kwong, Neal S.

2010-01-01

The earthquake engineering profession is increasingly utilizing nonlinear response history analyses (RHA) to evaluate seismic performance of existing structures and proposed designs of new structures. One of the main ingredients of nonlinear RHA is a set of ground-motion records representing the expected hazard environment for the structure. When recorded motions do not exist (as is the case for the central United States), or when high-intensity records are needed (as is the case for San Francisco and Los Angeles), ground motions from other tectonically similar regions need to be selected and scaled. The modal-pushover-based scaling (MPS) procedure recently was developed to determine scale factors for a small number of records, such that the scaled records provide accurate and efficient estimates of 'true' median structural responses. The adjective 'accurate' refers to the discrepancy between the benchmark responses and those computed from the MPS procedure. The adjective 'efficient' refers to the record-to-record variability of responses. Herein, the accuracy and efficiency of the MPS procedure are evaluated by applying it to four types of existing 'ordinary standard' bridges typical of reinforced-concrete bridge construction in California. These bridges are the single-bent overpass, multi span bridge, curved-bridge, and skew-bridge. As compared to benchmark analyses of unscaled records using a larger catalog of ground motions, it is demonstrated that the MPS procedure provided an accurate estimate of the engineering demand parameters (EDPs) accompanied by significantly reduced record-to-record variability of the responses. Thus, the MPS procedure is a useful tool for scaling ground motions as input to nonlinear RHAs of 'ordinary standard' bridges.

Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

Science.gov (United States)

Zhao, K. G.; Wang, L. F.; Xue, C.; Ye, W. H.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.

2018-03-01

On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

Evaluation of ground motion scaling methods for analysis of structural systems

Science.gov (United States)

O'Donnell, A. P.; Beltsar, O.A.; Kurama, Y.C.; Kalkan, E.; Taflanidis, A.A.

2011-01-01

Ground motion selection and scaling comprises undoubtedly the most important component of any seismic risk assessment study that involves time-history analysis. Ironically, this is also the single parameter with the least guidance provided in current building codes, resulting in the use of mostly subjective choices in design. The relevant research to date has been primarily on single-degree-of-freedom systems, with only a few studies using multi-degree-of-freedom systems. Furthermore, the previous research is based solely on numerical simulations with no experimental data available for the validation of the results. By contrast, the research effort described in this paper focuses on an experimental evaluation of selected ground motion scaling methods based on small-scale shake-table experiments of re-configurable linearelastic and nonlinear multi-story building frame structure models. Ultimately, the experimental results will lead to the development of guidelines and procedures to achieve reliable demand estimates from nonlinear response history analysis in seismic design. In this paper, an overview of this research effort is discussed and preliminary results based on linear-elastic dynamic response are presented. ?? ASCE 2011.

Nonlinear Lorentz-invariant theory of gravitation

International Nuclear Information System (INIS)

Petry, W.

1976-01-01

A nonlinear Lorentz-invariant theory of gravitation and a Lorentz-invariant Hamiltonian for a particle with spin in the gravitational field are developed. The equations of motions are studied. The theory is applied to the three well known tests of General Relativity. In the special case of the red shift of spectral lines and of the deflection of light, the theory gives the same results as the General Theory of Relativity, whereas in the case of the perihelion of the Mercury, the theory gives 40,3'', in good agreement with experimental results of Dicke. (author)

Non-linear wave loads and ship responses by a time-domain strip theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...

Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

Science.gov (United States)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Nonlinear analysis and enhancement of wing-based piezoaeroelastic energy harvesters

KAUST Repository

Abdelkefi, Abdessattar

2014-01-01

We investigate the level of harvested power from aeroelastic vibrations for an elastically mounted wing supported by nonlinear springs. The energy is harvested by attaching a piezoelectric transducer to the plunge degree of freedom. The considered wing has a low-aspect ratio and hence three dimensional aerodynamic effects cannot be neglected. To this end, the three dimensional unsteady vortex lattice method for the prediction of the unsteady aerodynamic loads is developed. A strong coupling scheme that is based on Hamming\\'s fourth-order predictor-corrector method and accounts for the interaction between the aerodynamic loads and the motion of the wing is employed. The effects of the electrical load resistance, nonlinear torsional spring and eccentricity between the elastic axis and the gravity axis on the level of the harvested power, pitch and plunge amplitudes are investigated for a range of operating wind speeds. The results show that there is a specific wind speed beyond which the pitch motion does not pick any further energy from the incident flow. As such, the displacement in the plunge direction grows significantly and causes enhanced energy harvesting. The results also show that the nonlinear torsional spring plays an important role in enhancing the level of the harvested power. Furthermore, the harvested power can be increased by an order of magnitude by properly choosing the eccentricity and the load resistance. This analysis is helpful in designing piezoaeroelastic energy harvesters that can operate optimally at specific wind speeds. © 2013 Elsevier Ltd.

Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference.

Science.gov (United States)

Venkataraman, Vinay; Turaga, Pavan

2016-12-01

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.

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

Contrast gain control in first- and second-order motion perception.

Science.gov (United States)

Lu, Z L; Sperling, G

1996-12-01

A novel pedestal-plus-test paradigm is used to determine the nonlinear gain-control properties of the first-order (luminance) and the second-order (texture-contrast) motion systems, that is, how these systems' responses to motion stimuli are reduced by pedestals and other masking stimuli. Motion-direction thresholds were measured for test stimuli consisting of drifting luminance and texture-contrast-modulation stimuli superimposed on pedestals of various amplitudes. (A pedestal is a static sine-wave grating of the same type and same spatial frequency as the moving test grating.) It was found that first-order motion-direction thresholds are unaffected by small pedestals, but at pedestal contrasts above 1-2% (5-10 x pedestal threshold), motion thresholds increase proportionally to pedestal amplitude (a Weber law). For first-order stimuli, pedestal masking is specific to the spatial frequency of the test. On the other hand, motion-direction thresholds for texture-contrast stimuli are independent of pedestal amplitude (no gain control whatever) throughout the accessible pedestal amplitude range (from 0 to 40%). However, when baseline carrier contrast increases (with constant pedestal modulation amplitude), motion thresholds increase, showing that gain control in second-order motion is determined not by the modulator (as in first-order motion) but by the carrier. Note that baseline contrast of the carrier is inherently independent of spatial frequency of the modulator. The drastically different gain-control properties of the two motion systems and prior observations of motion masking and motion saturation are all encompassed in a functional theory. The stimulus inputs to both first- and second-order motion process are normalized by feedforward, shunting gain control. The different properties arise because the modulator is used to control the first-order gain and the carrier is used to control the second-order gain.

A New Approach for Studying Nonlinear Dynamic Response of a Thin Plate with Internal Resonance in a Fractional Viscoelastic Medium

Directory of Open Access Journals (Sweden)

Yury A. Rossikhin

2015-01-01

Full Text Available In the previous analysis, the dynamic behaviour of a nonlinear plate embedded into a fractional derivative viscoelastic medium has been studied by the method of multiple time scales under the conditions of the internal resonances two-to-one and one-to-one, as well as the internal combinational resonances for the case when the linear parts of nonlinear equations of motion occur to be coupled. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The influence of viscosity on the energy exchange mechanism between interacting nonlinear modes has been analyzed. It has been shown that for some internal resonances there exist such particular cases when it is possible to obtain two first integrals, namely, the energy integral and the stream function, which allows one to reduce the problem to the calculation of elliptic integrals. The new approach enables one to solve the problems of vibrations of thin bodies more efficiently.

Influence of temperature on the dielectric nonlinearity of BaTiO{sub 3}-based multi-layer ceramic capacitors

Energy Technology Data Exchange (ETDEWEB)

Yoon, Seok-Hyun, E-mail: seokhyun72.yoon@samsung.com; Kim, Mi-Yang [LCR Materials Group, Corporate R& D Institute, Samsung Electro-Mechanics Co., Ltd., Suwon, Gyunggi-Do 443-743 (Korea, Republic of)

2016-06-13

Temperature dependence of the dielectric nonlinearity was investigated for the BaTiO{sub 3} multilayer ceramic capacitor. The decrease in temperature caused a significant increase in the degree of dielectric nonlinearity. The Preisach analysis shows that such effect corresponds to a decrease in reversible and a significant increase in irreversible domain wall contribution to polarization. The magnitude of spontaneous polarization (P{sub S}) was increased with decreasing temperature. It can be associated with phase transition from pseudo-cubic to monoclinic and its resultant change in the polar direction, which was observed through transmission electron microscopy. These results demonstrate that the increase in P{sub S} with the decrease in temperature inhibits domain wall motion in low driving field as it is anticipated to increase the degree of intergranular constraints during domain wall motion. But it results in a more steep increase in the dielectric constants beyond the threshold field where domain wall motion can occur.

Nonlinear generalization of special relativity

International Nuclear Information System (INIS)

Winterberg, F.

1985-01-01

In Poincares axiomatic formulation special relativity is a derived consequence of a true Lorentz contraction, for a rod in absolute motion through a substratum. Furthermore, Lorentz had shown that the rod contraction can be understood by an inverse square law interaction and therefore special relativity derived from more fundamental principles. The derivation by Lorentz shows that the root of the divergence problems is the singular inverse square law. By replacing the inverse square law with a regular one through the introduction of a finite length, the author has succeeded in deriving a nonlinear generalization of special relativity which eliminates all infinities. Besides the relative velocities, these nonlinear transformation equations also contain absolute velocities against a substratum, but in the limit of small energies they go over into the linear Lorentz transformations. Depending on the smallness of the fundamental length, departures from special relativity can be observed only at very high energies. The theorem that the velocity of light is the same in all reference systems still holds and likewise the conservation laws for energy and momentum

On the integration of equations of motion for particle-in-cell codes

Czech Academy of Sciences Publication Activity Database

Fuchs, Vladimír; Gunn, J. P.

2006-01-01

Roč. 214, - (2006), s. 299-315 ISSN 0021-9991 R&D Projects: GA ČR GA202/04/0360 Institutional research plan: CEZ:AV0Z20430508 Keywords : Equations of motion * 2nd order integration methods * nonlinear oscillations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.328, year: 2006

NONLINEAR DYNAMICS OF CARBON NANOTUBES UNDER LARGE ELECTROSTATIC FORCE

KAUST Repository

Xu, Tiantian

2015-06-01

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 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 typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, 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. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. 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. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

KAUST Repository

Xu, Tiantian

2015-06-01

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 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 typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, 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. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. 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. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

Theories of quantum dissipation and nonlinear coupling bath descriptors

Science.gov (United States)

Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing

2018-03-01

The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.

Nonlinear Dynamical Analysis for a Plain Bearing

Directory of Open Access Journals (Sweden)

Ali Belhamra

2014-03-01

Full Text Available This paper investigates the nonlinear dynamic behavior for a plain classic bearing (fluid bearing lubricated by a non-Newtonian fluid of a turbo machine rotating with high speed; this type of fluid contains additives viscosity (couple-stress fluid film. The solution of the nonlinear dynamic problem of this type of bearing is determined with a spatial discretisation of the modified Reynolds' equation written in dynamic mode by using the optimized short bearing theory and a temporal discretisation for equations of rotor motion by the help of Euler's explicit diagram. This study analyzes the dynamic behavior of a rotor supported by two couple-stress fluid film journal lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. The analysis shows that the dynamic behavior of a shaft which turns with high velocities is strongly nonlinear even for poor eccentricities of unbalance; the presence of parameters of couple stress allows strongly attenuating the will synchrony (unbalance and asynchrony (whipping amplitudes of vibrations of the shaft which supports more severe conditions (large unbalances.

Linear and nonlinear subspace analysis of hand movements during grasping.

Science.gov (United States)

Cui, Phil Hengjun; Visell, Yon

2014-01-01

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

Nonlinear control of marine vehicles using only position and attitude measurements

Energy Technology Data Exchange (ETDEWEB)

Paulsen, Marit Johanne

1996-12-31

This thesis presents new results on the design and analysis of nonlinear output feedback controllers for auto pilots and dynamic positioning systems for ships and underwater vehicles. Only position and attitude measurements of the vehicle are used in the control design. The underlying idea of the work is to use certain structural properties of the equations of motion in the controller design and analysis. New controllers for regulation and tracking have been developed and the stability of the resulting closed-loop systems has been rigorously established. The results are supported by simulations. The following problems have been investigated covering design of passive controller for regulation, comparison of two auto pilots, nonlinear damping compensation for tracking, tracking control for nonlinear ships, and output tracking control with wave filtering for multivariable models of possibly unstable vehicles. 97 refs., 32 figs.

Effect of nonlinear wave-particle interaction on electron-cyclotron absorption

Energy Technology Data Exchange (ETDEWEB)

Tsironis, C; Vlahos, L [Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece)

2006-09-15

We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER.

Effect of nonlinear wave-particle interaction on electron-cyclotron absorption

International Nuclear Information System (INIS)

Tsironis, C; Vlahos, L

2006-01-01

We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER

Effective basis for modelling outlines of envelopes generated by motion of surfaces of revolution

International Nuclear Information System (INIS)

Turlapov, V.E.; Yakunin, V.I.

1994-01-01

This paper considers effective solutions of problems on parallel processing of envelopes generated by three-dimensional movement of surfaces of revolution. In general, determining the points outlining the envelope corresponding to concrete values for motion parameters reduces to numerical solution of nonlinear equations in generatrix parameters. For surfaces of revolution whose generatrix is a circular arc, this problem reduces to solution of a fourth-degree algebraic equation. It is shown that an envelope outline can be specified in the form of an explicit function of the motion parameters for any motion if the generatrix of the surface of revolution is a strait line, and, for motion with a fixed point or a fixed axis for the surface of revolution, if the generatrix is a conic section, spline, or a number of other curves

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

Linear and nonlinear analysis of fluid slosh dampers

Science.gov (United States)

Sayar, B. A.; Baumgarten, J. R.

1982-11-01

A vibrating structure and a container partially filled with fluid are considered coupled in a free vibration mode. To simplify the mathematical analysis, a pendulum model to duplicate the fluid motion and a mass-spring dashpot representing the vibrating structure are used. The equations of motion are derived by Lagrange's energy approach and expressed in parametric form. For a wide range of parametric values the logarithmic decrements of the main system are calculated from theoretical and experimental response curves in the linear analysis. However, for the nonlinear analysis the theoretical and experimental response curves of the main system are compared. Theoretical predictions are justified by experimental observations with excellent agreement. It is concluded finally that for a proper selection of design parameters, containers partially filled with viscous fluids serve as good vibration dampers.

Stability properties of solutions to nonlinear models possessing a sign-undefined metric

International Nuclear Information System (INIS)

Barashenkov, I.V.

1983-01-01

Multicomponent field systems possessing a sign-undefined internal space metric, in particular models with a noncompact global invariance group are investigated. It is shown that the energy cannot have even a conditional relative minimum. It is demonstrated, nevertheless, that the corresponding nonlinear equations of motion are permitted to possess stable particle-like solutions

Bifurcation and chaos analysis for aeroelastic airfoil with freeplay structural nonlinearity in pitch

International Nuclear Information System (INIS)

De-Min, Zhao; Qi-Chang, Zhang

2010-01-01

The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincaré mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincaré section also approves the previous conclusion

Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs

International Nuclear Information System (INIS)

Yau, H.-T.

2008-01-01

This Letter presents a robust control scheme to generalized projective synchronization between two identical two-degrees-of-freedom heavy symmetric gyroscopes with dead zone nonlinear inputs. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. By the Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode. Then, two sliding mode controllers (SMC) are designed to guarantee the hitting of the sliding surfaces even when the control inputs contain dead-zone nonlinearity. This method allows us to arbitrarily direct the scaling factor onto a desired value. Numerical simulations show that this method works very well for the proposed controller

Stability of nonlinear Hamiltonian motion for a finite but very long time

International Nuclear Information System (INIS)

Warnock, R.L.; Ruth, R.D.

1991-01-01

By constructing action variables that are very nearly invariant in a region Ω of phase space, and by examining their residual variation, we set long-term bounds on any orbit starting in an open subregion of Ω. A new and generally applicable method for constructing the required high-precision invariants is applied. The technique is illustrated for transverse oscillations in a circular accelerator, a case with 21/2 degrees of freedom and strong nonlinearity

A comparative analysis of modal motions for the gyroscopic and non-gyroscopic two degree-of-freedom conservative systems

Science.gov (United States)

Yang, Xiao-Dong; An, Hua-Zhen; Qian, Ying-Jing; Zhang, Wei; Melnik, Roderick V. N.

2016-12-01

The synchronous in-unison motions in vibrational mechanics and the non-synchronous out-of-unison motions are the most frequently found periodic motions in every fields of science and everywhere in the universe. In contrast to the in-unison normal modes, the out-of-unison complex modes feature a π/2 phase difference. By the complex mode analysis we classify the out-of-unison planar motion into two types, gyroscopic motions and elliptic motions. It is found that the gyroscopic and elliptic motions have different characteristics for a two degree-of-freedom (2DOF) system. The gyroscopic motion involves two distinct frequencies with, respectively, two corresponding complex modes. However, the elliptic motion the nonlinear non-gyroscopic 2DOF system with repeated frequencies involves only single frequency with corresponding two complex modes. The study of the differences and similarities of the gyroscopic and elliptic modes sheds new light on the in-depth mechanism of the planar motions in the universe and the man-made engineering systems.

Darcy-Forchheimer flow of Maxwell nanofluid flow with nonlinear thermal radiation and activation energy

Directory of Open Access Journals (Sweden)

T. Sajid

2018-03-01

Full Text Available The present article is about the study of Darcy-Forchheimer flow of Maxwell nanofluid over a linear stretching surface. Effects like variable thermal conductivity, activation energy, nonlinear thermal radiation is also incorporated for the analysis of heat and mass transfer. The governing nonlinear partial differential equations (PDEs with convective boundary conditions are first converted into the nonlinear ordinary differential equations (ODEs with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with the help of shooting method and MATLAB built-in bvp4c solver. The impact of different physical parameters like Brownian motion, thermophoresis parameter, Reynolds number, magnetic parameter, nonlinear radiative heat flux, Prandtl number, Lewis number, reaction rate constant, activation energy and Biot number on Nusselt number, velocity, temperature and concentration profile has been discussed. It is viewed that both thermophoresis parameter and activation energy parameter has ascending effect on the concentration profile.

Nonlinear phononics and structural control of strongly correlated materials

Energy Technology Data Exchange (ETDEWEB)

Mankowsky, Roman

2016-01-20

Mid-infrared light pulses can be used to resonantly excite infrared-active vibrational modes for the phase control of strongly correlated materials on subpicosecond timescales. As the energy is transferred directly into atomic motions, dissipation into the electronic system is reduced, allowing for the emergence of unusual low energy collective properties. Light-induced superconductivity, insulator-metal transitions and melting of magnetic order demonstrate the potential of this method. An understanding of the mechanism, by which these transitions are driven, is however missing. The aim of this work is to uncover this process by investigating the nonlinear lattice dynamics induced by the excitation and to elucidate their contribution to the modulation of collective properties of strongly correlated materials. The first signature of nonlinear lattice dynamics was reported in the observation of coherent phonon oscillations, resonant with the excitation of an infrared-active phonon mode in a manganite. This nonlinear phononic coupling can be described within a model, which predicts not only oscillatory coherent phonons dynamics but also directional atomic displacements along the coupled modes on average, which could cause the previously observed transitions. We verified this directional response and quantified the anharmonic coupling constant by tracing the atomic motions in a time-resolved hard X-ray diffraction experiment with sub-picometer spatial and femtosecond temporal resolution. In a subsequent study, we investigated the role of nonlinear lattice dynamics in the emergence of superconductivity far above the equilibrium transition temperature, an intriguing effect found to follow lattice excitation of YBa{sub 2}Cu{sub 3}O{sub 6+x}. By combining density functional theory (DFT) calculations of the anharmonic coupling constants with time-resolved X-ray diffraction experiments, we identified a structural rearrangement, which appears and decays with the same temporal

Nonlinear dynamics of fractional order Duffing system

International Nuclear Information System (INIS)

Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

2015-01-01

In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

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

Science.gov (United States)

Haddout, Soufiane

2018-01-01

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

Field-theoretical investigations in nonlinear realizations of gauge symmetry

International Nuclear Information System (INIS)

Lee, Chenhan.

1989-01-01

A review of both linear realization and non-linear realization of gauge symmetries is given and the connection between the two recipes is carefully examined. The author then constructs both linear and non-linear realizations for of supersymmetric theories. The supermultiplets of the Goldstone modes contain Goldstone bosons, quasi-Goldstone bosons and quasi-Goldstone fermions. He makes an attempt to construct a specific model of a supersymmetric non-linear realization for the Nambu-Goldstone superfields and the quasi-Goldstone fermions are identified with the quarks and leptons. Further, he discusses a mechanism by which the components of the Nambu-Goldstone supermultiplets are given non-zero mass splittings by the coupling to a hidden sector. Next, he turns to anti-symmetric tensor gauge theories, which are shown to be classically equivalent to the non-linear models describing the complete symmetry breakdown. To study the quantum mechanical equivalence of these two models, he carries out the tensor gauge fixing and the quantization procedures for the anti-symmetric tensor theories and establish the global symmetry currents which connect the two models. He then builds the supersymmetric extensions of the anti-symmetric tensor gauge theories in both abelian and non-abelian versions. Such super-tensor gauge theories are shown, by using the superfield equations of motion, to be equivalent to the fully doubled supersymmetric non-linear models of complete symmetry breakdown

Chemical reaction for Carreau-Yasuda nanofluid flow past a nonlinear stretching sheet considering Joule heating

Science.gov (United States)

Khan, Mair; Shahid, Amna; Malik, M. Y.; Salahuddin, T.

2018-03-01

Current analysis has been made to scrutinize the consequences of chemical response against magneto-hydrodynamic Carreau-Yasuda nanofluid flow induced by a non-linear stretching surface considering zero normal flux, slip and convective boundary conditions. Joule heating effect is also considered. Appropriate similarity approach is used to convert leading system of PDE's for Carreau-Yasuda nanofluid into nonlinear ODE's. Well known mathematical scheme namely shooting method is utilized to solve the system numerically. Physical parameters, namely Weissenberg number We , thermal slip parameter δ , thermophoresis number NT, non-linear stretching parameter n, magnetic field parameter M, velocity slip parameter k , Lewis number Le, Brownian motion parameter NB, Prandtl number Pr, Eckert number Ec and chemical reaction parameter γ upon temperature, velocity and concentration profiles are visualized through graphs and tables. Numerical influence of mass and heat transfer rates and friction factor are also represented in tabular as well as graphical form respectively. Skin friction coefficient reduces when Weissenberg number We is incremented. Rate of heat transfer enhances for large values of Brownian motion constraint NB. By increasing Lewis quantity Le rate of mass transfer declines.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

Science.gov (United States)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

H∞ control for path tracking of autonomous underwater vehicle motion

Directory of Open Access Journals (Sweden)

Lin-Lin Wang

2015-05-01

Full Text Available In order to simplify the design of path tracking controller and solve the problem relating to nonlinear dynamic model of autonomous underwater vehicle motion planning, feedback linearization method is first adopted to transform the nonlinear dynamic model into an equivalent pseudo-linear dynamic model in horizontal coordinates. Then considering wave disturbance effect, mixed-sensitivity method of H∞ robust control is applied to design state-feedback controller for this equivalent dynamic model. Finally, control law of pseudo-linear dynamic model is transformed into state (surge velocity and yaw angular rate tracking control law of nonlinear dynamic model through inverse coordinate transformation. Simulation indicates that autonomous underwater vehicle path tracking is successfully implemented with this proposed method, and the influence of parameter variation in autonomous underwater vehicle dynamic model on its tracking performance is reduced by H∞ controller. All the results show that the method proposed in this article is effective and feasible.

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

Science.gov (United States)

Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang; Parker, Scott E.

2018-05-01

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.

Aerodynamics and Motion Performance of the H-Type Floating Vertical Axis Wind Turbine

Directory of Open Access Journals (Sweden)

Ying Guo

2018-02-01

Full Text Available Aerodynamics and motion performance of the floating vertical wind turbine (VAWT were studied in this paper, where the wind turbine was H-type and the floating foundation was truss spar type. Based on the double-multiple-stream-tube theory, the formulae were deduced to calculate the aerodynamic loads acting on the wind turbine considering the motions of the floating foundation. The surge-heave-pitch nonlinear coupling equations of the H-type floating VAWT were established. Aerodynamics and motion performance of a 5 MW H-type floating VAWT was studied, and the effect of the floating foundation motions on the aerodynamic loads was analyzed. It is shown that the motions of the floating foundation on the aerodynamics cannot be ignored. The motion of the H-type floating VAWT was also compared with that of the Φ-type floating VAWT: they have the same floating foundation, rated output power, mooring system and total displacement. The results show that the H-type floating VAWT has better motion performance, and the mean values of surge, heave and pitch of the H-type floating VAWT are much smaller comparing with the Φ-type floating VAWT.